Modeling of Coupled Chaotic Oscillators
International Nuclear Information System (INIS)
Lai, Y.; Grebogi, C.
1999-01-01
Chaotic dynamics may impose severe limits to deterministic modeling by dynamical equations of natural systems. We give theoretical argument that severe modeling difficulties may occur for high-dimensional chaotic systems in the sense that no model is able to produce reasonably long solutions that are realized by nature. We make these ideas concrete by investigating systems of coupled chaotic oscillators. They arise in many situations of physical and biological interests, and they also arise from discretization of nonlinear partial differential equations. copyright 1999 The American Physical Society
Chaotic Motion of Nonlinearly Coupled Quintic Oscillators | Adeloye ...
African Journals Online (AJOL)
With a fixed energy, we investigate the motion of two nonlinearly coupled quintic oscillators for various values of the coupling strength with the aid of the Poincare surface of section. It is observed that chaotic motion sets in for coupling strength as low as 0.001. The degree of chaoticity generally increases as the coupling ...
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik
2001-01-01
Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science...
Scaling Features of Multimode Motions in Coupled Chaotic Oscillators
DEFF Research Database (Denmark)
Pavlov, A.N.; Sosnovtseva, Olga; Mosekilde, Erik
2003-01-01
Two different methods (the WTMM- and DFA-approaches) are applied to investigate the scaling properties in the return-time sequences generated by a system of two coupled chaotic oscillators. Transitions from twomode asynchronous dynamics (torus or torus-Chaos) to different states of chaotic phase ...
Chaotic synchronization of three coupled oscillators with ring connection
International Nuclear Information System (INIS)
Kyprianidis, I.M.; Stouboulos, I.N.
2003-01-01
We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional)
Chaotic synchronization of three coupled oscillators with ring connection
Kyprianidis, I M
2003-01-01
We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional).
Synchronization of hyperchaotic oscillators via single unidirectional chaotic-coupling
International Nuclear Information System (INIS)
Zou Yanli; Zhu Jie; Chen Guanrong; Luo Xiaoshu
2005-01-01
In this paper, synchronization of two hyperchaotic oscillators via a single variable's unidirectional coupling is studied. First, the synchronizability of the coupled hyperchaotic oscillators is proved mathematically. Then, the convergence speed of this synchronization scheme is analyzed. In order to speed up the response with a relatively large coupling strength, two kinds of chaotic coupling synchronization schemes are proposed. In terms of numerical simulations and the numerical calculation of the largest conditional Lyapunov exponent, it is shown that in a given range of coupling strengths, chaotic-coupling synchronization is quicker than the typical continuous-coupling synchronization. Furthermore, A circuit realization based on the chaotic synchronization scheme is designed and Pspice circuit simulation validates the simulated hyperchaos synchronization mechanism
Dynamics of chaotic oscillations in mutually coupled microchip lasers
Uchida, A; Kinugawa, S; Yoshimori, S
2003-01-01
We have numerically and experimentally investigated the dynamics of mutually coupled microchip lasers. Chaotic oscillations are observed in the vicinity of the boundary of the injection-locking range when the coupling strength and the difference of the optical frequencies are varied. Synchronization of chaos is always achieved under the condition to generate chaos.
Stochastic Resonance in a System of Coupled Chaotic Oscillators
International Nuclear Information System (INIS)
Krawiecki, A.
1999-01-01
Noise-free stochastic resonance is investigated numerically in a system of two coupled chaotic Roessler oscillators. Periodic signal is applied either additively or multiplicatively to the coupling term. When the coupling constant is varied the oscillators lose synchronization via attractor bubbling or on-off intermittency. Properly chosen signals are analyzed which reflect the sequence of synchronized (laminar) phases and non-synchronized bursts in the time evolution of the oscillators. Maximum of the signal-to-noise ratio as a function of the coupling constant is observed. Dependence of the signal-to-noise ratio on the frequency of the periodic signal and parameter mismatch between the oscillators is investigated. Possible applications of stochastic resonance in the recovery of signals in secure communication systems based on chaotic synchronization are briefly discussed. (author)
Mixed synchronization in chaotic oscillators using scalar coupling
Energy Technology Data Exchange (ETDEWEB)
Bhowmick, Sourav K.; Hens, Chittaranjan [CSIR – Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India); Ghosh, Dibakar, E-mail: drghosh_math@yahoo.co.in [Department of Mathematics, University of Kalyani, West Bengal 741235 (India); Dana, Syamal K. [CSIR – Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India)
2012-07-23
We report experimental evidence of mixed synchronization in two unidirectionally coupled chaotic oscillators using a scalar coupling. In this synchronization regime, some of the state variables may be in complete synchronization while others may be in anti-synchronization state. We extended the theory by using an adaptive controller with an updating law based on Lyapunov function stability to include parameter fluctuation. Using the scheme, we implemented a cryptographic encoding for digital signal through parameter modulation. -- Highlights: ► We provided experimental evidence of the mixed synchronization scheme while other methods are mostly theoretical nature. ► We numerically studied adaptive mixed synchronization when the parameters are not completely known using scalar coupling. ► We proposed a secure communication system where three digital messages are transmitted using parameter modulation.
Chaotic weak chimeras and their persistence in coupled populations of phase oscillators
International Nuclear Information System (INIS)
Bick, Christian; Ashwin, Peter
2016-01-01
Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoherent oscillations. The recently-introduced notion of a weak chimera gives a rigorously testable characterization of chimera states for finite-dimensional phase oscillator networks. In this paper we give some persistence results for dynamically invariant sets under perturbations and apply them to coupled populations of phase oscillators with generalized coupling. In contrast to the weak chimeras with nonpositive maximal Lyapunov exponents constructed so far, we show that weak chimeras that are chaotic can exist in the limit of vanishing coupling between coupled populations of phase oscillators. We present numerical evidence that positive Lyapunov exponents can persist for a positive measure set of this inter-population coupling strength. (paper)
Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators
Energy Technology Data Exchange (ETDEWEB)
Semenova, N.; Anishchenko, V. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Zakharova, A.; Schöll, E. [Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin (Germany)
2016-06-08
In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.
How to induce multiple delays in coupled chaotic oscillators?
Energy Technology Data Exchange (ETDEWEB)
Bhowmick, Sourav K. [CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India); Department of Electronics, Asutosh College, Kolkata 700026 (India); Ghosh, Dibakar [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India); Roy, Prodyot K. [Department of Physics, Presidency University, Kolkata 700073 (India); Kurths, Jürgen [Potsdam Institute for Climate Impact Research, 14473 Potsdam (Germany); Institute for Physics, Humboldt University, 12489 Berlin (Germany); Dana, Syamal K. [CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India)
2013-12-15
Lag synchronization is a basic phenomenon in mismatched coupled systems, delay coupled systems, and time-delayed systems. It is characterized by a lag configuration that identifies a unique time shift between all pairs of similar state variables of the coupled systems. In this report, an attempt is made how to induce multiple lag configurations in coupled systems when different pairs of state variables attain different time shift. A design of coupling is presented to realize this multiple lag synchronization. Numerical illustration is given using examples of the Rössler system and the slow-fast Hindmarsh-Rose neuron model. The multiple lag scenario is physically realized in an electronic circuit of two Sprott systems.
Li, Bing-Wei; Cao, Xiao-Zhi; Fu, Chenbo
2017-12-01
Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual element communicates with each other is heterogeneous. Nevertheless, most of previous works considered the homogeneous case only. Here we investigated the dynamical behaviors in a population of spatially distributed chaotic oscillators immersed in a heterogeneous environment. Various dynamical synchronization states (such as oscillation death, phase synchronization, and complete synchronized oscillation) as well as their transitions were explored. In particular, we uncovered a non-traditional quorum sensing transition: increasing the population density leaded to a transition from oscillation death to synchronized oscillation at first, but further increasing the density resulted in degeneration from complete synchronization to phase synchronization or even from phase synchronization to desynchronization. The underlying mechanism of this finding was attributed to the dual roles played by the population density. What's more, by treating the environment as another component of the oscillator, the full system was then effectively equivalent to a locally coupled system. This fact allowed us to utilize the master stability functions approach to predict the occurrence of complete synchronization oscillation, which agreed with that from the direct numerical integration of the system. The potential candidates for the experimental realization of our model were also discussed.
Time delay induced different synchronization patterns in repulsively coupled chaotic oscillators
Yao, Chenggui; Yi, Ming; Shuai, Jianwei
2013-09-01
Time delayed coupling plays a crucial role in determining the system's dynamics. We here report that the time delay induces transition from the asynchronous state to the complete synchronization (CS) state in the repulsively coupled chaotic oscillators. In particular, by changing the coupling strength or time delay, various types of synchronous patterns, including CS, antiphase CS, antiphase synchronization (ANS), and phase synchronization, can be generated. In the transition regions between different synchronous patterns, bistable synchronous oscillators can be observed. Furthermore, we show that the time-delay-induced phase flip bifurcation is of key importance for the emergence of CS. All these findings may light on our understanding of neuronal synchronization and information processing in the brain.
Driving-induced multistability in coupled chaotic oscillators: Symmetries and riddled basins
Energy Technology Data Exchange (ETDEWEB)
Ujjwal, Sangeeta Rani; Ramaswamy, Ram [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India); Punetha, Nirmal; Prasad, Awadhesh [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Agrawal, Manish [Department of Physics, Sri Aurobindo College, University of Delhi, New Delhi 110017 (India)
2016-06-15
We study the multistability that results when a chaotic response system that has an invariant symmetry is driven by another chaotic oscillator. We observe that there is a transition from a desynchronized state to a situation of multistability. In the case considered, there are three coexisting attractors, two of which are synchronized and one is desynchronized. For large coupling, the asynchronous attractor disappears, leaving the system bistable. We study the basins of attraction of the system in the regime of multistability. The three attractor basins are interwoven in a complex manner, with extensive riddling within a sizeable region of (but not the entire) phase space. A quantitative characterization of the riddling behavior is made via the so–called uncertainty exponent, as well as by evaluating the scaling behavior of tongue–like structures emanating from the synchronization manifold.
Park, Jihoon; Mori, Hiroki; Okuyama, Yuji; Asada, Minoru
2017-01-01
Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.
Directory of Open Access Journals (Sweden)
Jihoon Park
Full Text Available Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random with a musculoskeletal model (i.e., a snake-like robot as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1 the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2 two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Blacher, S; Perdang, J [Institut d' Astrophysique, B-4200 Cointe-Ougree (Belgium)
1981-09-01
A numerical experiment on Hamiltonian oscillations demonstrates the existence of chaotic motions which satisfy the property of phase coherence. It is observed that the low-frequency end of the power spectrum of such motions is remarkably similar in structure to the low-frequency SCLERA spectra. Since the smallness of the observed solar amplitudes is not a sufficient mathematical ground for inefficiency of non-linear effects the possibility of chaos among solar oscillations cannot be discarded a priori.
Intermittent chaotic chimeras for coupled rotators
DEFF Research Database (Denmark)
Olmi, Simona; Martens, Erik Andreas; Thutupalli, Shashi
2015-01-01
Two symmetrically coupled populations of N oscillators with inertia m display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendulums. In particular, we report evidence of intermittent chaotic chimeras, where one population is synchronized and the other...
Anti-synchronization of chaotic oscillators
International Nuclear Information System (INIS)
Kim, Chil-Min; Rim, Sunghwan; Kye, Won-Ho; Ryu, Jung-Wan; Park, Young-Jai
2003-01-01
We have observed anti-synchronization phenomena in coupled identical chaotic oscillators. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. We have qualitatively analyzed its base mechanism by using the dynamics of the difference and the sum of the relevant variables in coupled chaotic oscillators. Near the threshold of the synchronization and anti-synchronization transition, we have obtained the novel characteristic relation
Synchronization of Time-Continuous Chaotic Oscillators
DEFF Research Database (Denmark)
Yanchuk, S.; Maistrenko, Yuri; Mosekilde, Erik
2003-01-01
Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded...
Transition to Coherence in Populations of Coupled Chaotic Oscillators: A Linear Response Approach
International Nuclear Information System (INIS)
Topaj, Dmitri; Kye, Won-Ho; Pikovsky, Arkady
2001-01-01
We consider the collective dynamics in an ensemble of globally coupled chaotic maps. The transition to the coherent state with a macroscopic mean field is analyzed in the framework of the linear response theory. The linear response function for the chaotic system is obtained using the perturbation approach to the Frobenius-Perron operator. The transition point is defined from this function by virtue of the self-excitation condition for the feedback loop. Analytical results for the coupled Bernoulli maps are confirmed by the numerics
Stochastic and Chaotic Relaxation Oscillations
Grasman, J.; Roerdink, J.B.T.M.
1988-01-01
For relaxation oscillators stochastic and chaotic dynamics are investigated. The effect of random perturbations upon the period is computed. For an extended system with additional state variables chaotic behavior can be expected. As an example, the Van der Pol oscillator is changed into a
Semenova, N. I.; Strelkova, G. I.; Anishchenko, V. S.; Zakharova, A.
2017-06-01
We describe numerical results for the dynamics of networks of nonlocally coupled chaotic maps. Switchings in time between amplitude and phase chimera states have been first established and studied. It has been shown that in autonomous ensembles, a nonstationary regime of switchings has a finite lifetime and represents a transient process towards a stationary regime of phase chimera. The lifetime of the nonstationary switching regime can be increased to infinity by applying short-term noise perturbations.
International Nuclear Information System (INIS)
Jiang Yu; Lozada-Cassou, M.; Vinet, A.
2003-01-01
The spatiotemporal dynamics of networks based on a ring of coupled oscillators with regular shortcuts beyond the nearest-neighbor couplings is studied by using master stability equations and numerical simulations. The generic criterion for dynamic synchronization has been extended to arbitrary network topologies with zero row-sum. The symmetry-breaking oscillation patterns that resulted from the Hopf bifurcation from synchronous states are analyzed by the symmetry group theory
TOWARDS THRESHOLD FREQUENCY IN CHAOTIC COLPITTS OSCILLATOR
DEFF Research Database (Denmark)
Lindberg, Erik; Tamasevicius, Arunas; Mykolaitis, Gytis
2007-01-01
A novel version of chaotic Colpitts oscillator is described. Instead of a linear loss resistor, it includes an extra inductor and diode in the collector circuit of the transistor. The modified circuit in comparison with the common Colpitts oscillator may generate chaotic oscillations at the funda......A novel version of chaotic Colpitts oscillator is described. Instead of a linear loss resistor, it includes an extra inductor and diode in the collector circuit of the transistor. The modified circuit in comparison with the common Colpitts oscillator may generate chaotic oscillations...
On the Design of Chaotic Oscillators
DEFF Research Database (Denmark)
Lindberg, Erik; Tamasevicius, A; Cenys, A.
1998-01-01
A discussion of the chaotic oscillator concept from a design methodology pointof view. The attributes of some chaoticoscillators are discussed and a systematicdesign method based on eigenvalue investigation is proposed. The method isillustrated with a chaotic Wien-bridgeoscillator design....
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
Jeevarekha, A.; Paul Asir, M.; Philominathan, P.
2016-06-01
This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.
Localized chaoticity in two linearly coupled inverted double-well ...
African Journals Online (AJOL)
Two linearly coupled inverted double-well oscillators for a fixed energy and varying coupling strength were studied. The dynamics yielded a chaotic system in which the Poincare surface was characterised by two non-mixing regions, one of regular motion and the other region that became chaotic as the coupling increased.
Hyperchaos in coupled Colpitts oscillators
DEFF Research Database (Denmark)
Cenys, Antanas; Tamasevicius, Arunas; Baziliauskas, Antanas
2003-01-01
The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R-k. The hyperchaotic output signal v(t) is a linear combination, specifically the mean of the individual...
poincare surface analysis of two coupled quintic oscillators in a ...
African Journals Online (AJOL)
DJFLEX
We have investigated the chaotic dynamics of two coupled quintic oscillators in a single well potential as the energy of the oscillator increases, keeping the coupling strength constant. The degree of chaoticity does not increase monotonously with the energy as regular regions reappear within chaotic seas as the energy ...
Poincare surface analysis of two coupled quintic oscillators in a ...
African Journals Online (AJOL)
We have investigated the chaotic dynamics of two coupled quintic oscillators in a single well potential as the energy of the oscillator increases, keeping the coupling strength constant. The degree of chaoticity does not increase monotonously with the energy as regular regions reappear within chaotic seas as the energy ...
Partial synchronization and spontaneous spatial ordering in coupled chaotic systems
International Nuclear Information System (INIS)
Ying Zhang; Gang Hu; Cerdeira, Hilda A.; Shigang Chen; Braun, Thomas; Yugui Yao
2000-11-01
A model of many symmetrically and locally coupled chaotic oscillators is studied. Partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated. Very rich patterns of the system are revealed, based on partial synchronization analysis. The stabilities of different partially synchronous spatiotemporal structures and some novel dynamical behaviors of these states are discussed both numerically and analytically. (author)
Synchronization of indirectly coupled Lorenz oscillators
Indian Academy of Sciences (India)
Synchronization of indirectly coupled Lorenz oscillators: An experimental study. Amit Sharma Manish Dev Shrimali. Synchronization, Coupled Systems and Networks Volume 77 Issue 5 November 2011 pp 881-889 ... The in-phase and anti-phase synchronization of indirectly coupled chaotic oscillators reported in Phys. Rev ...
Exact folded-band chaotic oscillator.
Corron, Ned J; Blakely, Jonathan N
2012-06-01
An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.
CHAOTIC DUFFING TYPE OSCILLATOR WITH INERTIAL DAMPING
DEFF Research Database (Denmark)
Tamaševicius, Arunas; Mykolaitis, Gytis; Kirvaitis, Raimundas
2009-01-01
A novel Duffing-Holmes type autonomous chaotic oscillator is described. In comparison with the well-known non-autonomous Duffing-Holmes circuit it lacks the external periodic drive, but includes two extra linear feedback sub-circuits, namely a direct positive feedback loop, and an inertial negati...... feedback loop. SPICE simulation and hardware experimental results are presented....
Synchronization of mobile chaotic oscillator networks
Energy Technology Data Exchange (ETDEWEB)
Fujiwara, Naoya, E-mail: fujiwara@csis.u-tokyo.ac.jp [Center for Spatial Information Science, The University of Tokyo, 277-8568 Chiba (Japan); Kurths, Jürgen [Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany and Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen (United Kingdom); Díaz-Guilera, Albert [Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain and Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona (Spain)
2016-09-15
We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.
Synchronization of mobile chaotic oscillator networks
International Nuclear Information System (INIS)
Fujiwara, Naoya; Kurths, Jürgen; Díaz-Guilera, Albert
2016-01-01
We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.
Synchronization of mobile chaotic oscillator networks.
Fujiwara, Naoya; Kurths, Jürgen; Díaz-Guilera, Albert
2016-09-01
We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.
Chaotic synchronization of two complex nonlinear oscillators
International Nuclear Information System (INIS)
Mahmoud, Gamal M.; Mahmoud, Emad E.; Farghaly, Ahmed A.; Aly, Shaban A.
2009-01-01
Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.
Study of chaotic oscillations in practical work on radio physics
International Nuclear Information System (INIS)
Ezdov, A.A.; Il'in, V.A.; Petrova, E.B.
1995-01-01
A description is given of a laboratory study of chaotic oscillations in deterministic dynamical systems. This work utilizes mathematical modeling and a computer experiment, as well as a direct study of the chaotic behavior of nonlinear electrical circuits
Digital chaotic sequence generator based on coupled chaotic systems
International Nuclear Information System (INIS)
Shu-Bo, Liu; Jing, Sun; Jin-Shuo, Liu; Zheng-Quan, Xu
2009-01-01
Chaotic systems perform well as a new rich source of cryptography and pseudo-random coding. Unfortunately their digital dynamical properties would degrade due to the finite computing precision. Proposed in this paper is a modified digital chaotic sequence generator based on chaotic logistic systems with a coupling structure where one chaotic subsystem generates perturbation signals to disturb the control parameter of the other one. The numerical simulations show that the length of chaotic orbits, the output distribution of chaotic system, and the security of chaotic sequences have been greatly improved. Moreover the chaotic sequence period can be extended at least by one order of magnitude longer than that of the uncoupled logistic system and the difficulty in decrypting increases 2 128 *2 128 times indicating that the dynamical degradation of digital chaos is effectively improved. A field programmable gate array (FPGA) implementation of an algorithm is given and the corresponding experiment shows that the output speed of the generated chaotic sequences can reach 571.4 Mbps indicating that the designed generator can be applied to the real-time video image encryption. (general)
Multiscality in the Dynamics of Coupled Chaotic Systems
DEFF Research Database (Denmark)
Pavlov, A.N.; Sosnovtseva, Olga; Ziganshin, A.R.
2002-01-01
We investigate the scaling features of complex motions in systems of two coupled chaotic oscillators by means of the wavelet-transform modulus maxima method and the detrended fluctuation analysis. We show that the transition from asynchronous to synchronous dynamics typically reduces the degree...
Globally Coupled Chaotic Maps with Constant Force
International Nuclear Information System (INIS)
Li Jinghui
2008-01-01
We investigate the motion of the globally coupled maps (logistic map) with a constant force. It is shown that the constant force can cause multi-synchronization for the globally coupled chaotic maps studied by us.
Autonomous third-order duffing-holmes type chaotic oscillator
DEFF Research Database (Denmark)
Lindberg, Erik; Tamaseviciute, E; Mykolaitis, G
2009-01-01
feedback loop. In contrast to many other autonomous chaotic oscillators, including linear unstable resonators and nonlinear damping loops, the novel circuit is based on nonlinear resonator and linear damping loop in the negative feedback. SPICE simulation and hardware experimental investigations...
Atypical transistor-based chaotic oscillators: Design, realization, and diversity
Minati, Ludovico; Frasca, Mattia; OświÈ©cimka, Paweł; Faes, Luca; DroŻdŻ, Stanisław
2017-07-01
In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predominantly anti-persistent monofractal dynamics. Notably, we recurrently found a circuit comprising one resistor, one transistor, two inductors, and one capacitor, which generates a range of attractors depending on the parameter values. We also found a circuit yielding an irregular quantized spike-train resembling some aspects of neural discharge and another one generating a double-scroll attractor, which represent the smallest known transistor-based embodiments of these behaviors. Through three representative examples, we additionally show that diffusive coupling of heterogeneous oscillators of this kind may give rise to complex entrainment, such as lag synchronization with directed information transfer and generalized synchronization. The replicability and reproducibility of the experimental findings are good.
Dynamic synchronization of a time-evolving optical network of chaotic oscillators.
Cohen, Adam B; Ravoori, Bhargava; Sorrentino, Francesco; Murphy, Thomas E; Ott, Edward; Roy, Rajarshi
2010-12-01
We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each node an adaptive synchronization algorithm dynamically estimates the current strength of the net coupling signal to that node. We experimentally demonstrate this scheme in a network of three bidirectionally coupled chaotic optoelectronic feedback loops and we present numerical simulations showing its application in larger networks. The stability of the synchronous state for arbitrary coupling topologies is analyzed via a master stability function approach. © 2010 American Institute of Physics.
Memcapacitor model and its application in chaotic oscillator with memristor.
Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching
2017-01-01
Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.
Kingni, Sifeu Takougang; Mbé, Jimmi Hervé Talla; Woafo, Paul
2012-09-01
In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate.
EEG simulation by 2D interconnected chaotic oscillators
International Nuclear Information System (INIS)
Kubany, Adam; Mhabary, Ziv; Gontar, Vladimir
2011-01-01
Research highlights: → ANN of 2D interconnected chaotic oscillators is explored for EEG simulation. → An inverse problem solution (PRCGA) is proposed. → Good matching between the simulated and experimental EEG signals has been achieved. - Abstract: An artificial neuronal network composed by 2D interconnected chaotic oscillators is explored for brain waves (EEG) simulation. For the inverse problem solution a parallel real-coded genetic algorithm (PRCGA) is proposed. In order to conduct thorough comparison between the simulated and target signal characteristics, a spectrum analysis of the signals is undertaken. A good matching between the theoretical and experimental EEG signals has been achieved. Numerical results of calculations are presented and discussed.
EEG simulation by 2D interconnected chaotic oscillators
Energy Technology Data Exchange (ETDEWEB)
Kubany, Adam, E-mail: adamku@bgu.ac.i [Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105 (Israel); Mhabary, Ziv; Gontar, Vladimir [Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105 (Israel)
2011-01-15
Research highlights: ANN of 2D interconnected chaotic oscillators is explored for EEG simulation. An inverse problem solution (PRCGA) is proposed. Good matching between the simulated and experimental EEG signals has been achieved. - Abstract: An artificial neuronal network composed by 2D interconnected chaotic oscillators is explored for brain waves (EEG) simulation. For the inverse problem solution a parallel real-coded genetic algorithm (PRCGA) is proposed. In order to conduct thorough comparison between the simulated and target signal characteristics, a spectrum analysis of the signals is undertaken. A good matching between the theoretical and experimental EEG signals has been achieved. Numerical results of calculations are presented and discussed.
Intermittent and sustained periodic windows in networked chaotic Rössler oscillators
International Nuclear Information System (INIS)
He, Zhiwei; Sun, Yong; Zhan, Meng
2013-01-01
Route to chaos (or periodicity) in dynamical systems is one of fundamental problems. Here, dynamical behaviors of coupled chaotic Rössler oscillators on complex networks are investigated and two different types of periodic windows with the variation of coupling strength are found. Under a moderate coupling, the periodic window is intermittent, and the attractors within the window extremely sensitively depend on the initial conditions, coupling parameter, and topology of the network. Therefore, after adding or removing one edge of network, the periodic attractor can be destroyed and substituted by a chaotic one, or vice versa. In contrast, under an extremely weak coupling, another type of periodic window appears, which insensitively depends on the initial conditions, coupling parameter, and network. It is sustained and unchanged for different types of network structure. It is also found that the phase differences of the oscillators are almost discrete and randomly distributed except that directly linked oscillators more likely have different phases. These dynamical behaviors have also been generally observed in other networked chaotic oscillators
A new kind of metal detector based on chaotic oscillator
Hu, Wenjing
2017-12-01
The sensitivity of a metal detector greatly depends on the identification ability to weak signals from the probe. In order to improve the sensitivity of metal detectors, this paper applies the Duffing chaotic oscillator to metal detectors based on its characteristic which is very sensitive to weak periodic signals. To make a suitable Duffing system for detectors, this paper computes two Lyapunov characteristics exponents of the Duffing oscillator, which help to obtain the threshold of the Duffing system in the critical state accurately and give quantitative criteria for chaos. Meanwhile, a corresponding simulation model of the chaotic oscillator is made by the Simulink tool box of Matlab. Simulation results shows that Duffing oscillator is very sensitive to sinusoidal signals in high frequency cases. And experimental results show that the measurable diameter of metal particles is about 1.5mm. It indicates that this new method can feasibly and effectively improve the metal detector sensitivity.
Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity
Paul Asir, M.; Jeevarekha, A.; Philominathan, P.
This paper deals with the generation of chaotic beats in a system of two forced dissipative LCR oscillators sharing a nonlinear element. The presence of two external periodic excitations and a common nonlinear element in the chosen system enables the facile generation of chaotic beats. Thus rendered chaotic beats were characterized in both time domain and phase space. Lyapunov exponents and envelope of the beats were computed to diagnose the chaotic nature of the signals. The role of common nonlinearity on the complexity of the generated beats is discussed. Real-time experimental hardware implementation has also been done to confirm the subsistence of the phenomenon, for the first time. Extensive Multisim simulations were carried out to understand, a bit more about the shrinkage and revivals of state variables in phase space.
Raby chaotic vacuum oscillations in resonator quantum electrodynamics
International Nuclear Information System (INIS)
Kon'kov, L.E.; Prants, S.V.
1997-01-01
It is shown in numerical experiments with two-level atoms, moving through a single-mode high-quality resonator, that a new type of spontaneous radiation - the Raby chaotic vacuum oscillation - originates in the mode of strong atom-field bonds
Energy Technology Data Exchange (ETDEWEB)
Chandra, J; Scott, A C
1983-01-01
Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.
Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach
Directory of Open Access Journals (Sweden)
Ricardo Aguilar-López
2014-01-01
Full Text Available The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves’ oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.
Multisynchronization of chaotic oscillators via nonlinear observer approach.
Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L
2014-01-01
The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.
Control of partial synchronization in chaotic oscillators
Indian Academy of Sciences (India)
2015-02-07
Feb 7, 2015 ... other real systems such as the brain network or the power grid, where multiple ..... 2D attractors of the driver oscillator (x2 vs. x3 plot) in the left and the response (y2 vs. y3 plot) in the right are given in the uppermost panels.
International Nuclear Information System (INIS)
Nakano, Hidehiro; Utani, Akihide; Miyauchi, Arata; Yamamoto, Hisao
2011-01-01
This paper studies chaos-based data gathering scheme in multiple sink wireless sensor networks. In the proposed scheme, each wireless sensor node has a simple chaotic oscillator. The oscillators generate spike signals with chaotic interspike intervals, and are impulsively coupled by the signals via wireless communication. Each wireless sensor node transmits and receives sensor information only in the timing of the couplings. The proposed scheme can exhibit various chaos synchronous phenomena and their breakdown phenomena, and can effectively gather sensor information with the significantly small number of transmissions and receptions compared with the conventional scheme. Also, the proposed scheme can flexibly adapt various wireless sensor networks not only with a single sink node but also with multiple sink nodes. This paper introduces our previous works. Through simulation experiments, we show effectiveness of the proposed scheme and discuss its development potential.
Persistent chimera states in nonlocally coupled phase oscillators
Suda, Yusuke; Okuda, Koji
2015-01-01
Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit, chimera states are chaotic transient and finally collapse into the completely synchronous solution. In this Rapid Communication, we numerically study chimera states by using the coupling function different from the previous studies and obtain the result that...
A Chaotic Oscillator Based on HP Memristor Model
Directory of Open Access Journals (Sweden)
Guangyi Wang
2015-01-01
Full Text Available This paper proposes a simple autonomous memristor-based oscillator for generating periodic signals. Applying an external sinusoidal excitation to the autonomous system, a nonautonomous oscillator is obtained, which contains HP memristor model and four linear circuit elements. This memristor-based oscillator can generate periodic, chaotic, and hyperchaotic signals under the periodic excitation and an appropriate set of circuit parameters. It also shows that the system exhibits alternately a hidden attractor with no equilibrium and a self-excited attractor with a line equilibrium as time goes on. Furthermore, some specialties including burst chaos, irregular periodic bifurcations, and nonintermittence chaos of the circuit are found by theoretical analysis and numerical simulations. Finally, a discrete model for the HP memristor is given and the main statistical properties of this memristor-based oscillator are verified via DSP chip experiments and NIST (National Institute of Standards and Technology tests.
International Nuclear Information System (INIS)
Sudheer, K. Sebastian; Sabir, M.
2009-01-01
This work investigates function projective synchronization of two-cell Quantum-CNN chaotic oscillators using adaptive method. Quantum-CNN oscillators produce nano scale chaotic oscillations under certain conditions. By Lyapunove stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.
Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations
Energy Technology Data Exchange (ETDEWEB)
Wang, Qiqi, E-mail: qiqi@mit.edu; Hu, Rui, E-mail: hurui@mit.edu; Blonigan, Patrick, E-mail: blonigan@mit.edu
2014-06-15
The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.
Acoustically levitated dancing drops: Self-excited oscillation to chaotic shedding
Lin, Po-Cheng; I, Lin
2016-02-01
We experimentally demonstrate self-excited oscillation and shedding of millimeter-sized water drops, acoustically levitated in a single-node standing waves cavity, by decreasing the steady acoustic wave intensity below a threshold. The perturbation of the acoustic field by drop motion is a possible source for providing an effective negative damping for sustaining the growing amplitude of the self-excited motion. Its further interplay with surface tension, drop inertia, gravity and acoustic intensities, select various self-excited modes for different size of drops and acoustic intensity. The large drop exhibits quasiperiodic motion from a vertical mode and a zonal mode with growing coupling, as oscillation amplitudes grow, until falling on the floor. For small drops, chaotic oscillations constituted by several broadened sectorial modes and corresponding zonal modes are self-excited. The growing oscillation amplitude leads to droplet shedding from the edges of highly stretched lobes, where surface tension no longer holds the rapid expanding flow.
Lu, Jia; Zhang, Xiaoxing; Xiong, Hao
The chaotic van der Pol oscillator is a powerful tool for detecting defects in electric systems by using online partial discharge (PD) monitoring. This paper focuses on realizing weak PD signal detection in the strong periodic narrowband interference by using high sensitivity to the periodic narrowband interference signals and immunity to white noise and PD signals of chaotic systems. A new approach to removing the periodic narrowband interference by using a van der Pol chaotic oscillator is described by analyzing the motion characteristic of the chaotic oscillator on the basis of the van der Pol equation. Furthermore, the Floquet index for measuring the amplitude of periodic narrowband signals is redefined. The denoising signal processed by the chaotic van der Pol oscillators is further processed by wavelet analysis. Finally, the denoising results verify that the periodic narrowband and white noise interference can be removed efficiently by combining the theory of the chaotic van der Pol oscillator and wavelet analysis.
Partial synchronization of different chaotic oscillators using robust PID feedback
Energy Technology Data Exchange (ETDEWEB)
Aguilar-Lopez, Ricardo [Departamento de Energia, Universidad Autonoma Metropolitana - Azcapotzalco, San Pablo 180, Reynosa-Tamaulipas, Azcapotzalco, 02200 Mexico, D.F. (Mexico)]. E-mail: raguilar@correo.azc.uam.mx; Martinez-Guerra, Rafael [Departamento de Control Automatico, CINVESTAV IPN, Apartado Postal 14-740, Mexico, D.F. C.P. 07360 (Mexico)]. E-mail: rguerra@ctrl.cinvestav.mx
2007-07-15
This work deals with the partial synchronization problem of two different chaotic oscillators considering model uncertainties in the slave system via control approach. The slave system is forced to follow the master signal via a linearizing controller based on model uncertainty reconstructor which leads to proportional-integral-derivative (PID) control structure. This reconstructor is related with a proportional-derivative (PD) reduced-order observer, it would be considered as a sub-slave system for the original slave of the synchronization procedure. The asymptotic performance of the synchronization methodology is proven via the dynamic of the synchronization error. Numerical experiment illustrates the closed-loop behavior of the proposed methodology.
Partial synchronization of different chaotic oscillators using robust PID feedback
International Nuclear Information System (INIS)
Aguilar-Lopez, Ricardo; Martinez-Guerra, Rafael
2007-01-01
This work deals with the partial synchronization problem of two different chaotic oscillators considering model uncertainties in the slave system via control approach. The slave system is forced to follow the master signal via a linearizing controller based on model uncertainty reconstructor which leads to proportional-integral-derivative (PID) control structure. This reconstructor is related with a proportional-derivative (PD) reduced-order observer, it would be considered as a sub-slave system for the original slave of the synchronization procedure. The asymptotic performance of the synchronization methodology is proven via the dynamic of the synchronization error. Numerical experiment illustrates the closed-loop behavior of the proposed methodology
Cognitive radio resource allocation based on coupled chaotic genetic algorithm
International Nuclear Information System (INIS)
Zu Yun-Xiao; Zhou Jie; Zeng Chang-Chang
2010-01-01
A coupled chaotic genetic algorithm for cognitive radio resource allocation which is based on genetic algorithm and coupled Logistic map is proposed. A fitness function for cognitive radio resource allocation is provided. Simulations are conducted for cognitive radio resource allocation by using the coupled chaotic genetic algorithm, simple genetic algorithm and dynamic allocation algorithm respectively. The simulation results show that, compared with simple genetic and dynamic allocation algorithm, coupled chaotic genetic algorithm reduces the total transmission power and bit error rate in cognitive radio system, and has faster convergence speed
Direction of coupling from phases of interacting oscillators: An information-theoretic approach
Paluš, Milan; Stefanovska, Aneta
2003-05-01
A directionality index based on conditional mutual information is proposed for application to the instantaneous phases of weakly coupled oscillators. Its abilities to distinguish unidirectional from bidirectional coupling, as well as to reveal and quantify asymmetry in bidirectional coupling, are demonstrated using numerical examples of quasiperiodic, chaotic, and noisy oscillators, as well as real human cardiorespiratory data.
Chaotic phase oscillation of a proton beam in a synchrotron
International Nuclear Information System (INIS)
Li Fei; Hai Wenhua; Ren Zhongzhou; Shu Weixing
2006-01-01
We investigate the chaotic phase oscillation of a proton beam in a cooler synchrotron. By using direct perturbation method, we construct the general solution of the 1st-order equation. It is demonstrated that the general solution is bounded under some initial and parameter conditions. From these conditions, we get a Melnikov function which predicts the existence of Smale-horseshoe chaos iff it has simple zeros. Our result under the 1st-order approximation is in good agreement with that in [H. Huang et al., Phys. Rev. E 48 (1993) 4678]. When the perturbation method is not suitable for the system, numerical simulation shows the system may present transient chaos before it goes into periodical oscillation; changing the damping parameter can result in or suppress stationary chaos
Bidirectional communication using delay coupled chaotic directly ...
Indian Academy of Sciences (India)
Corresponding author. ... 30 September 2009. Abstract. Chaotic synchronization of two directly modulated semiconductor lasers with ... For InGaAsP lasers used in optical communication systems, the nonlinear gain re- duction is very strong and its ...
Magnetically Coupled Magnet-Spring Oscillators
Donoso, G.; Ladera, C. L.; Martin, P.
2010-01-01
A system of two magnets hung from two vertical springs and oscillating in the hollows of a pair of coils connected in series is a new, interesting and useful example of coupled oscillators. The electromagnetically coupled oscillations of these oscillators are experimentally and theoretically studied. Its coupling is electromagnetic instead of…
Synchronization of chaotic neural networks via output or state coupling
International Nuclear Information System (INIS)
Lu Hongtao; Leeuwen, C. van
2006-01-01
We consider the problem of global exponential synchronization between two identical chaotic neural networks that are linearly and unidirectionally coupled. We formulate a general framework for the synchronization problem in which one chaotic neural network, working as the driving system (or master), sends its output or state values to the other, which serves as the response system (or slave). We use Lyapunov functions to establish general theoretical conditions for designing the coupling matrix. Neither symmetry nor negative (positive) definiteness of the coupling matrix are required; under less restrictive conditions, the two coupled chaotic neural networks can achieve global exponential synchronization regardless of their initial states. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws
International Nuclear Information System (INIS)
Megam Ngouonkadi, E B; Fotsin, H B; Louodop Fotso, P
2014-01-01
This paper investigates the dynamics of a memristor-based Van der Pol oscillator coupled to a linear circuit (VDPCL). This chaotic oscillator is a modification of the classical Van der Pol coupled to a linear circuit, and is obtained by replacing the classical cubic nonlinearity by the memristive one. The memristive VDPCL oscillator, in addition to having a very special stability property, exhibits interesting spectral characteristics, which makes it suitable for chaos-based secure communication applications. The memristor is realized by using off-the-shelf components. The basic properties of the circuit are analyzed by means of bifurcation analysis. Chaotic attractors from numerical and experimental analysis are presented, followed by a comparison of results obtained from the modified VDPCL oscillator and those from the classical VDPCL oscillator. An application to synchronization and chaos secure communication is also presented. (paper)
Insect flight on fluid interfaces: a chaotic interfacial oscillator
Mukundarajan, Haripriya; Prakash, Manu
2013-11-01
Flight is critical to the dominance of insect species on our planet, with about 98 percent of insect species having wings. How complex flight control systems developed in insects is unknown, and arboreal or aquatic origins have been hypothesized. We examine the biomechanics of aquatic origins of flight. We recently reported discovery of a novel mode of ``2D flight'' in Galerucella beetles, which skim along an air-water interface using flapping wing flight. This unique flight mode is characterized by a balance between capillary forces from the interface and biomechanical forces exerted by the flapping wings. Complex interactions on the fluid interface form capillary wave trains behind the insect, and produce vertical oscillations at the surface due to non-linear forces arising from deformation of the fluid meniscus. We present both experimental observations of 2D flight kinematics and a dynamic model explaining the observed phenomena. Careful examination of this interaction predicts the chaotic nature of interfacial flight and takeoff from the interface into airborne flight. The role of wingbeat frequency, stroke plane angle and body angle in determining transition between interfacial and fully airborne flight is highlighted, shedding light on the aquatic theory of flight evolution.
Application of fixed point theory to chaotic attractors of forced oscillators
International Nuclear Information System (INIS)
Stewart, H.B.
1990-11-01
A review of the structure of chaotic attractors of periodically forced second order nonlinear oscillators suggests that the theory of fixed points of transformations gives information about the fundamental topological structure of attractors. First a simple extension of the Levinson index formula is proved. Then numerical evidence is used to formulate plausible conjectures about absorbing regions containing chaotic attractors in forced oscillators. Applying the Levinson formula suggests a fundamental relation between the number of fixed points or periodic points in a section of the chaotic attractor on the one hand, and a topological invariant of an absorbing region on the other hand. (author)
Quenching oscillating behaviors in fractional coupled Stuart-Landau oscillators
Sun, Zhongkui; Xiao, Rui; Yang, Xiaoli; Xu, Wei
2018-03-01
Oscillation quenching has been widely studied during the past several decades in fields ranging from natural sciences to engineering, but investigations have so far been restricted to oscillators with an integer-order derivative. Here, we report the first study of amplitude death (AD) in fractional coupled Stuart-Landau oscillators with partial and/or complete conjugate couplings to explore oscillation quenching patterns and dynamics. It has been found that the fractional-order derivative impacts the AD state crucially. The area of the AD state increases along with the decrease of the fractional-order derivative. Furthermore, by introducing and adjusting a limiting feedback factor in coupling links, the AD state can be well tamed in fractional coupled oscillators. Hence, it provides one an effective approach to analyze and control the oscillating behaviors in fractional coupled oscillators.
International Nuclear Information System (INIS)
Woafo, P.
1999-12-01
This paper deals with the dynamics of a model describing systems consisting of the classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. Both the forced and autonomous cases are considered. Harmonic response is investigated along with its stability boundaries. Condition for quenching phenomena in the autonomous case is derived. Neimark bifurcation is observed and it is found that our model shows period doubling and period-m sudden transitions to chaos. Synchronization of two and more systems in their chaotic regime is presented. (author)
A survey of Wien bridge-based chaotic oscillators: Design and experimental issues
Energy Technology Data Exchange (ETDEWEB)
Kilic, Recai [Erciyes University, Department of Electrical and Electronic Engineering, 38039 Kayseri (Turkey)], E-mail: kilic@erciyes.edu.tr; Yildirim, Fatma [Erciyes University, Civil Aviation School, 38039 Kayseri (Turkey)
2008-12-15
This paper presents a comparative study on design and implementation of Wien type chaotic oscillators. By making a collection of almost all Wien bridge-based chaotic circuits, we have investigated these oscillators in terms of chaotic dynamics, circuit structures, active building blocks, nonlinear element structures and operating frequency by using PSpice simulations and laboratory experiments. In addition to this comparative investigation, we present our two basic experimental contributions to referred implementations. While the first of our experimental contributions consists of the experimentally implementation of CFOA-based Chua's circuit modified for very high chaotic oscillations, the scope of the second is to experimentally implement a Wien type high frequency chaos generator, which has the diode-inductor composite, in the inductorless form by using CFOA-based synthetic inductor.
A survey of Wien bridge-based chaotic oscillators: Design and experimental issues
International Nuclear Information System (INIS)
Kilic, Recai; Yildirim, Fatma
2008-01-01
This paper presents a comparative study on design and implementation of Wien type chaotic oscillators. By making a collection of almost all Wien bridge-based chaotic circuits, we have investigated these oscillators in terms of chaotic dynamics, circuit structures, active building blocks, nonlinear element structures and operating frequency by using PSpice simulations and laboratory experiments. In addition to this comparative investigation, we present our two basic experimental contributions to referred implementations. While the first of our experimental contributions consists of the experimentally implementation of CFOA-based Chua's circuit modified for very high chaotic oscillations, the scope of the second is to experimentally implement a Wien type high frequency chaos generator, which has the diode-inductor composite, in the inductorless form by using CFOA-based synthetic inductor
Does the classically chaotic Henon–Heiles oscillator exhibit ...
Indian Academy of Sciences (India)
–12]. In contrast to a classically chaotic system, where the exponential divergence of trajectories in phase-space is an unambiguous and confirmatory signature of chaos. [15–17], the decision about whether a quantum system is chaotic or not is ...
Tunable power law in the desynchronization events of coupled chaotic electronic circuits
International Nuclear Information System (INIS)
Oliveira, Gilson F. de; Lorenzo, Orlando di; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; Souza Cavalcante, Hugo L. D. de
2014-01-01
We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complex systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time
Chaotic behavior of current-carrying plasmas in external periodic oscillations
Energy Technology Data Exchange (ETDEWEB)
Ohno, Noriyasu; Tanaka, Masayoshi; Komori, Akio; Kawai, Yoshinobu
1989-01-01
A set of cascading bifurcations and a chaotic state in the presence of an external periodic oscillation are experimentally investigated in a current-carrying plasma. The measured bifurcation sequence leading to chaos, which is controlled by changing plasma densities and the frequencies of external oscillations, is in qualitative agreement with a theory which describes anharmonic systems in periodic fields. (author).
Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification
International Nuclear Information System (INIS)
Fotsin, H.B.; Daafouz, J.
2005-01-01
This Letter uses systematic tools from recent papers to design non-linear observers for synchronization of a chaotic colpitts oscillator both in the non adaptive and adaptive cases. It is shown that all parameters of a totally uncertain model of the oscillator can be estimated through adaptive synchronization. A strategy for practical implementation of a secure communication strategy is also discussed
Color image encryption based on Coupled Nonlinear Chaotic Map
International Nuclear Information System (INIS)
Mazloom, Sahar; Eftekhari-Moghadam, Amir Masud
2009-01-01
Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by conventional methods. The desirable cryptographic properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. Therefore, recent researches of image encryption algorithms have been increasingly based on chaotic systems, though the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper proposes a Coupled Nonlinear Chaotic Map, called CNCM, and a novel chaos-based image encryption algorithm to encrypt color images by using CNCM. The chaotic cryptography technique which used in this paper is a symmetric key cryptography with a stream cipher structure. In order to increase the security of the proposed algorithm, 240 bit-long secret key is used to generate the initial conditions and parameters of the chaotic map by making some algebraic transformations to the key. These transformations as well as the nonlinearity and coupling structure of the CNCM have enhanced the cryptosystem security. For getting higher security and higher complexity, the current paper employs the image size and color components to cryptosystem, thereby significantly increasing the resistance to known/chosen-plaintext attacks. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.
Bidirectional communication using delay coupled chaotic directly ...
Indian Academy of Sciences (India)
A symmetric bidirectional coupling is identified as a suitable method for isochronal synchronization of such lasers. The optimum values of coupling and feedback strength that can provide maximum quality of synchronization are identified. This method is successfully employed for encoding/decoding both analog and digital ...
ELMy-H mode as limit cycle and chaotic oscillations in tokamak plasmas
International Nuclear Information System (INIS)
Itoh, Sanae; Itoh, Kimitaka; Fukuyama, Atsushi.
1991-06-01
A model of Edge Localized Modes (ELMs) in tokamaks is presented. A limit cycle solution is found in time-dependent Ginzburg Landau type model equation of L/H transition, which has a hysteresis curve between the plasma gradient and flux. The oscillation of edge density appears near the L/H transition boundary. Spatial structure of the intermediate state (mesophase) is obtained in the edge region. Chaotic oscillation is predicted due to random neutrals and external oscillations. (author)
Regular and chaotic behaviors of plasma oscillations modeled by a modified Duffing equation
International Nuclear Information System (INIS)
Enjieu Kadji, H.G.; Chabi Orou, J.B.; Woafo, P.; Abdus Salam International Centre for Theoretical Physics, Trieste
2005-07-01
The regular and chaotic behavior of plasma oscillations governed by a modified Duffing equation is studied. The plasma oscillations are described by a nonlinear differential equation of the form x + w 0 2 x + βx 2 + αx 3 = 0 which is similar to a Duffing equation. By focusing on the quadratic term, which is mainly the term modifying the Duffing equation, the harmonic balance method and the fourth order Runge-Kutta algorithm are used to derive regular and chaotic motions respectively. A strong chaotic behavior exhibited by the system in that event when the system is subjected to an external periodic forcing oscillation is reported as β varies. (author)
Coupled oscillators with parity-time symmetry
Energy Technology Data Exchange (ETDEWEB)
Tsoy, Eduard N., E-mail: etsoy@uzsci.net
2017-02-05
Different models of coupled oscillators with parity-time (PT) symmetry are studied. Hamiltonian functions for two and three linear oscillators coupled via coordinates and accelerations are derived. Regions of stable dynamics for two coupled oscillators are obtained. It is found that in some cases, an increase of the gain-loss parameter can stabilize the system. A family of Hamiltonians for two coupled nonlinear oscillators with PT-symmetry is obtained. An extension to high-dimensional PT-symmetric systems is discussed. - Highlights: • A generalization of a Hamiltonian system of linear coupled oscillators with the parity-time (PT) symmetry is suggested. • It is found that an increase of the gain-loss parameter can stabilize the system. • A family of Hamiltonian functions for two coupled nonlinear oscillators with PT-symmetry is obtained.
Some chaotic features of intrinsically coupled Josephson junctions
International Nuclear Information System (INIS)
Kolahchi, M.R.; Shukrinov, Yu.M.; Hamdipour, M.; Botha, A.E.; Suzuki, M.
2013-01-01
Highlights: ► Intrinsically coupled Josephson junctions model a high-T c superconductor. ► Intrinsically coupled Josephson junctions can act as a chaotic nonlinear system. ► Chaos could be due to resonance overlap. ► Avoiding parameters that lead to chaos is important for the design of resonators. -- Abstract: We look for chaos in an intrinsically coupled system of Josephson junctions. This study has direct applications for the high-T c resonators which require coherence amongst the junctions
Synchronization of coupled chaotic dynamics on networks
Indian Academy of Sciences (India)
We review some recent work on the synchronization of coupled dynamical systems on a variety of networks. When nodes show synchronized behaviour, two interesting phenomena can be observed. First, there are some nodes of the floating type that show intermittent behaviour between getting attached to some clusters ...
Complex network synchronization of chaotic systems with delay coupling
International Nuclear Information System (INIS)
Theesar, S. Jeeva Sathya; Ratnavelu, K.
2014-01-01
The study of complex networks enables us to understand the collective behavior of the interconnected elements and provides vast real time applications from biology to laser dynamics. In this paper, synchronization of complex network of chaotic systems has been studied. Every identical node in the complex network is assumed to be in Lur’e system form. In particular, delayed coupling has been assumed along with identical sector bounded nonlinear systems which are interconnected over network topology
Energy Technology Data Exchange (ETDEWEB)
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it [MR-Lab, Center for Mind/Brain Science, University of Trento, Trento, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2014-09-01
In this paper, an experimental characterization of the dynamical properties of five autonomous chaotic oscillators, based on bipolar-junction transistors and obtained de-novo through a genetic algorithm in a previous study, is presented. In these circuits, a variable resistor connected in series to the DC voltage source acts as control parameter, for a range of which the largest Lyapunov exponent, correlation dimension, approximate entropy, and amplitude variance asymmetry are calculated, alongside bifurcation diagrams and spectrograms. Numerical simulations are compared to experimental measurements. The oscillators can generate a considerable variety of regular and chaotic sine-like and spike-like signals.
Feedback control and adaptive synchronization of chaotic forced Bonhoeffer-van der Pol oscillators
Energy Technology Data Exchange (ETDEWEB)
Kontchou, E W Chimi; Fotsin, H B [Laboratoire d' Electronique, Departement de Physique, Faculte des Sciences, Universite de Dschang, B P 67 Dschang (Cameroon); Woafo, P [Laboratory of Modelling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde (Cameroon)], E-mail: hbfotsin@yahoo.fr
2008-04-15
This paper deals with chaos control and synchronization in forced Bonhoeffer-van der Pol (FBVP) oscillators. The state equations of the model are first established and the stability is analysed. A feedback control strategy for stabilizing the chaotic dynamics on a periodic orbit of the phase space is investigated. Adaptive synchronization of two FBVP oscillators, based on parameter estimation and a nonlinear observer approach, is also investigated. It appears that a particular unknown parameter of the model can be estimated, which gives the possibility of recovering information through chaotic masking. An application in secure communications is presented.
Feedback control and adaptive synchronization of chaotic forced Bonhoeffer-van der Pol oscillators
International Nuclear Information System (INIS)
Kontchou, E W Chimi; Fotsin, H B; Woafo, P
2008-01-01
This paper deals with chaos control and synchronization in forced Bonhoeffer-van der Pol (FBVP) oscillators. The state equations of the model are first established and the stability is analysed. A feedback control strategy for stabilizing the chaotic dynamics on a periodic orbit of the phase space is investigated. Adaptive synchronization of two FBVP oscillators, based on parameter estimation and a nonlinear observer approach, is also investigated. It appears that a particular unknown parameter of the model can be estimated, which gives the possibility of recovering information through chaotic masking. An application in secure communications is presented
Fully Digital Chaotic Oscillators Applied to Pseudo Random Number Generation
Mansingka, Abhinav S.
2012-05-01
This thesis presents a generalized approach for the fully digital design and implementation of chaos generators through the numerical solution of chaotic ordinary differential equations. In particular, implementations use the Euler approximation with a fixed-point twos complement number representation system for optimal hardware and performance. In general, digital design enables significant benefits in terms of power, area, throughput, reliability, repeatability and portability over analog implementations of chaos due to lower process, voltage and temperature sensitivities and easy compatibility with other digital systems such as microprocessors, digital signal processing units, communication systems and encryption systems. Furthermore, this thesis introduces the idea of implementing multidimensional chaotic systems rather than 1-D chaotic maps to enable wider throughputs and multiplier-free architectures that provide significant performance and area benefits. This work focuses efforts on the well-understood family of autonomous 3rd order "jerk" chaotic systems. The effect of implementation precision, internal delay cycles and external delay cycles on the chaotic response are assessed. Multiplexing of parameters is implemented to enable switching between chaotic and periodic modes of operation. Enhanced chaos generators that exploit long-term divergence in two identical systems of different precision are also explored. Digital design is shown to enable real-time controllability of 1D multiscroll systems and 4th order hyperchaotic systems, essentially creating non-autonomous chaos that has thus far been difficult to implement in the analog domain. Seven different systems are mathematically assessed for chaotic properties, implemented at the register transfer level in Verilog HDL and experimentally verified on a Xilinx Virtex 4 FPGA. The statistical properties of the output are rigorously studied using the NIST SP. 800-22 statistical testing suite. The output is
Adiabatic regularization of power spectra in nonminimally coupled chaotic inflation
Energy Technology Data Exchange (ETDEWEB)
Alinea, Allan L., E-mail: alinea@het.phys.sci.osaka-u.ac.jp [Department of Physics, Osaka University, Toyonaka, Osaka 560-0043 (Japan)
2016-10-01
We investigate the effect of adiabatic regularization on both the tensor- and scalar-perturbation power spectra in nonminimally coupled chaotic inflation. Similar to that of the minimally coupled general single-field inflation, we find that the subtraction term is suppressed by an exponentially decaying factor involving the number of e -folds. By following the subtraction term long enough beyond horizon crossing, the regularized power spectrum tends to the ''bare'' power spectrum. This study justifies the use of the unregularized (''bare'') power spectrum in standard calculations.
Nonlocal synchronization in nearest neighbour coupled oscillators
International Nuclear Information System (INIS)
El-Nashar, H.F.; Elgazzar, A.S.; Cerdeira, H.A.
2002-02-01
We investigate a system of nearest neighbour coupled oscillators. We show that the nonlocal frequency synchronization, that might appear in such a system, occurs as a consequence of the nearest neighbour coupling. The power spectra of nonadjacent oscillators shows that there is no complete coincidence between all frequency peaks of the oscillators in the nonlocal cluster, while the peaks for neighbouring oscillators approximately coincide even if they are not yet in a cluster. It is shown that nonadjacent oscillators closer in frequencies, share slow modes with their adjacent oscillators which are neighbours in space. It is also shown that when a direct coupling between non-neighbours oscillators is introduced explicitly, the peaks of the spectra of the frequencies of those non-neighbours coincide. (author)
Compensation of oscillation coupling induced by solenoids
International Nuclear Information System (INIS)
Zelinskij, A.Yu.; Karnaukhov, I.M.; Shcherbakov, A.A.
1988-01-01
Methods for construction of various schemes of oscillation coupling compensation, induced by solenoids in charged particle storage rings, are described. Peculiarities of magnetic structure, enabling to localize oscillation coupling in wide energy range are discussed. Results of calculation of compensation schemes for design of NR-2000 storage ring spin rotation are presented
ELMy-H mode as limit cycle and chaotic oscillations in tokamak plasmas
International Nuclear Information System (INIS)
Itoh Sanae, I.; Itoh, Kimitaka; Fukuyama, Atsushi; Miura, Yukitoshi.
1991-05-01
A model of Edge Localized Modes (ELMs) in tokamak plasmas is presented. A limit cycle solution is found in the transport equation (time-dependent Ginzburg-Landau type), which a has hysteresis curve between the gradient and flux. Periodic oscillation of the particle outflux and L/H intermediate state are predicted near the L/H transition boundary. A mesophase in spatial structure appears near edge. Chaotic oscillation is also predicted. (author)
Yuan, Fang; Wang, Guangyi; Wang, Xiaowei
2017-03-01
In this paper, smooth curve models of meminductor and memcapacitor are designed, which are generalized from a memristor. Based on these models, a new five-dimensional chaotic oscillator that contains a meminductor and memcapacitor is proposed. By dimensionality reducing, this five-dimensional system can be transformed into a three-dimensional system. The main work of this paper is to give the comparisons between the five-dimensional system and its dimensionality reduction model. To investigate dynamics behaviors of the two systems, equilibrium points and stabilities are analyzed. And the bifurcation diagrams and Lyapunov exponent spectrums are used to explore their properties. In addition, digital signal processing technologies are used to realize this chaotic oscillator, and chaotic sequences are generated by the experimental device, which can be used in encryption applications.
Rabi oscillation between states of a coupled harmonic oscillator
International Nuclear Information System (INIS)
Park, Tae Jun
2003-01-01
Rabi oscillation between bound states of a single potential is well known. However the corresponding formula between the states of two different potentials has not been obtained yet. In this work, we derive Rabi formula between the states of a coupled harmonic oscillator which may be used as a simple model for the electron transfer. The expression is similar to typical Rabi formula for a single potential. This result may be used to describe transitions between coupled diabatic potential curves
Small-world networks of fuzzy chaotic oscillators
Bucolo, M; Fortuna, L
2003-01-01
Small-world topology has been used to build lattices of nonlinear fuzzy systems. Chaotic units, ruled by linguistic description and with specified Lyapunov exponent, have been realized and connected using linear diffusion coefficient. The dynamic features of the networks versus the number of systems connected have been investigated to underline phenomena like spatiotemporal chaos and complete regularization. The synchronization characteristics in case of sparse long-term connections and the performances comparison with regular and random network configurations are shown.
Energy Technology Data Exchange (ETDEWEB)
Aguilar-Lopez, Ricardo [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, 02200, Azcapotzalco, Mexico D.F. (Mexico)], E-mail: raguilar@correo.azc.uam.mx; Martinez-Guerra, Rafael [Departamento de Control Automatico, CINVESTAV-IPN, Apartado Postal 14-740, 07360 Mexico D.F. (Mexico)], E-mail: rguerra@ctrl.cinvestav.mx
2008-10-15
The goal of this work is related with the control of chaotic oscillators for chaos suppression and synchronization purposes. The proposed methodology is related with a class of robust active control (RAC) law, where the stabilizing part of the control structure is related with an integral high order sliding-mode and proportional form of the so-called control error. The proposed controller is applied to chaos suppression, synchronization and anti-synchronization tasks for nonlinear oscillators with different order and structure. Numerical experiments illustrate the satisfactory performance of the proposed methodology, when it is applied to Duffing and Chen oscillators.
International Nuclear Information System (INIS)
Aguilar-Lopez, Ricardo; Martinez-Guerra, Rafael
2008-01-01
The goal of this work is related with the control of chaotic oscillators for chaos suppression and synchronization purposes. The proposed methodology is related with a class of robust active control (RAC) law, where the stabilizing part of the control structure is related with an integral high order sliding-mode and proportional form of the so-called control error. The proposed controller is applied to chaos suppression, synchronization and anti-synchronization tasks for nonlinear oscillators with different order and structure. Numerical experiments illustrate the satisfactory performance of the proposed methodology, when it is applied to Duffing and Chen oscillators
Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom
International Nuclear Information System (INIS)
Musielak, D.E.; Musielak, Z.E.; Benner, J.W.
2005-01-01
New results are reported on the routes to chaos in increasingly complex Duffing oscillator systems, which are formed by coupling several oscillators, thereby increasing the number of degrees of freedom. Other forms of increasing system complexity through distributed excitation, different forcing function phasing, different excitation frequency ratios, and higher order coupling are also studied. Changes in the quantitative aspects of the chaotic regions and in the routes to chaos of complex Duffing systems are investigated by performing numerical simulations. It is shown that the number of chaotic regions in these systems is significantly reduced when compared to the original Duffing system, and that crisis replaces period doubling as the dominant route to chaos when the number of degrees of freedom is increased. A new discovered phenomenon is that chaos emerges in the symmetrically and asymmetrically coupled Duffing oscillators only after the quasi-periodic torus breaks down through a 3-periodic and 2-periodic window, respectively
Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A
2012-03-01
We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.
Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator
Mansingka, Abhinav S.
2012-07-29
This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.
Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator
Mansingka, Abhinav S.; Radwan, Ahmed G.; Salama, Khaled N.; Zidan, Mohammed A.
2012-01-01
This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.
Higher-order chaotic oscillator using active bessel filter
DEFF Research Database (Denmark)
Lindberg, Erik; Mykolaitis, Gytis; Bumelien, Skaidra
2010-01-01
A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending...
International Nuclear Information System (INIS)
Deng Bin; Wang Jiang; Fei Xiangyang
2006-01-01
Backstepping design is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller. In this paper, the backstepping control is used to synchronize two coupled chaotic neurons in external electrical stimulation. The coupled model is based on the nonlinear cable model and only one state variable can be controlled in practice. The backstepping design needs only one controller to synchronize two chaotic systems and it can be applied to a variety of chaotic systems whether they contain external excitation or not, so the two coupled chaotic neurons in external electrical stimulation can be synchronized perfectly by backstepping control. Numerical simulations demonstrate the effectiveness of this design
Synchronisation in coupled quantum Hamiltonian superconducting oscillator via a control potential
International Nuclear Information System (INIS)
Al-Khawaja, Sameer
2009-01-01
This paper presents chaos synchronisation in a SQUID device mutually coupled to a resonant LC classical circuit. Via the Hamiltonian of the coupled quantum-classical system and by means of a 'control potential' in the form of a double-well, measure synchronisation has been found to exist. A transition from quasi-periodic to chaotically synchronised orbits in the phase space has been observed, as the strength of coupling is increased between both oscillators. The system reaches a non-synchronised state if the choice of the control potential were to render both oscillators non-identical.
Fouladi, Ehsan; Mojallali, Hamed
2018-01-01
In this paper, an adaptive backstepping controller has been tuned to synchronise two chaotic Colpitts oscillators in a master-slave configuration. The parameters of the controller are determined using shark smell optimisation (SSO) algorithm. Numerical results are presented and compared with those of particle swarm optimisation (PSO) algorithm. Simulation results show better performance in terms of accuracy and convergence for the proposed optimised method compared to PSO optimised controller or any non-optimised backstepping controller.
Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder
Energy Technology Data Exchange (ETDEWEB)
Nono Dueyou Buckjohn, C., E-mail: bucknono@yahoo.f [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon); Siewe Siewe, M., E-mail: martinsiewesiewe@yahoo.f [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon); Tchawoua, C., E-mail: ctchawa@yahoo.f [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon); Kofane, T.C., E-mail: tckofane@yahoo.co [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon)
2010-08-02
In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.
Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder
International Nuclear Information System (INIS)
Nono Dueyou Buckjohn, C.; Siewe Siewe, M.; Tchawoua, C.; Kofane, T.C.
2010-01-01
In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.
Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder
Nono Dueyou Buckjohn, C.; Siewe Siewe, M.; Tchawoua, C.; Kofane, T. C.
2010-08-01
In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.
Simple Chaotic Oscillator: From Mathematical Model to Practical Experiment
Directory of Open Access Journals (Sweden)
S. Hanus
2006-04-01
Full Text Available This paper shows the circuitry implementation and practical verification of the autonomous nonlinear oscillator. Since it is described by a single third-order differential equation, its state variables can be considered as the position, velocity and acceleration and thus have direct connection to a real physical system. Moreover, for some specific configurations of internal system parameters, it can exhibit a period doubling bifurcation leading to chaos. Two different structures of the nonlinear element were verified by a comparison of numerically integrated trajectory with the oscilloscope screenshots .
Local instability driving extreme events in a pair of coupled chaotic electronic circuits
de Oliveira, Gilson F.; Di Lorenzo, Orlando; de Silans, Thierry Passerat; Chevrollier, Martine; Oriá, Marcos; Cavalcante, Hugo L. D. de Souza
2016-06-01
For a long time, extreme events happening in complex systems, such as financial markets, earthquakes, and neurological networks, were thought to follow power-law size distributions. More recently, evidence suggests that in many systems the largest and rarest events differ from the other ones. They are dragon kings, outliers that make the distribution deviate from a power law in the tail. Understanding the processes of formation of extreme events and what circumstances lead to dragon kings or to a power-law distribution is an open question and it is a very important one to assess whether extreme events will occur too often in a specific system. In the particular system studied in this paper, we show that the rate of occurrence of dragon kings is controlled by the value of a parameter. The system under study here is composed of two nearly identical chaotic oscillators which fail to remain in a permanently synchronized state when coupled. We analyze the statistics of the desynchronization events in this specific example of two coupled chaotic electronic circuits and find that modifying a parameter associated to the local instability responsible for the loss of synchronization reduces the occurrence of dragon kings, while preserving the power-law distribution of small- to intermediate-size events with the same scaling exponent. Our results support the hypothesis that the dragon kings are caused by local instabilities in the phase space.
Quadrupole oscillations as paradigm of the chaotic motion in nuclei
International Nuclear Information System (INIS)
Berezovoj, V.P.; Bolotin, Yu.L.; Gonchar, V.Yu.; Granovsky, M.Ya.
2003-01-01
A complete description of classical dynamics, generated by the Hamiltonian of quadrupole nuclear oscillations, is presented. Those peculiarities of quantum dynamics, which can be interpreted as quantum manifestations of classical stochasticity are identified. Semiclassical approximation to an energy spectrum is developed through quantization of the Birkhoff-Gustavson normal form. We show that the type of classical motion is correlated with the structure of the stationary wave functions. Correlations were found both in the coordinate space (the lattice of nodal curves and the distribution of the probability density) and in the Hilbert space associated with the integrable part of the Hamiltonian. Quadrupole oscillations of nuclei were used to investigate the shell structure destruction induced by the increase of nonintegrable perturbation, which models residual nucleon-nucleon interaction. The process of wave packet tunneling through potential barrier is considered for the case of finite motion. We demonstrate that the stringent correlation between the level quasi-crossing and the wave function delocalization, which leads to the resonant tunneling, takes place [ru
Anticipating synchronization in a chain of chaotic oscillators with switching parameters
Energy Technology Data Exchange (ETDEWEB)
Pyragienė, T., E-mail: tatjana.pyragiene@ftmc.lt; Pyragas, K.
2015-12-18
A new coupling scheme for anticipating synchronization of chaotic systems is proposed. The scheme consists of a master system and two in series coupled slave systems with periodically switching parameters. The scheme does not require the presence of any time-delay terms either in a master or in slave systems and provides long-term anticipation. The value of anticipation time as well as the conditions of synchronization are derived in an analytical form. Analytical results are tested by numerical experiments with the chaotic Rössler and Lorenz systems as well as the Hindmarsh–Rose neuron in a regime of chaotic bursting. Also a robustness of the scheme with respect to parameter mismatch and noise is demonstrated. - Highlights: • A new coupling scheme for anticipating chaotic synchronization is proposed. • The scheme consists of three coupled systems with periodically switching parameters. • Long-term anticipation is achieved without using time-delay terms. • The method is verified for the Rössler, Lorenz and Hindmarsh–Rose neuron systems.
Anticipating synchronization in a chain of chaotic oscillators with switching parameters
International Nuclear Information System (INIS)
Pyragienė, T.; Pyragas, K.
2015-01-01
A new coupling scheme for anticipating synchronization of chaotic systems is proposed. The scheme consists of a master system and two in series coupled slave systems with periodically switching parameters. The scheme does not require the presence of any time-delay terms either in a master or in slave systems and provides long-term anticipation. The value of anticipation time as well as the conditions of synchronization are derived in an analytical form. Analytical results are tested by numerical experiments with the chaotic Rössler and Lorenz systems as well as the Hindmarsh–Rose neuron in a regime of chaotic bursting. Also a robustness of the scheme with respect to parameter mismatch and noise is demonstrated. - Highlights: • A new coupling scheme for anticipating chaotic synchronization is proposed. • The scheme consists of three coupled systems with periodically switching parameters. • Long-term anticipation is achieved without using time-delay terms. • The method is verified for the Rössler, Lorenz and Hindmarsh–Rose neuron systems.
International Nuclear Information System (INIS)
Chen, H.-H.; Chen, C.-S.; Lee, C.-I
2009-01-01
This paper investigates the synchronization of unidirectional and bidirectional coupled unified chaotic systems. A balanced coupling coefficient control method is presented for global asymptotic synchronization using the Lyapunov stability theorem and a minimum scheme with no constraints/constraints. By using the result of the above analysis, the balanced coupling coefficients are then designed to achieve the chaos synchronization of linearly coupled unified chaotic systems. The feasibility and effectiveness of the proposed chaos synchronization scheme are verified via numerical simulations.
Adaptive elimination of synchronization in coupled oscillator
Zhou, Shijie; Ji, Peng; Zhou, Qing; Feng, Jianfeng; Kurths, Jürgen; Lin, Wei
2017-08-01
We present here an adaptive control scheme with a feedback delay to achieve elimination of synchronization in a large population of coupled and synchronized oscillators. We validate the feasibility of this scheme not only in the coupled Kuramoto’s oscillators with a unimodal or bimodal distribution of natural frequency, but also in two representative models of neuronal networks, namely, the FitzHugh-Nagumo spiking oscillators and the Hindmarsh-Rose bursting oscillators. More significantly, we analytically illustrate the feasibility of the proposed scheme with a feedback delay and reveal how the exact topological form of the bimodal natural frequency distribution influences the scheme performance. We anticipate that our developed scheme will deepen the understanding and refinement of those controllers, e.g. techniques of deep brain stimulation, which have been implemented in remedying some synchronization-induced mental disorders including Parkinson disease and epilepsy.
Adaptive elimination of synchronization in coupled oscillator
International Nuclear Information System (INIS)
Zhou, Shijie; Lin, Wei; Ji, Peng; Feng, Jianfeng; Zhou, Qing; Kurths, Jürgen
2017-01-01
We present here an adaptive control scheme with a feedback delay to achieve elimination of synchronization in a large population of coupled and synchronized oscillators. We validate the feasibility of this scheme not only in the coupled Kuramoto’s oscillators with a unimodal or bimodal distribution of natural frequency, but also in two representative models of neuronal networks, namely, the FitzHugh–Nagumo spiking oscillators and the Hindmarsh–Rose bursting oscillators. More significantly, we analytically illustrate the feasibility of the proposed scheme with a feedback delay and reveal how the exact topological form of the bimodal natural frequency distribution influences the scheme performance. We anticipate that our developed scheme will deepen the understanding and refinement of those controllers, e.g. techniques of deep brain stimulation, which have been implemented in remedying some synchronization-induced mental disorders including Parkinson disease and epilepsy. (paper)
Sync or anti-sync – dynamical pattern selection in coupled self-sustained oscillator systems
International Nuclear Information System (INIS)
Davidova, Larissa; Újvári, Szeréna; Néda, Zoltán
2014-01-01
The dynamics of similar, self-sustained oscillators coupled by a common platform exhibits fascinating collective behavior. Experiments performed with pendulum clocks and metronomes reported both the absence of synchronization, in-phase synchronization, antiphase synchronization, beat-death phenomenon, or even chaotic dynamics. Here we present a numerical study on two identical self-sustained oscillators placed on a common movable platform. As order parameter for synchronization we use the Pearson correlation coefficient between the oscillators coordinates. As a function of the relevant physical parameters of this system we reproduce all the experimentally reported dynamics. We provide conditions for obtaining stable and emergent in-phase or anti-phase synchronization.
Chaotic behavior in Casimir oscillators: A case study for phase-change materials.
Tajik, Fatemeh; Sedighi, Mehdi; Khorrami, Mohammad; Masoudi, Amir Ali; Palasantzas, George
2017-10-01
Casimir forces between material surfaces at close proximity of less than 200 nm can lead to increased chaotic behavior of actuating devices depending on the strength of the Casimir interaction. We investigate these phenomena for phase-change materials in torsional oscillators, where the amorphous to crystalline phase transitions lead to transitions between high and low Casimir force and torque states, respectively, without material compositions. For a conservative system bifurcation curve and Poincare maps analysis show the absence of chaotic behavior but with the crystalline phase (high force-torque state) favoring more unstable behavior and stiction. However, for a nonconservative system chaotic behavior can take place introducing significant risk for stiction, which is again more pronounced for the crystalline phase. The latter illustrates the more general scenario that stronger Casimir forces and torques increase the possibility for chaotic behavior. The latter is making it impossible to predict whether stiction or stable actuation will occur on a long-term basis, and it is setting limitations in the design of micronano devices operating at short-range nanoscale separations.
Flashing coupled density wave oscillation
International Nuclear Information System (INIS)
Jiang Shengyao; Wu Xinxin; Zhang Youjie
1997-07-01
The experiment was performed on the test loop (HRTL-5), which simulates the geometry and system design of the 5 MW reactor. The phenomenon and mechanism of different kinds of two-phase flow instabilities, namely geyser instability, flashing instability and flashing coupled density wave instability are described. The especially interpreted flashing coupled density wave instability has never been studied well, it is analyzed by using a one-dimensional non-thermo equilibrium two-phase flow drift model computer code. Calculations are in good agreement with the experiment results. (5 refs.,5 figs., 1 tab.)
Mixed coherent states in coupled chaotic systems: Design of secure wireless communication
Vigneshwaran, M.; Dana, S. K.; Padmanaban, E.
2016-12-01
A general coupling design is proposed to realize a mixed coherent (MC) state: coexistence of complete synchronization, antisynchronization, and amplitude death in different pairs of similar state variables of the coupled chaotic system. The stability of coupled system is ensured by the Lyapunov function and a scaling of each variable is also separately taken care of. When heterogeneity as a parameter mismatch is introduced in the coupled system, the coupling function facilitates to retain its coherence and displays the global stability with renewed scaling factor. Robust synchronization features facilitated by a MC state enable to design a dual modulation scheme: binary phase shift key (BPSK) and parameter mismatch shift key (PMSK), for secure data transmission. Two classes of decoders (coherent and noncoherent) are discussed, the noncoherent decoder shows better performance over the coherent decoder, mostly a noncoherent demodulator is preferred in biological implant applications. Both the modulation schemes are demonstrated numerically by using the Lorenz oscillator and the BPSK scheme is demonstrated experimentally using radio signals.
Mode coupling in spin torque oscillators
International Nuclear Information System (INIS)
Zhang, Steven S.-L.; Zhou, Yan; Li, Dong; Heinonen, Olle
2016-01-01
A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator, such as observed mode-hopping or mode coexistence. There has been some initial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In the present work, we rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature. - Highlights: • Deriving equations for coupled modes in spin torque oscillators. • Including Hamiltonian formalism and elimination of three–magnon processes. • Thermal bath of magnons central to mode coupling. • Numerical examples of circular and elliptical devices.
Mode coupling in spin torque oscillators
Energy Technology Data Exchange (ETDEWEB)
Zhang, Steven S.-L., E-mail: ZhangShule@missouri.edu [Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211 (United States); Zhou, Yan, E-mail: yanzhou@hku.hk [Department of Physics, The University of Hong Kong, Hong Kong (China); Center of Theoretical and Computational Physics, University of Hong Kong, Hong Kong (China); Li, Dong, E-mail: geodesic.ld@gmail.com [Department of Physics, Centre for Nonlinear Studies, and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China); Heinonen, Olle, E-mail: heinonen@anl.gov [Material Science Division, Argonne National Laboratory, Lemont, IL 60439 (United States); Northwestern-Argonne Institute of Science and Technology, 2145 Sheridan Road, Evanston, IL 60208 (United States); Computation Institute, The Unversity of Chicago, 5735 S Ellis Avenue, Chicago, IL 60637 (United States)
2016-09-15
A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator, such as observed mode-hopping or mode coexistence. There has been some initial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In the present work, we rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature. - Highlights: • Deriving equations for coupled modes in spin torque oscillators. • Including Hamiltonian formalism and elimination of three–magnon processes. • Thermal bath of magnons central to mode coupling. • Numerical examples of circular and elliptical devices.
Synchronization in Coupled Oscillators with Two Coexisting Attractors
International Nuclear Information System (INIS)
Han-Han, Zhu; Jun-Zhong, Yang
2008-01-01
Dynamics in coupled Duffing oscillators with two coexisting symmetrical attractors is investigated. For a pair of Duffing oscillators coupled linearly, the transition to the synchronization generally consists of two steps: Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions. (general)
Synchronisation phenomenon in three blades rotor driven by regular or chaotic oscillations
Directory of Open Access Journals (Sweden)
Szmit Zofia
2018-01-01
Full Text Available The goal of the paper is to analysed the influence of the different types of excitation on the synchronisation phenomenon in case of the rotating system composed of a rigid hub and three flexible composite beams. In the model is assumed that two blades, due to structural differences, are de-tuned. Numerical calculation are divided on two parts, firstly the rotating system is exited by a torque given by regular harmonic function, than in the second part the torque is produced by chaotic Duffing oscillator. The synchronisation phenomenon between the beams is analysed both either for regular or chaotic motions. Partial differential equations of motion are solved numerically and resonance curves, time series and Poincaré maps are presented for selected excitation torques.
Chaotic oscillation and random-number generation based on nanoscale optical-energy transfer.
Naruse, Makoto; Kim, Song-Ju; Aono, Masashi; Hori, Hirokazu; Ohtsu, Motoichi
2014-08-12
By using nanoscale energy-transfer dynamics and density matrix formalism, we demonstrate theoretically and numerically that chaotic oscillation and random-number generation occur in a nanoscale system. The physical system consists of a pair of quantum dots (QDs), with one QD smaller than the other, between which energy transfers via optical near-field interactions. When the system is pumped by continuous-wave radiation and incorporates a timing delay between two energy transfers within the system, it emits optical pulses. We refer to such QD pairs as nano-optical pulsers (NOPs). Irradiating an NOP with external periodic optical pulses causes the oscillating frequency of the NOP to synchronize with the external stimulus. We find that chaotic oscillation occurs in the NOP population when they are connected by an external time delay. Moreover, by evaluating the time-domain signals by statistical-test suites, we confirm that the signals are sufficiently random to qualify the system as a random-number generator (RNG). This study reveals that even relatively simple nanodevices that interact locally with each other through optical energy transfer at scales far below the wavelength of irradiating light can exhibit complex oscillatory dynamics. These findings are significant for applications such as ultrasmall RNGs.
Regular self-oscillating and chaotic behaviour of a PID controlled gimbal suspension gyro
International Nuclear Information System (INIS)
Perez Polo, Manuel F.; Perez Molina, Manuel
2004-01-01
The dynamics of a gyro in gimbal with a PID controller to obtain steady state, self-oscillating and chaotic motion is considered in this paper. The mathematical model of the whole system is deduced from the gyroscope nutation theory and from a feedback control system formed by a PID controller with constrained integral action. The paper shows that the gyro and the associated PID feedback control system have multiple equilibrium points, and from the analysis of a Poincare-Andronov-Hopf bifurcation at the equilibrium points, it is possible to deduce the conditions, which give regular and self-oscillating behaviour. The calculation of the first Lyapunov value is used to predict the motion of the gyro in order to obtain a desired equilibrium point or self-oscillating behaviour. The mechanism of the stability loss of the gyro under small vibrations of the gyro platform and the appearance of chaotic motion is also presented. Numerical simulations are performed to verify the analytical results
Output-Feedback Control of a Chaotic MEMS Resonator for Oscillation Amplitude Enhancement
Directory of Open Access Journals (Sweden)
Alexander Jimenez-Triana
2014-01-01
Full Text Available The present work addresses the problem of chaos control in an electrostatic MEMS resonator by using an output-feedback control scheme. One of the unstable orbits immersed in the chaotic attractor is stabilized in order to produce a sustained oscillation of the movable plate composing the microstructure. The orbit is carefully chosen so as to produce a high amplitude oscillation. This approach allows the enhancement of oscillation amplitude of the resonator at a reduced control effort, since the unstable orbit already exists in the system and it is not necessary to spend energy to create it. Realistic operational conditions of the MEMS are considered including parametric uncertainties in the model and constraints due to the difficulty in measuring the speed of the plates of the microstructure. A control law is constructed recursively by using the technique of backstepping. Finally, numerical simulations are carried out to confirm the validity of the developed control scheme and to demonstrate the effect of controlling orbits immersed in the chaotic attractor.
International Nuclear Information System (INIS)
Wu, C.Y.; Wang, S.B.; Pan, C.
1996-01-01
The oscillation characteristics of a low pressure two-phase natural circulation loop have been investigated experimentally in this study. Experimental results indicate that the characteristics of the thermal hydraulic oscillations can be periodic, with 2-5 fundamental frequencies, or chaotic, depending on the heating power and inlet subcooling. The number of fundamental frequencies of oscillation increases if the inlet subcooling is increased at a given heating power or the heating power is decreased at a given inlet subcooling; chaotic oscillations appear if the inlet subcooling is further increased and/or the heating power is further decreased. A map of the oscillation characteristics is thus established. The change in oscillation characteristics is evident from the time evolution and power spectrum of a thermal hydraulic parameter and the phase portraits of two thermal hydraulic parameters. These results reveal that a strange attractor exists in a low pressure two-phase natural circulation loop with low power and very high inlet subcooling. (orig.)
Global pulse synchronization of chaotic oscillators through fast-switching: theory and experiments
International Nuclear Information System (INIS)
Porfiri, Maurizio; Fiorilli, Francesca
2009-01-01
We study pulse synchronization of chaotic systems in master-slave configuration. The slave system is unidirectionally coupled to the master system through an intermittent linear error feedback coupling, whose gain matrix periodically switches among a finite set of constant matrices. Using Lyapunov-stability theory, fast-switching techniques, and the concept of matrix measure, we derive sufficient conditions for global synchronization. The derived conditions are specialized to the case of Chua's circuits. An inductorless realization of coupled Chua's circuits is developed to illustrate the effectiveness of the proposed approach.
Kuwahara, Jun; Miyata, Hajime; Konno, Hidetoshi
2017-09-01
Recently, complex dynamics of globally coupled oscillators have been attracting many researcher's attentions. In spite of their numerous studies, their features of nonlinear oscillator systems with global and local couplings in two-dimension (2D) are not understood fully. The paper focuses on 2D states of coherent, clustered and chaotic oscillation especially under the effect of negative global coupling (NGC) in 2D Alief-Panfilov model. It is found that the tuning NGC can cause various new coupling-parameter dependency on the features of oscillations. Then quantitative characterization of various states of oscillations (so called spiral wave turbulence) is examined by using the pragmatic information (PI) which have been utilized in analyzing multimode laser, solar activity and neuronal systems. It is demonstrated that the dynamics of the PI for various oscillations can be characterized successfully by the Hyper-Gamma stochastic process.
Dynamics of microbubble oscillators with delay coupling
Heckman, C. R.; Sah, S. M.; Rand, R. H.
2010-10-01
We investigate the stability of the in-phase mode in a system of two delay-coupled bubble oscillators. The bubble oscillator model is based on a 1956 paper by Keller and Kolodner. Delay coupling is due to the time it takes for a signal to travel from one bubble to another through the liquid medium that surrounds them. Using techniques from the theory of differential-delay equations as well as perturbation theory, we show that the equilibrium of the in-phase mode can be made unstable if the delay is long enough and if the coupling strength is large enough, resulting in a Hopf bifurcation. We then employ Lindstedt's method to compute the amplitude of the limit cycle as a function of the time delay. This work is motivated by medical applications involving noninvasive localized drug delivery via microbubbles.
Chaotic Synchronization in Nearest-Neighbor Coupled Networks of 3D CNNs
Serrano-Guerrero, H.; Cruz-Hernández, C.; López-Gutiérrez, R.M.; Cardoza-Avendaño, L.; Chávez-Pérez, R.A.
2013-01-01
In this paper, a synchronization of Cellular Neural Networks (CNNs) in nearest-neighbor coupled arrays, is numerically studied. Synchronization of multiple chaotic CNNs is achieved by appealing to complex systems theory. In particular, we consider dynamical networks composed by 3D CNNs, as interconnected nodes, where the interactions in the networks are defined by coupling the first state of each node. Four cases of interest are considered: i) synchronization without chaotic master, ii) maste...
International Nuclear Information System (INIS)
Fang Xiaoling; Yu Hongjie; Jiang Zonglai
2009-01-01
The chaotic synchronization of Hindmarsh-Rose neural networks linked by a nonlinear coupling function is discussed. The HR neural networks with nearest-neighbor diffusive coupling form are treated as numerical examples. By the construction of a special nonlinear-coupled term, the chaotic system is coupled symmetrically. For three and four neurons network, a certain region of coupling strength corresponding to full synchronization is given, and the effect of network structure and noise position are analyzed. For five and more neurons network, the full synchronization is very difficult to realize. All the results have been proved by the calculation of the maximum conditional Lyapunov exponent.
International Nuclear Information System (INIS)
Wu, C.W.
2003-01-01
In a recent paper, wavelet analysis is used to perturb the coupling matrix in an array of identical chaotic systems in order to improve its synchronization. When the coupling matrix is symmetric, the synchronization criterion is determined by the second smallest eigenvalue λ 2 of the coupling matrix and the problem is reduced to studying how λ 2 of the coupling matrix changes with perturbation. In the aforementioned paper, a small percentage of the wavelet coefficients are modified. However, this results in a perturbed matrix where every element is modified and nonzero. The purpose of this Letter is to present some results on the change of λ 2 due to perturbation. In particular, we show that as the number of systems n→∞, perturbations which only add local coupling will not change λ 2 . On the other hand, we show that there exists perturbations which modify an arbitrarily small percentage of matrix elements, each of which is changed by an arbitrarily small amount and yet can make λ 2 arbitrarily large. These results give conditions on what the perturbation should be in order to improve the synchronizability in an array of coupled chaotic systems. This analysis allows us to justify and explain some of the synchronization phenomena observed in a recently studied network where random coupling is added to a locally connected array. We propose to classify various classes of coupling matrices such as small world networks and scale free networks according to their synchronizability in the limit. Finally, we briefly discuss the case of time-varying coupling
Directory of Open Access Journals (Sweden)
Jesus Manuel Munoz-Pacheco
2013-01-01
Full Text Available An algorithm to compute the Lyapunov exponents of piecewise linear function-based multidirectional multiscroll chaotic oscillators is reported. Based on the m regions in the piecewise linear functions, the suggested algorithm determines the individual expansion rate of Lyapunov exponents from m-piecewise linear variational equations and their associated m-Jacobian matrices whose entries remain constant during all computation cycles. Additionally, by considering OpAmp-based chaotic oscillators, we study the impact of two analog design procedures on the magnitude of Lyapunov exponents. We focus on analyzing variations of both frequency bandwidth and voltage/current dynamic range of the chaotic signals at electronic system level. As a function of the design parameters, a renormalization factor is proposed to estimate correctly the Lyapunov spectrum. Numerical simulation results in a double-scroll type chaotic oscillator and complex chaotic oscillators generating multidirectional multiscroll chaotic attractors on phase space confirm the usefulness of the reported algorithm.
International Nuclear Information System (INIS)
Sun Jun-Wei; Shen Yi; Zhang Guo-Dong; Wang Yan-Feng; Cui Guang-Zhao
2013-01-01
According to the Lyapunov stability theorem, a new general hybrid projective complete dislocated synchronization scheme with non-derivative and derivative coupling based on parameter identification is proposed under the framework of drive-response systems. Every state variable of the response system equals the summation of the hybrid drive systems in the previous hybrid synchronization. However, every state variable of the drive system equals the summation of the hybrid response systems while evolving with time in our method. Complete synchronization, hybrid dislocated synchronization, projective synchronization, non-derivative and derivative coupling, and parameter identification are included as its special item. The Lorenz chaotic system, Rössler chaotic system, memristor chaotic oscillator system, and hyperchaotic Lü system are discussed to show the effectiveness of the proposed methods. (general)
Bogomolov, Sergey A.; Slepnev, Andrei V.; Strelkova, Galina I.; Schöll, Eckehard; Anishchenko, Vadim S.
2017-02-01
We explore the bifurcation transition from coherence to incoherence in ensembles of nonlocally coupled chaotic systems. It is firstly shown that two types of chimera states, namely, amplitude and phase, can be found in a network of coupled logistic maps, while only amplitude chimera states can be observed in a ring of continuous-time chaotic systems. We reveal a bifurcation mechanism by analyzing the evolution of space-time profiles and the coupling function with varying coupling coefficient and formulate the necessary and sufficient conditions for realizing the chimera states in the ensembles.
Energy Technology Data Exchange (ETDEWEB)
Hramov, Alexander E., E-mail: aeh@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation); Koronovskii, Alexey A., E-mail: alkor@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation); Kurkin, Semen, E-mail: KurkinSA@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation)
2010-07-05
In this Letter the results of theoretical investigations of the chaotic microwave oscillator based on the electron beam with a virtual cathode are presented. Nonlinear non-stationary processes in these electron systems are studied by means of numerical analysis of 2.5D model. It was discovered that the non-uniform external magnetic field value controls the dynamical regime of oscillations in the virtual cathode oscillator. The processes of the chaotization of output microwave radiation are described and interpreted from the point of view of the formation and interaction of electron structures (bunches) in the electron beams. The numerical results have shown that the investigated electron system with virtual cathode could be considered as a promising controlled source of wideband chaotic oscillations in the microwave range.
Chimera states in coupled Kuramoto oscillators with inertia
International Nuclear Information System (INIS)
Olmi, Simona
2015-01-01
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry
Chimera states in coupled Kuramoto oscillators with inertia
Energy Technology Data Exchange (ETDEWEB)
Olmi, Simona, E-mail: simona.olmi@fi.isc.cnr.it [CNR - Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); INFN Sez. Firenze, via Sansone, 1 - I-50019 Sesto Fiorentino (Italy)
2015-12-15
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.
Chimera states in coupled Kuramoto oscillators with inertia.
Olmi, Simona
2015-12-01
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.
Coupled oscillators and Feynman's three papers
International Nuclear Information System (INIS)
Kim, Y S
2007-01-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the 'rest of the universe' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators
Coupled chaotic oscillators and their relation to a central pattern ...
Indian Academy of Sciences (India)
Abstract. Animal locomotion employs different periodic patterns known as animal gaits. In 1993, Collins and Stewart recognized that gaits possessed certain symmetries and characterized the gaits of quadrupeds and bipeds using permutation symmetry groups, which impose constraints on the locomotion center called the ...
Modulation response, mixed-mode oscillations and chaotic spiking in quantum dot light emitting diode
International Nuclear Information System (INIS)
Al Husseini, Hussein B.; Al Naimee, Kais A.; Al Khursan, Amin H.; Abdalah, Sora F.; Khedir, Ali H.; Meucci, Riccardo; Arecchi, F. Tito
2015-01-01
In this work quantum dot light emitting diode (QD-LED) was modeled in a dimensionless rate equations system where it is not done earlier. The model was examined first under bias current without any external perturbation where it exhibits chaotic phenomena since the model has multi-degrees of freedom. Then, it is perturbed by both small signal and direct current modulations (DCM), separately. The system exhibits mixed-mode oscillations (MMOs) under DCM. This behavior was reasoned to continuous states of two dimensional wetting layer (WL) which works as a reservoir to quantum dot (QD) states. QD capture was the dominant rate controlling the dynamic behavior in QD-LED. The nonlinear dynamic behavior of our model is compared very well to the experimental observations in the QD-LED
International Nuclear Information System (INIS)
Lopez-Ruiz, Ricardo; Fournier-Prunaret, Daniele
2005-01-01
A cubic discrete coupled logistic equation is proposed to model the predator-prey problem. The coupling depends on the population size of both species and on a positive constant λ, which could depend on the prey reproduction rate and on the predator hunting strategy. Different dynamical regimes are obtained when λ is modified. For small λ, the species become extinct. For a bigger λ, the preys survive but the predators extinguish. Only when the prey population reaches a critical value then predators can coexist with preys. For increasing λ, a bistable regime appears where the populations apart of being stabilized in fixed quantities can present periodic, quasiperiodic and chaotic oscillations. Finally, bistability is lost and the system settles down in a steady state, or, for the biggest permitted λ, in an invariant curve. We also present the basins for the different regimes. The use of the critical curves lets us determine the influence of the zones with different number of first rank preimages in the bifurcation mechanisms of those basins
Effects of Coupling Distance on Synchronization and Coherence in Chaotic Neural Networks
International Nuclear Information System (INIS)
Wang Maosheng
2009-01-01
Effects of coupling distance on synchronization and coherence of chaotic neurons in complex networks are numerically investigated. We find that it is not beneficial to neurons synchronization if confining the coupling distance of random edges to a limit d max , but help to improve their coherence. Moreover, there is an optimal value of d max at which the coherence is maximum.
Chaos in generically coupled phase oscillator networks with nonpairwise interactions.
Bick, Christian; Ashwin, Peter; Rodrigues, Ana
2016-09-01
The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling-including three and four-way interactions of the oscillator phases-that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
Universality for the parameter-mismatching effect on weak synchronization in coupled chaotic systems
International Nuclear Information System (INIS)
Lim, Woochang; Kim, Sang-Yoon
2004-01-01
To examine the universality for the parameter-mismatching effect on weak chaotic synchronization, we study coupled multidimensional invertible systems such as the coupled Henon maps and coupled pendula. By generalizing the method proposed in coupled one-dimensional (1D) noninvertible maps, we introduce the parameter sensitivity exponent δ to measure the degree of the parameter sensitivity of a weakly stable synchronous chaotic attractor. In terms of the parameter sensitivity exponents, we characterize the effect of the parameter mismatch on the intermittent bursting and the basin riddling occurring in the regime of weak synchronization. It is thus found that the scaling exponent μ for the average characteristic time (i.e., the average interburst time and the average chaotic transient lifetime) for both the bubbling and riddling cases is given by the reciprocal of the parameter sensitivity exponent, as in the simple system of coupled 1D maps. Hence, the reciprocal relation (i.e., μ = 1/δ) seems to be 'universal', in the sense that it holds in typical coupled chaotic systems of different nature
Chaos in generically coupled phase oscillator networks with nonpairwise interactions
Energy Technology Data Exchange (ETDEWEB)
Bick, Christian; Ashwin, Peter; Rodrigues, Ana [Centre for Systems, Dynamics and Control and Department of Mathematics, University of Exeter, Exeter EX4 4QF (United Kingdom)
2016-09-15
The Kuramoto–Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.
Chemical event chain model of coupled genetic oscillators.
Jörg, David J; Morelli, Luis G; Jülicher, Frank
2018-03-01
We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.
Chemical event chain model of coupled genetic oscillators
Jörg, David J.; Morelli, Luis G.; Jülicher, Frank
2018-03-01
We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.
On the New Scenario of Annihilation of the Cross-Well Chaotic Attractor in a Nonlinear Oscillator
International Nuclear Information System (INIS)
Szemplinska, W.; Zubrzycki, A.; Tyrkiel, E.
1999-01-01
The twin-well potential Duffing oscillator is considered and the investigations are focused on a new scenario of destruction of the cross-well chaotic attractor. The new phenomenon belongs to the category of subduction bifurcation and consists in replacement of the cross-well chaotic attractor by a pair of unsymmetric 2T-periodic attractors. It is shown that the new scenario forms a transition zone in the system control parameter plane, the zone, which separates the two known scenarios of annihilation of the cross-well chaotic attractor: the boundary crisis, and the subduction in which the two single-well T-periodic attractors are born in a saddle-node bifurcation. (author)
Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators
Energy Technology Data Exchange (ETDEWEB)
Wolfrum, Matthias; Omel' chenko, Oleh E. [Weierstrass Institute, Mohrenstrasse 39, Berlin 10117 (Germany); Sieber, Jan [College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF (United Kingdom)
2015-05-15
We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.
Behavior of orbits of two coupled oscillators
International Nuclear Information System (INIS)
Greene, J.M.
1984-06-01
There has been very considerable progress in the past few years on the theory of two conservative, coupled, nonlinear oscillators. This is a very general theory, and applies to many equivalent systems. A typical problem of this class has a solution that is so complicated that it is impossible to find an expression for the state of the system that is valid for all time. However, recent results are making it possible to determine the next most useful type of information. This is the asymptotic behavior of individual orbits in the limit of very long times. It is just the information that is desired in many situations. For example, it determines the stability of the motion. The key to our present understanding is renormalization. The present state of the art has been described in Robert MacKay's thesis, for which this is an advertisement
Generalized projective synchronization of chaotic nonlinear gyros coupled with dead-zone input
International Nuclear Information System (INIS)
Hung, M.-L.; Yan, J.-J.; Liao, T.-L.
2008-01-01
This paper addresses the synchronization problem of drive-response chaotic gyros coupled with dead-zone nonlinear input. Using the sliding mode control technique, a novel control law is established which guarantees generalized projective synchronization even when the dead-zone nonlinearity is present. Numerical simulations are presented to verify that the synchronization can be achieved by using the proposed synchronization scheme
International Nuclear Information System (INIS)
Stan, Cristina; Cristescu, C.P.; Agop, M.
2007-01-01
In this work, we present a novel evidence of the importance of the golden mean criticality of a system of oscillators in agreement with El Naschie's E-infinity theory. We focus on chaos inhibition in a system of two coupled modified van der Pol oscillators. Depending on the coupling between the two oscillators, the system shows chaotic behavior for different ranges of the coupling parameter. Chaos suppression, as a transition from irregular behavior to a periodical one, is induced by perturbing the system with a harmonic signal with amplitude considerably lower than the value which causes entrainment. The frequency of the perturbation is related to the main frequencies in the spectrum of the freely running system (without perturbation) by the golden mean. We demonstrate that this effect is also obtained for a perturbation with frequency such that the ratio of half the frequency of the first main component in the freely running chaotic spectrum over the frequency of the perturbation is very close (five digits coincidence) to the golden mean. This result is shown to hold for arbitrary values of the coupling parameter in the various ranges of chaotic dynamics of the free running system
Wave fronts and spatiotemporal chaos in an array of coupled Lorenz oscillators
International Nuclear Information System (INIS)
Pazo, Diego; Montejo, Noelia; Perez-Munuzuri, Vicente
2001-01-01
The effects of coupling strength and single-cell dynamics (SCD) on spatiotemporal pattern formation are studied in an array of Lorenz oscillators. Different spatiotemporal structures (stationary patterns, propagating wave fronts, short wavelength bifurcation) arise for bistable SCD, and two well differentiated types of spatiotemporal chaos for chaotic SCD (in correspondence with the transition from stationary patterns to propagating fronts). Wave-front propagation in the bistable regime is studied in terms of global bifurcation theory, while a short wavelength pattern region emerges through a pitchfork bifurcation
Dynamics of nonlinear oscillators with time-varying conjugate coupling
Indian Academy of Sciences (India)
oscillators. We analyze the behavior of coupled systems with respect to the coupling switching frequency using ..... are of potential utility in appropriate design strategies and/or understanding of complex systems with dynamic interaction ...
Phase patterns of coupled oscillators with application to wireless communication
Energy Technology Data Exchange (ETDEWEB)
Arenas, A.
2008-01-02
Here we study the plausibility of a phase oscillators dynamical model for TDMA in wireless communication networks. We show that emerging patterns of phase locking states between oscillators can eventually oscillate in a round-robin schedule, in a similar way to models of pulse coupled oscillators designed to this end. The results open the door for new communication protocols in a continuous interacting networks of wireless communication devices.
Directory of Open Access Journals (Sweden)
Esteban Tlelo-Cuautle
Full Text Available Nowadays, chaos generators are an attractive field for research and the challenge is their realization for the development of engineering applications. From more than three decades ago, chaotic oscillators have been designed using discrete electronic devices, very few with integrated circuit technology, and in this work we propose the use of field-programmable gate arrays (FPGAs for fast prototyping. FPGA-based applications require that one be expert on programming with very-high-speed integrated circuits hardware description language (VHDL. In this manner, we detail the VHDL descriptions of chaos generators for fast prototyping from high-level programming using Python. The cases of study are three kinds of chaos generators based on piecewise-linear (PWL functions that can be systematically augmented to generate even and odd number of scrolls. We introduce new algorithms for the VHDL description of PWL functions like saturated functions series, negative slopes and sawtooth. The generated VHDL-code is portable, reusable and open source to be synthesized in an FPGA. Finally, we show experimental results for observing 2, 10 and 30-scroll attractors.
Tlelo-Cuautle, Esteban; Quintas-Valles, Antonio de Jesus; de la Fraga, Luis Gerardo; Rangel-Magdaleno, Jose de Jesus
2016-01-01
Nowadays, chaos generators are an attractive field for research and the challenge is their realization for the development of engineering applications. From more than three decades ago, chaotic oscillators have been designed using discrete electronic devices, very few with integrated circuit technology, and in this work we propose the use of field-programmable gate arrays (FPGAs) for fast prototyping. FPGA-based applications require that one be expert on programming with very-high-speed integrated circuits hardware description language (VHDL). In this manner, we detail the VHDL descriptions of chaos generators for fast prototyping from high-level programming using Python. The cases of study are three kinds of chaos generators based on piecewise-linear (PWL) functions that can be systematically augmented to generate even and odd number of scrolls. We introduce new algorithms for the VHDL description of PWL functions like saturated functions series, negative slopes and sawtooth. The generated VHDL-code is portable, reusable and open source to be synthesized in an FPGA. Finally, we show experimental results for observing 2, 10 and 30-scroll attractors.
Surprises of the Transformer as a Coupled Oscillator System
Silva, J. P.; Silvestre, A. J.
2008-01-01
We study a system of two RLC oscillators coupled through a variable mutual inductance. The system is interesting because it exhibits some peculiar features of coupled oscillators: (i) there are two natural frequencies; (ii) in general, the resonant frequencies do not coincide with the natural frequencies; (iii) the resonant frequencies of both…
Surprises of the transformer as a coupled oscillator system
International Nuclear Information System (INIS)
Silva, J P; Silvestre, A J
2008-01-01
We study a system of two RLC oscillators coupled through a variable mutual inductance. The system is interesting because it exhibits some peculiar features of coupled oscillators: (i) there are two natural frequencies; (ii) in general, the resonant frequencies do not coincide with the natural frequencies; (iii) the resonant frequencies of both oscillators differ; (iv) for certain choices of parameters, there is only one resonant frequency, instead of the two expected
Surprises of the transformer as a coupled oscillator system
Energy Technology Data Exchange (ETDEWEB)
Silva, J P; Silvestre, A J [Instituto Superior de Engenharia de Lisboa, Rua Conselheiro EmIdio Navarro, 1950-062 Lisboa (Portugal)], E-mail: jpsilva@deea.isel.ipl.pt, E-mail: asilvestre@deq.isel.ipl.pt
2008-05-15
We study a system of two RLC oscillators coupled through a variable mutual inductance. The system is interesting because it exhibits some peculiar features of coupled oscillators: (i) there are two natural frequencies; (ii) in general, the resonant frequencies do not coincide with the natural frequencies; (iii) the resonant frequencies of both oscillators differ; (iv) for certain choices of parameters, there is only one resonant frequency, instead of the two expected.
Synchronization and chaotic dynamics of coupled mechanical metronomes
Ulrichs, Henning; Mann, Andreas; Parlitz, Ulrich
2009-12-01
Synchronization scenarios of coupled mechanical metronomes are studied by means of numerical simulations showing the onset of synchronization for two, three, and 100 globally coupled metronomes in terms of Arnol'd tongues in parameter space and a Kuramoto transition as a function of coupling strength. Furthermore, we study the dynamics of metronomes where overturning is possible. In this case hyperchaotic dynamics associated with some diffusion process in configuration space is observed, indicating the potential complexity of metronome dynamics.
Chimera states in nonlocally coupled phase oscillators with biharmonic interaction
Cheng, Hongyan; Dai, Qionglin; Wu, Nianping; Feng, Yuee; Li, Haihong; Yang, Junzhong
2018-03-01
Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between oscillators, for example, sinusoidal coupling or diffusive coupling. Here, we investigate chimera dynamics in nonlocally coupled phase oscillators with biharmonic interaction. We find novel chimera states with features such as that oscillators in the same coherent cluster may split into two groups with a phase difference around π/2 and that oscillators in adjacent coherent clusters may have a phase difference close to π/2. The different impacts of the coupling ranges in the first and the second harmonic interactions on chimera dynamics are investigated based on the synchronous dynamics in globally coupled phase oscillators. Our study suggests a new direction in the field of chimera dynamics.
Coupled chaotic attractors and driving-induced bistability: A brief ...
Indian Academy of Sciences (India)
2015-02-04
Feb 4, 2015 ... In the 'drive–response' scenario, a system is unidirectionally coupled to another sys- tem. Here, the ... where R1 and R2 are the dynamical variables of the drive and response systems, respec- tively. F and G ..... [3] K Kaneko, Theory and applications of coupled map lattices (John Wiley and Sons, NY, 1993).
International Nuclear Information System (INIS)
Sanid, C; Murugesh, S
2014-01-01
We propose a system of two coupled spin-torque nano-oscillators (STNOs), one driver and another response, and demonstrate using numerical studies the synchronization of the response system to the frequency of the driver system. To this end we use a high-speed operational amplifier in the form of a voltage follower, which essentially isolates the drive system from the response system. We find the occurrence of 1 : 1 as well as 2 : 1 synchronization in the system, wherein the oscillators show limit cycle dynamics. An increase in power output is noticed when the two oscillators are locked in 1 : 1 synchronization. Moreover in the crossover region between these two synchronization dynamics we show the existence of chaotic dynamics in the slave system. The coupled dynamics under periodic forcing, using a small ac input current in addition to that of the dc part, is also studied. The slave oscillator is seen to retain its qualitative identity in the parameter space in spite of being fed in, at times, a chaotic signal. Such electrically coupled STNOs will be highly useful in fabricating commercial spin-valve oscillators with high power output, when integrated with other spintronic devices. (paper)
Coupled harmonic oscillators and their quantum entanglement
Makarov, Dmitry N.
2018-04-01
A system of two coupled quantum harmonic oscillators with the Hamiltonian H ̂=1/2 (1/m1p̂1 2+1/m2p̂2 2+A x12+B x22+C x1x2) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H ̂Ψ =i ℏ ∂/Ψ ∂ t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.
Behavior of orbits of two coupled oscillators
International Nuclear Information System (INIS)
Greene, J.M.
1985-01-01
There has been very considerable progress in the past few years on the theory of two conservative, coupled, nonlinear oscillators. This work also applies to many equivalent systems, so it has applications to particle containment and heating, for example, and wherever else in plasma physics that the validity of adiabatic invariants is a matter of concern. A general problem of this class has a solution that is so complicated that it is impossible to find an expression for the state of the system that is valid for all time. However, recent results are making it possible to determine the next most useful type of information. This is the asymptotic behavior of individual orbits in the limit of very long times. This is just the information that is desired in many situations. For example, it determines the stability of the motion. The key to our present understanding is renormalization. The present state of the art has been described in Robert Mackay's thesis, for which this is an advertisement
Basin stability measure of different steady states in coupled oscillators
Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-04-01
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.
Photon–phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator
International Nuclear Information System (INIS)
Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping
2017-01-01
A direct photon–phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field. (paper)
Directory of Open Access Journals (Sweden)
Muhammad Iqbal
2014-01-01
Full Text Available This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN neurons with unknown parameters under external electrical stimulation (EES. The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.
Iqbal, Muhammad; Rehan, Muhammad; Khaliq, Abdul; Saeed-ur-Rehman; Hong, Keum-Shik
2014-01-01
This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.
Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure
International Nuclear Information System (INIS)
Jiang Hai-Bo; Zhang Li-Ping; Yu Jian-Jiang
2015-01-01
Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics. This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure. By constructing a proper Poincaré map of the non-smooth system, an analytical expression of the Jacobian matrix of Poincaré map is given. Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge–Kutta method. When the period is fixed and the coupling strength changes, the system undergoes stable, periodic, quasi-periodic, and hyper-chaotic solutions, etc. Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations. (paper)
Restoration of oscillation in network of oscillators in presence of direct and indirect interactions
Energy Technology Data Exchange (ETDEWEB)
Majhi, Soumen; Bera, Bidesh K. [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108 (India); Bhowmick, Sourav K. [Department of Electronics, Asutosh College, Kolkata-700026 (India); Ghosh, Dibakar, E-mail: diba.ghosh@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108 (India)
2016-10-23
The suppression of oscillations in coupled systems may lead to several unwanted situations, which requires a suitable treatment to overcome the suppression. In this paper, we show that the environmental coupling in the presence of direct interaction, which can suppress oscillation even in a network of identical oscillators, can be modified by introducing a feedback factor in the coupling scheme in order to restore the oscillation. We inspect how the introduction of the feedback factor helps to resurrect oscillation from various kinds of death states. We numerically verify the resurrection of oscillations for two paradigmatic limit cycle systems, namely Landau–Stuart and Van der Pol oscillators and also in generic chaotic Lorenz oscillator. We also study the effect of parameter mismatch in the process of restoring oscillation for coupled oscillators. - Highlights: • Amplitude death is observed using direct and indirect coupling. • Revival of oscillation using feedback parameter is discussed. • Restoration of oscillation is observed in limit cycle and chaotic systems.
Phase Multistability in Coupled Oscillator Systems
DEFF Research Database (Denmark)
Mosekilde, Erik; Postnov, D.E.; Sosnovtseva, Olga
2003-01-01
along the orbit of the individual oscillator. Focusing on the mechanisms underlying the appearance of phase multistability, the paper examines a variety of phase-locked patterns. In particular we demonstrate the nested structure of synchronization regions for oscillations with multicrest wave forms...
Dynamics of delayed-coupled chaotic logistic maps: Influence
Indian Academy of Sciences (India)
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume that the elements of the network are identical ( logistic maps in the regime where ...
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
The existence of generalized synchronisation of three bidirectionally coupled chaotic systems
International Nuclear Information System (INIS)
Ai-Hua, Hu; Zhen-Yuan, Xu; Liu-Xiao, Guo
2010-01-01
The existence of two types of generalized synchronisation is studied. The model considered here includes three bidirectionally coupled chaotic systems, and two of them denote the driving systems, while the rest stands for the response system. Under certain conditions, the existence of generalised synchronisation can be turned to a problem of compression fixed point in the family of Lipschitz functions. In addition, theoretical proofs are proposed to the exponential attractive property of generalised synchronisation manifold. Numerical simulations validate the theory. (general)
Weakly Coupled Oscillators in a Slowly Varying World
Park, Youngmin; Ermentrout, Bard
2016-01-01
We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through ...
Detecting phase synchronization between coupled non-phase-coherent oscillators
International Nuclear Information System (INIS)
Follmann, Rosangela; Macau, Elbert E.N.; Rosa, Epaminondas
2009-01-01
We compare two methods for detecting phase synchronization in coupled non-phase-coherent oscillators. One method is based on the locking of self-sustained oscillators with an irregular signal. The other uses trajectory recurrences in phase space. We identify the pros and cons of both methods and propose guidelines to detect phase synchronization in data series.
Emergent organization of oscillator clusters in coupled self ...
Indian Academy of Sciences (India)
Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a ...
Ku, Wai Lim; Girvan, Michelle; Ott, Edward
2015-12-01
In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.
Observational consequences of chaotic inflation with nonmimimal coupling to gravity
International Nuclear Information System (INIS)
Linde, Andrei; Noorbala, Mahdiyar
2011-02-01
Recently there was an extensive discussion of Higgs inflation in the theory with the potential (λ)/(4)(φ 2 -υ 2 ) 2 and nonminimal coupling to gravity (ξ)/(2)φ 2 R, for ξ>>1 and υ 2 )/(2)φ 2 and (λ)/(4)(φ 2 -υ 2 ) 2 with arbitrary values of ξ and υ and describe implementation of these models in supergravity. We analyze observational consequences of these models and find a surprising coincidence of the inflationary predictions of the model (λ)/(4)(φ 2 -υ 2 ) 2 with ξ 2 →1 with the predictions of the Higgs inflation scenario for ξ>>1. (orig.)
Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Senthilkumar, D. V., E-mail: skumarusnld@gmail.com [School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016 (India); Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401 (India); Suresh, K. [Department of Physics, Anjalai Ammal-Engineering College, Kovilvenni 614 403, Tamilnadu (India); Centre for Nonlinear Dynamics, Bharathidasan University, Trichy 620024, Tamilnadu (India); Chandrasekar, V. K. [Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401 (India); Zou, Wei [School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 (China); Centre for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074 (China); Dana, Syamal K. [CSIR-Indian Institute of Chemical Biology, Kolkata 700032 (India); Kathamuthu, Thamilmaran [Centre for Nonlinear Dynamics, Bharathidasan University, Trichy 620024, Tamilnadu (India); Kurths, Jürgen [Potsdam Institute for Climate Impact Research, Telegrafenberg, Potsdam D-14415 (Germany); Institute of Physics, Humboldt University Berlin, Berlin D-12489 (Germany); Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX (United Kingdom); Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod (Russian Federation)
2016-04-15
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.
Quantifying the dynamics of coupled networks of switches and oscillators.
Directory of Open Access Journals (Sweden)
Matthew R Francis
Full Text Available Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's evolution. We, therefore, introduce a new modeling framework that describes the dynamics of networks composed of both oscillators and switches. Both oscillator synchronization and switch stability are preserved in these heterogeneous, coupled networks. Furthermore, this model recapitulates the qualitative dynamics for the yeast cell cycle consistent with the hypothesized dynamics resulting from decomposition of the regulatory network into dynamic motifs. Introducing feedback into the cell-cycle network induces qualitative dynamics analogous to limitless replicative potential that is a hallmark of cancer. As a result, the proposed model of switch and oscillator coupling provides the ability to incorporate mechanisms that underlie the synchronized stimulus response ubiquitous in biochemical systems.
Monlinear fish-scale metamaterial via coupled duffing oscillators
Kochetov, Bogdan; Tuz, Vladimir; Mladyonov, Pavel; Prosvirnin, Sergey; Kochetova, Lyudmila
2012-01-01
The dynamic system of two coupled Duffing oscillators is considered in order to predict the optical response of the nonlinear planar fish-scale metamaterial. The direct numerical calculation of meta material response confirms the correctness of the proposed model
A quantitative analysis of coupled oscillations using mobile accelerometer sensors
International Nuclear Information System (INIS)
Castro-Palacio, Juan Carlos; Velázquez-Abad, Luisberis; Giménez, Fernando; Monsoriu, Juan A
2013-01-01
In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses. (paper)
A quantitative analysis of coupled oscillations using mobile accelerometer sensors
Castro-Palacio, Juan Carlos; Velázquez-Abad, Luisberis; Giménez, Fernando; Monsoriu, Juan A.
2013-05-01
In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses.
Modelling chaotic Hamiltonian systems as a Markov Chain ...
African Journals Online (AJOL)
The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...
Observational consequences of chaotic inflation with nonmimimal coupling to gravity
Energy Technology Data Exchange (ETDEWEB)
Linde, Andrei; Noorbala, Mahdiyar [Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics and Dept. of Physics; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2011-02-15
Recently there was an extensive discussion of Higgs inflation in the theory with the potential ({lambda})/(4)({phi}{sup 2}-{upsilon}{sup 2}){sup 2} and nonminimal coupling to gravity ({xi})/(2){phi}{sup 2}R, for {xi}>>1 and {upsilon} <<1. We extend this investigation to the theories (m{sup 2})/(2){phi}{sup 2} and ({lambda})/(4)({phi}{sup 2}-{upsilon}{sup 2}){sup 2} with arbitrary values of {xi} and {upsilon} and describe implementation of these models in supergravity. We analyze observational consequences of these models and find a surprising coincidence of the inflationary predictions of the model ({lambda})/(4)({phi}{sup 2}-{upsilon}{sup 2}){sup 2} with {xi} < 0 in the limit vertical stroke {xi} vertical stroke {upsilon}{sup 2}{yields}1 with the predictions of the Higgs inflation scenario for {xi}>>1. (orig.)
Analytically solvable chaotic oscillator based on a first-order filter
Energy Technology Data Exchange (ETDEWEB)
Corron, Ned J.; Cooper, Roy M.; Blakely, Jonathan N. [Charles M. Bowden Laboratory, Aviation and Missile Research, Development and Engineering Center, U.S. Army RDECOM, Redstone Arsenal, Alabama 35898 (United States)
2016-02-15
A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.
The vertical oscillations of coupled magnets
International Nuclear Information System (INIS)
Li Kewei; Lin Jiahuang; Kang Zi Yang; Liang, Samuel Yee Wei; Juan, Jeremias Wong Say
2011-01-01
The International Young Physicists' Tournament (IYPT) is a worldwide, annual competition for high school students. This paper is adapted from the winning solution to Problem 14, Magnetic Spring, as presented in the final round of the 23rd IYPT in Vienna, Austria. Two magnets were arranged on top of each other on a common axis. One was fixed, while the other could move vertically. Various parameters of interest were investigated, including the effective gravitational acceleration, the strength, size, mass and geometry of the magnets, and damping of the oscillations. Despite its simplicity, this setup yielded a number of interesting and unexpected relations. The first stage of the investigation was concerned only with the undamped oscillations of small amplitudes, and the period of small amplitude oscillations was found to be dependent only on the eighth root of important magnet properties such as its strength and mass. The second stage sought to investigate more general oscillations. A numerical model which took into account magnet size, magnet geometry and damping effects was developed to model the general oscillations. Air resistance and friction were found to be significant sources of damping, while eddy currents were negligible.
Suppression and revival of oscillation in indirectly coupled limit cycle oscillators
International Nuclear Information System (INIS)
Sharma, P.R.; Kamal, N.K.; Verma, U.K.; Suresh, K.; Thamilmaran, K.; Shrimali, M.D.
2016-01-01
Highlights: • The phenomena of suppression and revival of oscillations are studied in indirectly coupled nonlinear oscillators. • The decay parameter and a feedback factor play a crucial role in emergent dynamical behavior of oscillators. • The critical curves for different dynamical regions are obtained analytically using linear stability analysis. • Electronic circuit experiments demonstrate these emergent dynamical states. - Abstract: We study the phenomena of suppression and revival of oscillations in a system of limit cycle oscillators coupled indirectly via a dynamic local environment. The dynamics of the environment is assumed to decay exponentially with time. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). We also show that introducing a feedback factor in the diffusion term revives the oscillations in this system. The critical curves for the regions of different emergent states as a function of coupling strength, decay parameter of the environment and feedback factor in the coupling are obtained analytically using linear stability analysis. These results are found to be consistent with the numerics and are also observed experimentally.
Kanter, Ido; Butkovski, Maria; Peleg, Yitzhak; Zigzag, Meital; Aviad, Yaara; Reidler, Igor; Rosenbluh, Michael; Kinzel, Wolfgang
2010-08-16
Random bit generators (RBGs) constitute an important tool in cryptography, stochastic simulations and secure communications. The later in particular has some difficult requirements: high generation rate of unpredictable bit strings and secure key-exchange protocols over public channels. Deterministic algorithms generate pseudo-random number sequences at high rates, however, their unpredictability is limited by the very nature of their deterministic origin. Recently, physical RBGs based on chaotic semiconductor lasers were shown to exceed Gbit/s rates. Whether secure synchronization of two high rate physical RBGs is possible remains an open question. Here we propose a method, whereby two fast RBGs based on mutually coupled chaotic lasers, are synchronized. Using information theoretic analysis we demonstrate security against a powerful computational eavesdropper, capable of noiseless amplification, where all parameters are publicly known. The method is also extended to secure synchronization of a small network of three RBGs.
Seizure Dynamics of Coupled Oscillators with Epileptor Field Model
Zhang, Honghui; Xiao, Pengcheng
The focus of this paper is to investigate the dynamics of seizure activities by using the Epileptor coupled model. Based on the coexistence of seizure-like event (SLE), refractory status epilepticus (RSE), depolarization block (DB), and normal state, we first study the dynamical behaviors of two coupled oscillators in different activity states with Epileptor model by linking them with slow permittivity coupling. Our research has found that when one oscillator in normal states is coupled with any oscillator in SLE, RSE or DB states, these two oscillators can both evolve into SLE states under appropriate coupling strength. And then these two SLE oscillators can perform epileptiform synchronization or epileptiform anti-synchronization. Meanwhile, SLE can be depressed when considering the fast electrical or chemical coupling in Epileptor model. Additionally, a two-dimensional reduced model is also given to show the effect of coupling number on seizures. Those results can help to understand the dynamical mechanism of the initiation, maintenance, propagation and termination of seizures in focal epilepsy.
Synchronization of three electrochemical oscillators: From local to global coupling
Liu, Yifan; Sebek, Michael; Mori, Fumito; Kiss, István Z.
2018-04-01
We investigate the formation of synchronization patterns in an oscillatory nickel electrodissolution system in a network obtained by superimposing local and global coupling with three electrodes. We explored the behavior through numerical simulations using kinetic ordinary differential equations, Kuramoto type phase models, and experiments, in which the local to global coupling could be tuned by cross resistances between the three nickel wires. At intermediate coupling strength with predominant global coupling, two of the three oscillators, whose natural frequencies are closer, can synchronize. By adding even a relatively small amount of local coupling (about 9%-25%), a spatially organized partially synchronized state can occur where one of the two synchronized elements is in the center. A formula was derived for predicting the critical coupling strength at which full synchronization will occur independent of the permutation of the natural frequencies of the oscillators over the network. The formula correctly predicts the variation of the critical coupling strength as a function of the global coupling fraction, e.g., with local coupling the critical coupling strength is about twice than that required with global coupling. The results show the importance of the topology of the network on the synchronization properties in a simple three-oscillator setup and could provide guidelines for decrypting coupling topology from identification of synchronization patterns.
PT -symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
We provide a systematic analysis of a prototypical nonlinear oscillator ... recently, a number of nonlinear variants have been explored, like split-ring resonator chain .... Note that these solutions are valid for any value of ǫ (and hence δ) including ǫ ..... [16] M Abramowitz and I A Stegun, Handbook of mathematical functions ...
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing
2010-12-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing; Arcak, Murat; Salama, Khaled N.
2010-01-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
International Nuclear Information System (INIS)
Al-Khawaja, S.
2011-01-01
In this paper, synchronising two coupled ratchet Josephson junctions subjected to a quasiperiodic field is achieved. In the limit of weak perturbation of irrational frequencies equal to the square root of the transcendental number π and for small damping parameters, phase locking occurs as the coupling between both junctions is increased. It turns out that the transition from non-synchronous to synchronous chaotic state does not involve attractors appearing and disappearing. The undertaken symmetry analysis of the system demonstrates the suppression of the massive phase fluctuations as the coupling rises, allowing chaos synchronisation between both junctions to take place. The calculations also reveal the persistence of the synchronous state for high coupling strengths, taking into consideration the symmetry particularity of the external drive and potential. (author)
International Nuclear Information System (INIS)
Sameer Al-Khawaja
2010-01-01
In this paper, synchronising two coupled ratchet Josephson junctions subjected to a quasiperiodic field is achieved. In the limit of weak perturbation of irrational frequencies equal to the square root of the transcendental number π and for small damping parameters, phase locking occurs as the coupling between both junctions is increased. It turns out that the transition from non-synchronous to synchronous chaotic state does not involve attractors appearing and disappearing. The undertaken symmetry analysis of the system demonstrates the suppression of the massive phase fluctuations as the coupling rises, allowing chaos synchronisation between both junctions to take place. The calculations also reveal the persistence of the synchronous state for high coupling strengths, taking into consideration the symmetry particularity of the external drive and potential. (author)
Hong, Hyunsuk; Strogatz, Steven H
2011-02-04
We consider a generalization of the Kuramoto model in which the oscillators are coupled to the mean field with random signs. Oscillators with positive coupling are "conformists"; they are attracted to the mean field and tend to synchronize with it. Oscillators with negative coupling are "contrarians"; they are repelled by the mean field and prefer a phase diametrically opposed to it. The model is simple and exactly solvable, yet some of its behavior is surprising. Along with the stationary states one might have expected (a desynchronized state, and a partially-synchronized state, with conformists and contrarians locked in antiphase), it also displays a traveling wave, in which the mean field oscillates at a frequency different from the population's mean natural frequency.
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
Energy Technology Data Exchange (ETDEWEB)
Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br [Associate Laboratory for Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE (Brazil); Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de [Department of Physics and Astronomy, University of Potsdam, Germany and Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2015-04-15
We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.
Coupled slow and fast surface dynamics in an electrocatalytic oscillator: Model and simulations
International Nuclear Information System (INIS)
Nascimento, Melke A.; Nagao, Raphael; Eiswirth, Markus; Varela, Hamilton
2014-01-01
The co-existence of disparate time scales is pervasive in many systems. In particular for surface reactions, it has been shown that the long-term evolution of the core oscillator is decisively influenced by slow surface changes, such as progressing deactivation. Here we present an in-depth numerical investigation of the coupled slow and fast surface dynamics in an electrocatalytic oscillator. The model consists of four nonlinear coupled ordinary differential equations, investigated over a wide parameter range. Besides the conventional bifurcation analysis, the system was studied by means of high-resolution period and Lyapunov diagrams. It was observed that the bifurcation diagram changes considerably as the irreversible surface poisoning evolves, and the oscillatory region shrinks. The qualitative dynamics changes accordingly and the chaotic oscillations are dramatically suppressed. Nevertheless, periodic cascades are preserved in a confined region of the resistance vs. voltage diagram. Numerical results are compared to experiments published earlier and the latter reinterpreted. Finally, the comprehensive description of the time-evolution in the period and Lyapunov diagrams suggests further experimental studies correlating the evolution of the system's dynamics with changes of the catalyst structure
Synchronization of diffusively coupled oscillators near the homoclinic bifurcation
International Nuclear Information System (INIS)
Postnov, D.; Han, Seung Kee; Kook, Hyungtae
1998-09-01
It has been known that a diffusive coupling between two limit cycle oscillations typically leads to the inphase synchronization and also that it is the only stable state in the weak coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which often occurs especially for the neuronal oscillators. In this paper we propose a simple physical model using the modified van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe changes in the synchronization behaviors between the distinctive regimes as well. The dephasing mechanism is analyzed both qualitatively and quantitatively in the weak coupling limit. A general form of coupling is introduced and the synchronization behaviors over a wide range of the coupling parameters are explored to construct the phase diagram using the bifurcation analysis. (author)
Dynamics of multi-frequency oscillator ensembles with resonant coupling
Lück, S.; Pikovsky, A.
2011-07-01
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two interacting subpopulations are in relation 2:1. Depending on the parameter of coupling, ensembles can demonstrate fully synchronous clusters, partial synchrony (only one subpopulation synchronizes), or asynchrony in both subpopulations. Theoretical description of the dynamics based on the Watanabe-Strogatz approach is developed.
Coupled oscillators as models of phantom and scalar field cosmologies
International Nuclear Information System (INIS)
Faraoni, Valerio
2004-01-01
We study a toy model for phantom cosmology recently introduced in the literature and consisting of two oscillators, one of which carries negative kinetic energy. The results are compared with the exact phase space picture obtained for similar dynamical systems describing, respectively, a massive canonical scalar field conformally coupled to the spacetime curvature and a conformally coupled massive phantom. Finally, the dynamical system describing exactly a minimally coupled phantom is studied and compared with the toy model
Novel four-wing and eight-wing attractors using coupled chaotic Lorenz systems
International Nuclear Information System (INIS)
Grassi, Giuseppe
2008-01-01
This paper presents the problem of generating four-wing (eight-wing) chaotic attractors. The adopted method consists in suitably coupling two (three) identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings (eight wings) of these novel attractors are located around the four (eight) equilibria with two (three) pairs of unstable complex-conjugate eigenvalues. (general)
Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators.
O'Keeffe, Kevin P; Krapivsky, P L; Strogatz, Steven H
2015-08-07
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators progressively coalesce into larger ones. Using tools from the study of aggregation phenomena, we obtain exact results for the time-dependent distribution of cluster sizes as the system evolves from disorder to synchrony.
Solvable model for chimera states of coupled oscillators.
Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A
2008-08-22
Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.
Oscillations in magnetoresistance and interlayer coupling in magnetic sandwich structures
International Nuclear Information System (INIS)
Barnas, J.; Bulka, B.
1997-01-01
Kubo formalism is used to calculate the magnetoresistance due to magnetization rotation in a structure consisting two magnetic films separated by nonmagnetic layer. In the approximation of an uniform relaxation time of each layer, the oscillatory term in magnetoresistance corresponds to the oscillation period which depends on the potential barriers at the interfaces. This period is longer than the oscillation period observed in the coupling parameter. (author)
Synchronization properties of coupled chaotic neurons: The role of random shared input
Energy Technology Data Exchange (ETDEWEB)
Kumar, Rupesh [School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067 (India); Bilal, Shakir [Department of Physics and Astrophysics, University of Delhi, Delhi 110 007 (India); Ramaswamy, Ram [School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067 (India); School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India)
2016-06-15
Spike-time correlations of neighbouring neurons depend on their intrinsic firing properties as well as on the inputs they share. Studies have shown that periodically firing neurons, when subjected to random shared input, exhibit asynchronicity. Here, we study the effect of random shared input on the synchronization of weakly coupled chaotic neurons. The cases of so-called electrical and chemical coupling are both considered, and we observe a wide range of synchronization behaviour. When subjected to identical shared random input, there is a decrease in the threshold coupling strength needed for chaotic neurons to synchronize in-phase. The system also supports lag–synchronous states, and for these, we find that shared input can cause desynchronization. We carry out a master stability function analysis for a network of such neurons and show agreement with the numerical simulations. The contrasting role of shared random input for complete and lag synchronized neurons is useful in understanding spike-time correlations observed in many areas of the brain.
Synchronization properties of coupled chaotic neurons: The role of random shared input
International Nuclear Information System (INIS)
Kumar, Rupesh; Bilal, Shakir; Ramaswamy, Ram
2016-01-01
Spike-time correlations of neighbouring neurons depend on their intrinsic firing properties as well as on the inputs they share. Studies have shown that periodically firing neurons, when subjected to random shared input, exhibit asynchronicity. Here, we study the effect of random shared input on the synchronization of weakly coupled chaotic neurons. The cases of so-called electrical and chemical coupling are both considered, and we observe a wide range of synchronization behaviour. When subjected to identical shared random input, there is a decrease in the threshold coupling strength needed for chaotic neurons to synchronize in-phase. The system also supports lag–synchronous states, and for these, we find that shared input can cause desynchronization. We carry out a master stability function analysis for a network of such neurons and show agreement with the numerical simulations. The contrasting role of shared random input for complete and lag synchronized neurons is useful in understanding spike-time correlations observed in many areas of the brain.
Synchronization of indirectly coupled Lorenz oscillators: An ...
Indian Academy of Sciences (India)
[7], the magnetoencephalographic activity of Parkinsonian patients [8], electrosensitive cells of paddlefish [9] ... with coherent electromagnetic field [16]. ... can also be explained with a model of two excitatory synaptically coupled neurons in the.
Limit cycle analysis of nuclear coupled density wave oscillations
International Nuclear Information System (INIS)
Ward, M.E.
1985-01-01
An investigation of limit cycle behavior for the nuclear-coupled density wave oscillation (NCDWO) in a boiling water reactor (BWR) was performed. A simplified nonlinear model of BWR core behavior was developed using a two-region flow channel representation, coupled with a form of the point-kinetics equation. This model has been used to investigate the behavior of large amplitude NCDWO's through conventional time-integration solutions and through application of a direct relaxation-oscillation limit cycle solution in phase space. The numerical solutions demonstrate the potential for severe global power and flow oscillations in a BWR core at off-normal conditions, such as might occur during Anticipated Transients without Scram. Because of the many simplifying assumptions used, it is felt that the results should not be interpreted as an absolute prediction of core behavior, but as an indication of the potential for large oscillations and a demonstration of the corresponding limit cycle mechanisms. The oscillations in channel density drive the core power variations, and are reinforced by heat flux variations due to the changing fuel temperature. A global temperature increase occurs as energy is accumulated in the fuel, and limits the magnitude of the oscillations because as the average channel density decreases, the amplitude and duration of positive void reactivity at a given oscillation amplitude is lessened
Control of coupled oscillator networks with application to microgrid technologies.
Skardal, Per Sebastian; Arenas, Alex
2015-08-01
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.
Control of coupled oscillator networks with application to microgrid technologies
Arenas, Alex
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable syn- chronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.
Damped driven coupled oscillators: entanglement, decoherence and the classical limit
Energy Technology Data Exchange (ETDEWEB)
Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M [Grupo de Optica e Informacion Cuantica, Departamento de Fisica, Universidad Nacional de Colombia, Bogota (Colombia)], E-mail: rdguerrerom@unal.edu.co, E-mail: rrreyg@unal.edu.co, E-mail: kmfonsecar@unal.edu.co
2009-03-13
We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.
Damped driven coupled oscillators: entanglement, decoherence and the classical limit
International Nuclear Information System (INIS)
Mancilla, R D Guerrero; Rey-Gonzalez, R R; Fonseca-Romero, K M
2009-01-01
We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, comprising a first subsystem (a harmonic oscillator) coupled to a driven and damped second subsystem (another harmonic oscillator). We choose initial states whose dynamics is confined to a couple of two-level systems, and show that the maximum value of entanglement between the two subsystems, as measured by concurrence, depends on the dissipation rate to the coupling-constant ratio and the initial state. While in a related model the entropy of the first subsystem (a two-level system) never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model
Resumption of dynamism in damaged networks of coupled oscillators
Kundu, Srilena; Majhi, Soumen; Ghosh, Dibakar
2018-05-01
Deterioration in dynamical activities may come up naturally or due to environmental influences in a massive portion of biological and physical systems. Such dynamical degradation may have outright effect on the substantive network performance. This requires us to provide some proper prescriptions to overcome undesired circumstances. In this paper, we present a scheme based on external feedback that can efficiently revive dynamism in damaged networks of active and inactive oscillators and thus enhance the network survivability. Both numerical and analytical investigations are performed in order to verify our claim. We also provide a comparative study on the effectiveness of this mechanism for feedbacks to the inactive group or to the active group only. Most importantly, resurrection of dynamical activity is realized even in time-delayed damaged networks, which are considered to be less persistent against deterioration in the form of inactivity in the oscillators. Furthermore, prominence in our approach is substantiated by providing evidence of enhanced network persistence in complex network topologies taking small-world and scale-free architectures, which makes the proposed remedy quite general. Besides the study in the network of Stuart-Landau oscillators, affirmative influence of external feedback has been justified in the network of chaotic Rössler systems as well.
The dynamics of two linearly coupled Goodwin oscillators
Antonova, A. O.; Reznik, S. N.; Todorov, M. D.
2017-10-01
In this paper the Puu model of the interaction of Goodwin's business cycles for two regions is reconsidered. We investigated the effect of the accelerator coefficients and the Hicksian 'ceiling' and 'floor' parameters on the time dynamics of incomes for different values of marginal propensity to import. The cases when the periods of isolated Goodwin's cycles are close, and when they differ approximately twice are considered. By perturbation theory we obtained the formulas for slowly varying amplitudes and phase difference of weakly nonlinear coupled Goodwin oscillations. The coupled oscillations of two Goodwin's cycles with piecewise linear accelerators with only 'floor' are considered.
Bonkobara, Yasuhiro; Mori, Hiroki; Kondou, Takahiro; Ayabe, Takashi
Self-synchronized phenomena generated in rotor-type oscillators mounted on a straight-line spring-mass system are investigated experimentally and analytically. In the present study, we examine the occurrence region and pattern of self-synchronization in two types of coupled oscillators: rigidly coupled oscillators and elastically coupled oscillators. It is clarified that the existence regions of stable solutions are governed mainly by the linear natural frequency of each spring-mass system. The results of numerical analysis confirm that the self-synchronized solutions of the elastically coupled oscillators correspond to those of the rigidly coupled oscillators. In addition, the results obtained in the present study are compared with the previously reported results for a metronome system and a moving apparatus and the different properties of the phenomena generated in the rotor-type oscillators and the pendulum-type oscillators are shown in terms of the construction of branches of self-synchronized solution and the stability.
Sushko, Iryna; Gardini, Laura; Matsuyama, Kiminori
2018-05-01
We consider a two-dimensional continuous noninvertible piecewise smooth map, which characterizes the dynamics of innovation activities in the two-country model of trade and product innovation proposed in [7]. This two-dimensional map can be viewed as a coupling of two one-dimensional skew tent maps, each of which characterizes the innovation dynamics in each country in the absence of trade, and the coupling parameter depends inversely on the trade cost between the two countries. Hence, this model offers a laboratory for studying how a decline in the trade cost, or globalization, might synchronize endogenous fluctuations of innovation activities in the two countries. In this paper, we focus on the bifurcation scenarios, how the phase portrait of the two-dimensional map changes with a gradual decline of the trade cost, leading to border collision, merging, expansion and final bifurcations of the coexisting chaotic attractors. An example of peculiar border collision bifurcation leading to an increase of dimension of the chaotic attractor is also presented.
Trajectory-probed instability and statistics of desynchronization events in coupled chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Gilson F. de, E-mail: gilson@otica.ufpb.br; Chevrollier, Martine; Oriá, Marcos [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900 João Pessoa-PB (Brazil); Passerat de Silans, Thierry [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900 João Pessoa-PB (Brazil); UAF, Universidade Federal de Campina Grande, 58429-900 Campina Grande, PB (Brazil); Souza Cavalcante, Hugo L. D. de [Departamento de Informática, Centro de Informática, Universidade Federal da Paraíba, Av. dos Escoteiros s/n, Mangabeira VII, 58055-000 João Pessoa, PB (Brazil)
2015-11-15
Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability.
Trajectory-probed instability and statistics of desynchronization events in coupled chaotic systems
International Nuclear Information System (INIS)
Oliveira, Gilson F. de; Chevrollier, Martine; Oriá, Marcos; Passerat de Silans, Thierry; Souza Cavalcante, Hugo L. D. de
2015-01-01
Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability
Trajectory-probed instability and statistics of desynchronization events in coupled chaotic systems
de Oliveira, Gilson F.; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; de Souza Cavalcante, Hugo L. D.
2015-11-01
Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability.
Chaos desynchronization in strongly coupled systems
International Nuclear Information System (INIS)
Wu Ye; Liu Weiqing; Xiao, Jinghua; Zhan Meng
2007-01-01
The dynamics of chaos desynchronization in strongly coupled oscillator systems is studied. We find a new bifurcation from synchronous chaotic state, chaotic short wave bifurcation, i.e. a chaotic desynchronization attractor is new born in the systems due to chaos desynchronization. In comparison with the usual periodic short wave bifurcation, very rich but distinct phenomena are observed
Phase dynamics of oscillating magnetizations coupled via spin pumping
Taniguchi, Tomohiro
2018-05-01
A theoretical formalism is developed to simultaneously solve equation of motion of the magnetizations in two ferromagnets and the spin-pumping induced spin transport equation. Based on the formalism, a coupled motion of the magnetizations in a self-oscillation state is studied. The spin pumping is found to induce an in-phase synchronization of the magnetizations for the oscillation around the easy axis. For an out-of-plane self-oscillation around the hard axis, on the other hand, the spin pumping leads to an in-phase synchronization in a small current region, whereas an antiphase synchronization is excited in a large current region. An analytical theory based on the phase equation reveals that the phase difference between the magnetizations in a steady state depends on the oscillation direction, clockwise or counterclockwise, of the magnetizations.
Energy Technology Data Exchange (ETDEWEB)
Hayashi, Kenta [Department of Mechanical Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu-shi, Shiga 525-8577 (Japan); Department of Chemistry, Biology, and Biotechnology, University of Perugia, 06123 Perugia (Italy); Gotoda, Hiroshi [Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585 (Japan); Gentili, Pier Luigi, E-mail: pierluigi.gentili@unipg.it [Department of Chemistry, Biology, and Biotechnology, University of Perugia, 06123 Perugia (Italy)
2016-05-15
The convective motions within a solution of a photochromic spiro-oxazine being irradiated by UV only on the bottom part of its volume, give rise to aperiodic spectrophotometric dynamics. In this paper, we study three nonlinear properties of the aperiodic time series: permutation entropy, short-term predictability and long-term unpredictability, and degree distribution of the visibility graph networks. After ascertaining the extracted chaotic features, we show how the aperiodic time series can be exploited to implement all the fundamental two-inputs binary logic functions (AND, OR, NAND, NOR, XOR, and XNOR) and some basic arithmetic operations (half-adder, full-adder, half-subtractor). This is possible due to the wide range of states a nonlinear system accesses in the course of its evolution. Therefore, the solution of the convective photochemical oscillator results in hardware for chaos-computing alternative to conventional complementary metal-oxide semiconductor-based integrated circuits.
Heterogeneity of time delays determines synchronization of coupled oscillators.
Petkoski, Spase; Spiegler, Andreas; Proix, Timothée; Aram, Parham; Temprado, Jean-Jacques; Jirsa, Viktor K
2016-07-01
Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.
Controllability in tunable chains of coupled harmonic oscillators
Buchmann, L. F.; Mølmer, K.; Petrosyan, D.
2018-04-01
We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N -1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach any desired Gaussian state requires at most 3 N (N -1 )/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides.
Controllability in tunable chains of coupled harmonic oscillators
DEFF Research Database (Denmark)
Buchmann, Lukas Filip; Mølmer, Klaus; Petrosyan, David
2018-01-01
We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N −1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach...... any desired Gaussian state requires at most 3 N ( N −1)/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can...... be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides....
Controllability in tunable chains of coupled harmonic oscillators
DEFF Research Database (Denmark)
Buchmann, Lukas Filip; Mølmer, Klaus; Petrosyan, David
2018-01-01
any desired Gaussian state requires at most 3 N ( N −1)/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can......We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N −1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach...... be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides....
Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.
2017-05-01
This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron.
Synchronization of coupled stochastic oscillators: The effect of ...
Indian Academy of Sciences (India)
as an approximate means of accounting for a separation of time-scales between ... phase relationships between coupled oscillator systems as well as to effect a variety ... ations are often termed as internal noise since their origin is in the very ..... design and control of synthetic biological networks where synchronous ...
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...
Chen, Xin; Fan, Ruihua; Chen, Yiming; Zhai, Hui; Zhang, Pengfei
2017-11-17
The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties, holographic duality, and maximally chaotic behavior. In this work, we consider a generalization of the SYK model that contains two SYK models with a different number of Majorana modes coupled by quadratic terms. This model is also solvable, and the solution shows a zero-temperature quantum phase transition between two non-Fermi liquid chaotic phases. This phase transition is driven by tuning the ratio of two mode numbers, and a nonchaotic Fermi liquid sits at the critical point with an equal number of modes. At a finite temperature, the Fermi liquid phase expands to a finite regime. More intriguingly, a different non-Fermi liquid phase emerges at a finite temperature. We characterize the phase diagram in terms of the spectral function, the Lyapunov exponent, and the entropy. Our results illustrate a concrete example of the quantum phase transition and critical behavior between two non-Fermi liquid phases.
Coupling-induced oscillations in nonhomogeneous, overdamped, bistable systems
International Nuclear Information System (INIS)
Hernandez, Mayra; In, Visarath; Longhini, Patrick; Palacios, Antonio; Bulsara, Adi; Kho, Andy
2008-01-01
Coupling-induced oscillations in a homogeneous network of overdamped bistable systems have been previously studied both theoretically and experimentally for a system of N (odd) elements, unidirectionally coupled in a ring topology. In this work, we extend the analysis of this system to include a network of nonhomogeneous elements with respect to the parameter that controls the topology of the potential function and the bistability of each element. In particular, we quantify the effects of the nonhomogeneity on the onset of oscillations and the response of the network to external (assumed to be constant and very small) perturbations, using our (recently developed) coupled core fluxgate magnetometer as a representative system. The potential applications of this work include signal detection and characterization for a large class of sensor systems
Coupling-induced oscillations in nonhomogeneous, overdamped, bistable systems
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Mayra [Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182 (United States)], E-mail: mayra.alina@yahoo.com; In, Visarath [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: visarath.in@navy.mil; Longhini, Patrick [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: longhini@navy.mil; Palacios, Antonio [Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182 (United States)], E-mail: palacios@euler.sdsu.edu; Bulsara, Adi [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: bulsara@spawar.navy.mil; Kho, Andy [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: kho@spawar.navy.mil
2008-06-09
Coupling-induced oscillations in a homogeneous network of overdamped bistable systems have been previously studied both theoretically and experimentally for a system of N (odd) elements, unidirectionally coupled in a ring topology. In this work, we extend the analysis of this system to include a network of nonhomogeneous elements with respect to the parameter that controls the topology of the potential function and the bistability of each element. In particular, we quantify the effects of the nonhomogeneity on the onset of oscillations and the response of the network to external (assumed to be constant and very small) perturbations, using our (recently developed) coupled core fluxgate magnetometer as a representative system. The potential applications of this work include signal detection and characterization for a large class of sensor systems.
Dynamics of multi-frequency oscillator ensembles with resonant coupling
International Nuclear Information System (INIS)
Lueck, S.; Pikovsky, A.
2011-01-01
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two interacting subpopulations are in relation 2:1. Depending on the parameter of coupling, ensembles can demonstrate fully synchronous clusters, partial synchrony (only one subpopulation synchronizes), or asynchrony in both subpopulations. Theoretical description of the dynamics based on the Watanabe-Strogatz approach is developed. -- Highlights: → Kuramoto model is generalized on the case of resonantly interacting oscillators having frequency ratio 2:1. → Regimes of full and partial synchrony, as well as non-synchronous ones are reported. → Analytical description is developed on the basis of the Watanabe-Strogatz approach.
Dynamics of multi-frequency oscillator ensembles with resonant coupling
Energy Technology Data Exchange (ETDEWEB)
Lueck, S. [Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Str. 24-25, 14476 Potsdam (Germany); Pikovsky, A., E-mail: pikovsky@stat.physik.uni-potsdam.de [Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Str. 24-25, 14476 Potsdam (Germany)
2011-07-11
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two interacting subpopulations are in relation 2:1. Depending on the parameter of coupling, ensembles can demonstrate fully synchronous clusters, partial synchrony (only one subpopulation synchronizes), or asynchrony in both subpopulations. Theoretical description of the dynamics based on the Watanabe-Strogatz approach is developed. -- Highlights: → Kuramoto model is generalized on the case of resonantly interacting oscillators having frequency ratio 2:1. → Regimes of full and partial synchrony, as well as non-synchronous ones are reported. → Analytical description is developed on the basis of the Watanabe-Strogatz approach.
Breathing multichimera states in nonlocally coupled phase oscillators
Suda, Yusuke; Okuda, Koji
2018-04-01
Chimera states for the one-dimensional array of nonlocally coupled phase oscillators in the continuum limit are assumed to be stationary states in most studies, but a few studies report the existence of breathing chimera states. We focus on multichimera states with two coherent and incoherent regions and numerically demonstrate that breathing multichimera states, whose global order parameter oscillates temporally, can appear. Moreover, we show that the system exhibits a Hopf bifurcation from a stationary multichimera to a breathing one by the linear stability analysis for the stationary multichimera.
Coupled Langmuir oscillations in 2-dimensional quantum plasmas
International Nuclear Information System (INIS)
Akbari-Moghanjoughi, M.
2014-01-01
In this work, we present a hydrodynamic model to study the coupled quantum electron plasma oscillations (QEPO) for two dimensional (2D) degenerate plasmas, which incorporates all the essential quantum ingredients such as the statistical degeneracy pressure, electron-exchange, and electron quantum diffraction effect. Effects of diverse physical aspects like the electronic band-dispersion effect, the electron exchange-correlations and the quantum Bohm-potential as well as other important plasma parameters such as the coupling parameter (plasma separation) and the plasma electron number-densities on the linear response of the coupled system are investigated. By studying three different 2D plasma coupling types, namely, graphene-graphene, graphene-metalfilm, and metalfilm-metalfilm coupling configurations, it is remarked that the collective quantum effects can influence the coupled modes quite differently, depending on the type of the plasma configuration. It is also found that the slow and fast QEPO frequency modes respond very differently to the change in plasma parameters. Current findings can help in understanding of the coupled density oscillations in multilayer graphene, graphene-based heterojunctions, or nanofabricated integrated circuits
Pulse-coupled Belousov-Zhabotinsky oscillators with frequency modulation
Horvath, Viktor; Epstein, Irving R.
2018-04-01
Inhibitory perturbations to the ferroin-catalyzed Belousov-Zhabotinsky (BZ) chemical oscillator operated in a continuously fed stirred tank reactor cause long term changes to the limit cycle: the lengths of the cycles subsequent to the perturbation are longer than that of the unperturbed cycle, and the unperturbed limit cycle is recovered only after several cycles. The frequency of the BZ reaction strongly depends on the acid concentration of the medium. By adding strong acid or base to the perturbing solutions, the magnitude and the direction of the frequency changes concomitant to excitatory or inhibitory perturbations can be controlled independently of the coupling strength. The dynamics of two BZ oscillators coupled through perturbations carrying a coupling agent (activator or inhibitor) and a frequency modulator (strong acid or base) was explored using a numerical model of the system. Here, we report new complex temporal patterns: higher order, partially synchronized modes that develop when inhibitory coupling is combined with positive frequency modulation (FM), and complex bursting patterns when excitatory coupling is combined with negative FM. The role of time delay between the peak and perturbation (the analog of synaptic delays in networks of neurons) has also been studied. The complex patterns found under inhibitory coupling and positive FM vanish when the delay is significant, whereas a sufficiently long time delay is required for the complex temporal dynamics to occur when coupling is excitatory and FM is negative.
International Nuclear Information System (INIS)
Shi, X.
1996-01-01
We investigate in detail the parameter space of active-sterile neutrino oscillations that amplifies neutrino chemical potentials at the epoch of big bang nucleosynthesis. We calculate the magnitude of the amplification and show evidence of chaos in the amplification process. We also discuss the implications of the neutrino chemical potential amplification in big bang nucleosynthesis. It is shown that with a ∼1 eV ν e , the amplification of its chemical potential by active-sterile neutrino oscillations can lower the effective number of neutrino species at big bang nucleosynthesis to significantly below three. copyright 1996 The American Physical Society
Energy Technology Data Exchange (ETDEWEB)
Shi, X. [Department of Physics, Queen`s University, Kingston, Ontario, K7L 3N6 (CANADA)
1996-08-01
We investigate in detail the parameter space of active-sterile neutrino oscillations that amplifies neutrino chemical potentials at the epoch of big bang nucleosynthesis. We calculate the magnitude of the amplification and show evidence of chaos in the amplification process. We also discuss the implications of the neutrino chemical potential amplification in big bang nucleosynthesis. It is shown that with a {approximately}1 eV {nu}{sub {ital e}}, the amplification of its chemical potential by active-sterile neutrino oscillations can lower the effective number of neutrino species at big bang nucleosynthesis to significantly below three. {copyright} {ital 1996 The American Physical Society.}
Breaking of ensembles of linear and nonlinear oscillators
International Nuclear Information System (INIS)
Buts, V.A.
2016-01-01
Some results concerning the study of the dynamics of ensembles of linear and nonlinear oscillators are stated. It is shown that, in general, a stable ensemble of linear oscillator has a limited number of oscillators. This number has been defined for some simple models. It is shown that the features of the dynamics of linear oscillators can be used for conversion of the low-frequency energy oscillations into high frequency oscillations. The dynamics of coupled nonlinear oscillators in most cases is chaotic. For such a case, it is shown that the statistical characteristics (moments) of chaotic motion can significantly reduce potential barriers that keep the particles in the capture region
Time-dependent coupled harmonic oscillators: classical and quantum solutions
International Nuclear Information System (INIS)
Macedo, D.X.; Guedes, I.
2014-01-01
In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m 1 = m 2 = m 0 e γt , ω 1 = ω 01 e -γt/2 , ω 2 = ω 02 e -γt/2 and k = k 0 . (author)
Partially coherent twisted states in arrays of coupled phase oscillators
Energy Technology Data Exchange (ETDEWEB)
Omel' chenko, Oleh E.; Wolfrum, Matthias [Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin (Germany); Laing, Carlo R. [INMS, Massey University, Private Bag 102-904 NSMC, Auckland (New Zealand)
2014-06-15
We consider a one-dimensional array of phase oscillators with non-local coupling and a Lorentzian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly “twisted” in space. To analyze these, we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies, and study the resulting spatio-temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We find that stable twisted states with different wave numbers appear for increasing coupling strength in the well-known Eckhaus scenario. Simulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system.
Partially coherent twisted states in arrays of coupled phase oscillators
International Nuclear Information System (INIS)
Omel'chenko, Oleh E.; Wolfrum, Matthias; Laing, Carlo R.
2014-01-01
We consider a one-dimensional array of phase oscillators with non-local coupling and a Lorentzian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly “twisted” in space. To analyze these, we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies, and study the resulting spatio-temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We find that stable twisted states with different wave numbers appear for increasing coupling strength in the well-known Eckhaus scenario. Simulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system
Oscillation thresholds for "striking outwards" reeds coupled to a resonator
Silva , Fabrice; Kergomard , Jean; Vergez , Christophe
2007-01-01
International audience; This paper considers a "striking outwards" reed coupled to a resonator. This expression, due to Helmholtz, is not discussed here : it corresponds to the most common model of a lip-type valve, when the valve is assumed to be a one degree of freedom oscillator. The presented work is an extension of the works done by Wilson and Beavers (1974), Tarnopolsky (2000). The range of the playing frequencies is investigated. The first results are analytical : when no losses are pr...
Ponomarenko, V I; Kulminskiy, D D; Prokhorov, M D
2017-08-01
We study the collective dynamics of oscillators in a network of identical bistable time-delayed feedback systems globally coupled via the mean field. The influence of delay and inertial properties of the mean field on the collective behavior of globally coupled oscillators is investigated. A variety of oscillation regimes in the network results from the presence of bistable states with substantially different frequencies in coupled oscillators. In the physical experiment and numerical simulation we demonstrate the existence of chimeralike states, in which some of the oscillators in the network exhibit synchronous oscillations, while all other oscillators remain asynchronous.
Eigenmode analysis of coupled magnetohydrodynamic oscillations in the magnetosphere
International Nuclear Information System (INIS)
Fujita, S.; Patel, V.L.
1992-01-01
The authors have performed an eigenmode analysis of the coupled magnetohydrodynamic oscillations in the magnetosphere with a dipole magnetic field. To understand the behavior of the spatial structure of the field perturbations with a great accuracy, they use the finite element method. The azimuthal and radial electric field perturbations are assumed to vanish at the ionosphere, and the azimuthal electric field is assumed to be zero on the outer boundary. The global structures of the electromagnetic field perturbations associated with the coupled magnetohydrodynamic oscillations are presented. In addition, the three-dimensional current system associated with the coupled oscillations is numerically calculated and the following characteristics are found: (1) A strong field-aligned current flows along a resonant field line. The current is particularly strong near the ionosphere. (2) The radial current changes its direction on the opposite sides of the resonant L shell. Unlike the field-aligned current, the radial currents exist in the entire magnetosphere. (3) Although the azimuthal and radial currents are intense on the resonant field line, these currents do not form a loop in the plane perpendicular to the ambient magnetic field. Therefore the field-aligned component of the perturbed magnetic field does not have a maximum at the resonant L shell
On the chaoticity of active-sterile neutrino oscillations in the early universe
DEFF Research Database (Denmark)
Braad, Poul-Erik; Hannestad, Steen
2000-01-01
We have investigated the evolution of the neutrino asymmetry in active-sterile neutrino oscillations in the early universe. We find that there are large regions of parameter space where the asymmetry is extremely sensitive to variations in the initial asymmetry as well as the external parameters ...... asymmetry is stochastic. We discuss the implications of our findings for Big Bang nucleosynthesis (BBN) and the cosmic microwave background (CMB)....
International Nuclear Information System (INIS)
Morimoto, Y.; Madarame, H.; Okamoto, K.
2001-01-01
Japan Atomic Energy Research Institute (JAERI) proposed a passive safety reactor called the System-integrated Pressurized Water Reactor (SPWR). In a loss of coolant accident, the Pressurizing Line (PL) and the Injection Line (IL) are passively opened. Vapor generated by residual heat pushes down the water level in the Reactor Vessel (RV). When the level is lower than the inlet of the PL, the vapor is ejected into the Containment Vessel (CV) through the PL. Then boronized water in the CV is injected into the RV through the IL by the static head. In an experiment using a simple apparatus, gas ejection and water injection were found to occur alternately under certain conditions. The gas ejection interval was observed to fluctuate considerably. Though stochastic noise affected the interval, the experimental results suggested that the large fluctuation was produced by an inherent character in the system. A set of piecewise linear differential equations was derived to describe the experimental result. The large fluctuation was reproduced in the analytical solution. Thus it was shown to occur even in a deterministic system without any source of stochastic noise. Though the derived equations simulated the experiment well, they had ten independent parameters governing the behavior of the solution. There appeared chaotic features and bifurcation, but the analytical model was too complicated to examine the features and mechanism of bifurcation. In this study, a new simple model is proposed which consists of a set of piecewise linear ordinary differential equations with only four independent parameters. (authors)
Chimera and phase-cluster states in populations of coupled chemical oscillators
Tinsley, Mark R.; Nkomo, Simbarashe; Showalter, Kenneth
2012-09-01
Populations of coupled oscillators may exhibit two coexisting subpopulations, one with synchronized oscillations and the other with unsynchronized oscillations, even though all of the oscillators are coupled to each other in an equivalent manner. This phenomenon, discovered about ten years ago in theoretical studies, was then further characterized and named the chimera state after the Greek mythological creature made up of different animals. The highly counterintuitive coexistence of coherent and incoherent oscillations in populations of identical oscillators, each with an equivalent coupling structure, inspired great interest and a flurry of theoretical activity. Here we report on experimental studies of chimera states and their relation to other synchronization states in populations of coupled chemical oscillators. Our experiments with coupled Belousov-Zhabotinsky oscillators and corresponding simulations reveal chimera behaviour that differs significantly from the behaviour found in theoretical studies of phase-oscillator models.
Chaotic Patterns in Aeroelastic Signals
Directory of Open Access Journals (Sweden)
F. D. Marques
2009-01-01
patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.
Kaewkhao, Narakorn; Gumjudpai, Burin
2018-06-01
We consider, in Palatini formalism, a modified gravity of which the scalar field derivative couples to Einstein tensor. In this scenario, Ricci scalar, Ricci tensor and Einstein tensor are functions of connection field. As a result, the connection field gives rise to relation, hμν = fgμν between effective metric, hμν and the usual metric gμν where f = 1 - κϕ,αϕ,α / 2. In FLRW universe, NMDC coupling constant is limited in a range of - 2 /ϕ˙2 - 1 / 3. Power-law potentials of chaotic inflation are considered. For V ∝ϕ2 and V ∝ϕ4, it is possible to obtain tensor-to-scalar ratio lower than that of GR so that it satisfies r < 0 . 12 as constrained by Planck 2015 (Ade et al., 2016). The V ∝ϕ2 case yields acceptable range of spectrum index and r values. The quartic potential's spectrum index is disfavored by the Planck results. Viable range of κ for V ∝ϕ2 case lies in positive region, resulting in less blackhole's entropy, superluminal metric, more amount of inflation, avoidance of super-Planckian field initial value and stronger gravitational constant.
Strange attractors and synchronization dynamics of coupled Van der Pol-Duffing oscillators
International Nuclear Information System (INIS)
Yamapi, R.; Filatrella, G.
2006-07-01
We consider in this paper the dynamics and synchronization of coupled chaotic Van der Pol-Duffing systems. The stability of the synchronization process between two coupled autonomous Van der Pol model is first analyzed analytically and numerically, before following the problem of synchronizing chaos both on the same and different chaotic orbits of two coupled Van der Pol-Duffing systems. The stability boundaries of the synchronization process are derived and the effects of the amplitude of the periodic perturbation of the coupling parameter on these boundaries are analyzed. The results are provided on the stability map in the (q, K) plane. (author)
Border-Collision Bifurcations and Chaotic Oscillations in a Piecewise-Smooth Dynamical System
DEFF Research Database (Denmark)
Zhusubaliyev, Z.T.; Soukhoterin, E.A.; Mosekilde, Erik
2002-01-01
Many problems of engineering and applied science result in the consideration of piecewise-smooth dynamical systems. Examples are relay and pulse-width control systems, impact oscillators, power converters, and various electronic circuits with piecewise-smooth characteristics. The subject...... of investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border......-collision bifurcations. The paper contains a detailed analysis of this type of bifurcational transition in the dynamics of the voltage converter, in particular, the merging and subsequent disappearance of cycles of different types, change of solution type, and period-doubling, -tripling, -quadrupling and -quintupling...
Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays
International Nuclear Information System (INIS)
Bi, Ping; Ruan, Shigui; Zhang, Xinan
2014-01-01
In this paper, a tumor and immune system interaction model consisted of two differential equations with three time delays is considered in which the delays describe the proliferation of tumor cells, the process of effector cells growth stimulated by tumor cells, and the differentiation of immune effector cells, respectively. Conditions for the asymptotic stability of equilibria and existence of Hopf bifurcations are obtained by analyzing the roots of a second degree exponential polynomial characteristic equation with delay dependent coefficients. It is shown that the positive equilibrium is asymptotically stable if all three delays are less than their corresponding critical values and Hopf bifurcations occur if any one of these delays passes through its critical value. Numerical simulations are carried out to illustrate the rich dynamical behavior of the model with different delay values including the existence of regular and irregular long periodic oscillations
Role of the Absorbing Area in Chaotic Synchronization
DEFF Research Database (Denmark)
Maistrenko, Yu.L.; Maistrenko, V.L.; Popovich, A.
1998-01-01
When two identical chaotic oscillators interact, one or more intervals of coupling parameters generally exist in which the synchronized state is weakly stable, and its basin of attraction is riddled with holes that are repelled from it. The paper discusses the role of the absorbing area for the e......When two identical chaotic oscillators interact, one or more intervals of coupling parameters generally exist in which the synchronized state is weakly stable, and its basin of attraction is riddled with holes that are repelled from it. The paper discusses the role of the absorbing area...
Awakened Oscillations in Coupled Consumer-Resource Pairs
Directory of Open Access Journals (Sweden)
Almaz Mustafin
2014-01-01
Full Text Available The paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the problem. This is done by treating consumers and resources in the coupled system as fast-scale and slow-scale variables, respectively, and subsequently considering developments in phase planes of these variables, fast and slow, as if they are independent. When uncoupled, each pair has unique asymptotically stable steady state and no self-sustained oscillatory behavior (although damped oscillations about the equilibrium are admitted. When the consumer-resource pairs are weakly coupled through direct reciprocal inhibition of consumers, the whole system exhibits self-sustained relaxation oscillations with a period that can be significantly longer than intrinsic relaxation time of either pair. It is shown that the model equations adequately describe locally linked consumer-resource systems of quite different nature: living populations under interspecific interference competition and lasers coupled via their cavity losses.
Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim
2017-06-01
We study the transition from coherence (complete synchronization) to incoherence (spatio-temporal chaos) in ensembles of nonlocally coupled chaotic maps with nonhyperbolic and hyperbolic attractors. As basic models of a partial element we use the Henon map and the Lozi map. We show that the transition to incoherence in a ring of coupled Henon maps occurs through the appearance of phase and amplitude chimera states. An ensemble of coupled Lozi maps demonstrates the coherence-incoherence transition via solitary states and no chimera states are observed in this case.
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...
Coupled-oscillator based active-array antennas
Pogorzelski, Ronald J
2012-01-01
Describing an innovative approach to phased-array control in antenna design This book explores in detail phased-array antennas that use coupled-oscillator arrays, an arrangement featuring a remarkably simple beam steering control system and a major reduction in complexity compared with traditional methods of phased-array control. It brings together in one convenient, self-contained volume the many salient research results obtained over the past ten to fifteen years in laboratories around the world, including the California Institute of Technology's Jet Propulsion Laboratory.
Probing the Chaotic Dynamics of Fluids using Insights from Coupled Map Lattices
Barbish, Johnathon; Xu, Mu; Paul, Mark
2017-11-01
Many difficult fluid challenges exhibit high-dimensional spatiotemporal chaos. Natural examples include the dynamics of the atmosphere and oceans. New insights have been gained by studying canonical fluid problems such as Rayleigh-Bénard convection where significant progress has been made using large-scale computations of the partial differential equations that describe the fluid flow. However, these computations remain very expensive which makes it difficult, if not currently impossible, to explore new ideas that require large sample sets, vast sweeps of parameter space, and long-time statistics. We study these questions using coupled map lattices (CML) in one and two dimensions. We compute the covariant Lyapunov vectors to probe fundamental features of the CML's including the Lyapunov spectrum, fractal dimension, and the principal angle between the stable and unstable manifolds. We are particularly interested in the role of a conservation law on the chaotic dynamics, the use of ideas from equilibrium thermodynamics to yield a coarse-grained representation, and in the development of reduced order models. This work is supported by NSF DMS-1622299.
Coupled oscillations of flow along a perforated plate
International Nuclear Information System (INIS)
Celik, E.; Rockwell, D.
2004-01-01
Turbulent shear flow past a perforated plate bounded by a closed cavity can give rise to highly coherent oscillations, which have a wavelength of the order of the plate length. The present investigation focuses on the coupling between unsteady events on either side of the plate when the oscillations are self-sustaining. A cinema technique of high-image-density particle image velocimetry, which provides a space-time representation of the unsteadiness at a large number of locations over entire planes, is employed to characterize the distinctively different patterns of flow structure on the back (low-speed) side of the plate relative to those on the front (high-speed) side. Global cross-spectral analysis leads to patterns of spectral peaks and phase variations, along and across the plate. This approach, along with complementary types of image evaluation, delineates the physics of the oscillations, which include downstream propagating disturbances along either side of the plate and a coherent region of unsteadiness at its trailing-edge. On the backside of the plate, a sequence of upstream-oriented, pulsatile jets are formed, and the time-averaged flow pattern is a counterflow wall jet
de Oliveira, G. L.; Ramos, R. V.
2018-03-01
In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.
Chaotic Darcy-Brinkman convection in a fluid saturated porous layer subjected to gravity modulation
Directory of Open Access Journals (Sweden)
Moli Zhao
2018-06-01
Full Text Available On the basis of Darcy-Brinkman model, the chaotic convection in a couple stress fluid saturated porous media under gravity modulation is investigated using the nonlinear stability analyses. The transition from steady convection to chaos is analysed with the effect of Darcy-Brinkman couple stress parameter and the gravity modulation. The results show that the chaotic behavior is connected with the critical value of Rayleigh number which is dependent upon the oscillation frequency and the Darcy-Brinkman couple stress parameter. If the oscillation frequency Ω is not zero, the Rayleigh number value R of the chaotic behavior increases with the increase of the Darcy-Brinkman couple stress parameter. The Darcy-Brinkman couple stress parameter and the gravity modulation decrease the rate of heat transfer. Keywords: Darcy-Brinkman model, Gravity modulation, Nonlinear stability, Chaotic convection
Spontaneous decoherence of coupled harmonic oscillators confined in a ring
Gong, ZhiRui; Zhang, ZhenWei; Xu, DaZhi; Zhao, Nan; Sun, ChangPu
2018-04-01
We study the spontaneous decoherence of coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry-breaking field or surrounding environment, the quantum superposition state prepared in the relative degrees of freedom gradually loses its quantum coherence spontaneously. This spontaneous decoherence is interpreted by the gauge couplings between the center-of-mass and the relative degrees of freedoms, which actually originate from the symmetries of the ring geometry and the corresponding nontrivial boundary conditions. In particular, such spontaneous decoherence does not occur at all at the thermodynamic limit because the nontrivial boundary conditions become the trivial Born-von Karman boundary conditions when the perimeter of the ring container tends to infinity. Our investigation shows that a thermal macroscopic object with certain symmetries has a chance for its quantum properties to degrade even without applying an external symmetry-breaking field or surrounding environment.
On the (Frequency) Modulation of Coupled Oscillator Arrays in Phased Array Beam Control
Pogorzelski, R.; Acorn, J.; Zawadzki, M.
2000-01-01
It has been shown that arrays of voltage controlled oscillators coupled to nearest neighbors can be used to produce useful aperture phase distributions for phased array antennas. However, placing information of the transmitted signal requires that the oscillations be modulated.
Non-linear phenomena in electronic systems consisting of coupled single-electron oscillators
International Nuclear Information System (INIS)
Kikombo, Andrew Kilinga; Hirose, Tetsuya; Asai, Tetsuya; Amemiya, Yoshihito
2008-01-01
This paper describes non-linear dynamics of electronic systems consisting of single-electron oscillators. A single-electron oscillator is a circuit made up of a tunneling junction and a resistor, and produces simple relaxation oscillation. Coupled with another, single electron oscillators exhibit complex behavior described by a combination of continuous differential equations and discrete difference equations. Computer simulation shows that a double-oscillator system consisting of two coupled oscillators produces multi-periodic oscillation with a single attractor, and that a quadruple-oscillator system consisting of four oscillators also produces multi-periodic oscillation but has a number of possible attractors and takes one of them determined by initial conditions
Hybrid Systems: Cold Atoms Coupled to Micro Mechanical Oscillators =
Montoya Monge, Cris A.
Micro mechanical oscillators can serve as probes in precision measurements, as transducers to mediate photon-phonon interactions, and when functionalized with magnetic material, as tools to manipulate spins in quantum systems. This dissertation includes two projects where the interactions between cold atoms and mechanical oscillators are studied. In one of the experiments, we have manipulated the Zeeman state of magnetically trapped Rubidium atoms with a magnetic micro cantilever. The results show a spatially localized effect produced by the cantilever that agrees with Landau-Zener theory. In the future, such a scalable system with highly localized interactions and the potential for single-spin sensitivity could be useful for applications in quantum information science or quantum simulation. In a second experiment, work is in progress to couple a sample of optically trapped Rubidium atoms to a levitated nanosphere via an optical lattice. This coupling enables the cooling of the center-of-mass motion of the nanosphere by laser cooling the atoms. In this system, the atoms are trapped in the optical lattice while the sphere is levitated in a separate vacuum chamber by a single-beam optical tweezer. Theoretical analysis of such a system has determined that cooling the center-of-mass motion of the sphere to its quantum ground state is possible, even when starting at room temperature, due to the excellent environmental decoupling achievable in this setup. Nanospheres cooled to the quantum regime can provide new tests of quantum behavior at mesoscopic scales and have novel applications in precision sensing.
Fluid-structure coupling for an oscillating hydrofoil
Münch, C.; Ausoni, P.; Braun, O.; Farhat, M.; Avellan, F.
2010-08-01
Fluid-structure investigations in hydraulic machines using coupled simulations are particularly time-consuming. In this study, an alternative method is presented that linearizes the hydrodynamic load of a rigid, oscillating hydrofoil. The hydrofoil, which is surrounded by incompressible, turbulent flow, is modeled with forced and free pitching motions, where the mean incidence angle is 0° with a maximum angle amplitude of 2°. Unsteady simulations of the flow, performed with ANSYS CFX, are presented and validated with experiments which were carried out in the EPFL High-Speed Cavitation Tunnel. First, forced motion is investigated for reduced frequencies ranging from 0.02 to 100. The hydrodynamic load is modeled as a simple combination of inertia, damping and stiffness effects. As expected, the potential flow analysis showed the added moment of inertia is constant, while the fluid damping and the fluid stiffness coefficients depend on the reduced frequency of the oscillation motion. Behavioral patterns were observed and two cases were identified depending on if vortices did or did not develop in the hydrofoil wake. Using the coefficients identified in the forced motion case, the time history of the profile incidence is then predicted analytically for the free motion case and excellent agreement is found for the results from coupled fluid-structure simulations. The model is validated and may be extended to more complex cases, such as blade grids in hydraulic machinery.
Directory of Open Access Journals (Sweden)
Petar eTomov
2014-09-01
Full Text Available The cerebral cortex exhibits neural activity even in the absence of externalstimuli. This self-sustained activity is characterized by irregular firing ofindividual neurons and population oscillations with a broad frequency range.Questions that arise in this context, are: What are the mechanismsresponsible for the existence of neuronal spiking activity in the cortexwithout external input? Do these mechanisms depend on the structural organization of the cortical connections? Do they depend onintrinsic characteristics of the cortical neurons? To approach the answers to these questions, we have used computer simulations of cortical network models. Our networks have hierarchical modular architecture and are composedof combinations of neuron models that reproduce the firing behavior of the five main cortical electrophysiological cell classes: regular spiking (RS, chattering (CH, intrinsically bursting (IB, low threshold spiking (LTS and fast spiking (FS. The population of excitatory neurons is built of RS cells(always present and either CH or IB cells. Inhibitoryneurons belong to the same class, either LTS or FS. Long-lived self-sustained activity states in our networksimulations display irregular single neuron firing and oscillatoryactivity similar to experimentally measured ones. The duration of self-sustained activity strongly depends on the initial conditions,suggesting a transient chaotic regime. Extensive analysis of the self-sustainedactivity states showed that their lifetime expectancy increases with the numberof network modules and is favored when the network is composed of excitatory neurons of the RS and CH classes combined with inhibitory neurons of the LTS class. These results indicate that the existence and properties of the self-sustained cortical activity states depend on both the topology of the network and the neuronal mixture that comprises the network.
Momentum diffusion for coupled atom-cavity oscillators
International Nuclear Information System (INIS)
Murr, K.; Maunz, P.; Pinkse, P. W. H.; Puppe, T.; Schuster, I.; Rempe, G.; Vitali, D.
2006-01-01
It is shown that the momentum diffusion of free-space laser cooling has a natural correspondence in optical cavities when the internal state of the atom is treated as a harmonic oscillator. We derive a general expression for the momentum diffusion, which is valid for most configurations of interest: The atom or the cavity or both can be probed by lasers, with or without the presence of traps inducing local atomic frequency shifts. It is shown that, albeit the (possibly strong) coupling between atom and cavity, it is sufficient for deriving the momentum diffusion to consider that the atom couples to a mean cavity field, which gives a first contribution, and that the cavity mode couples to a mean atomic dipole, giving a second contribution. Both contributions have an intuitive form and present a clear symmetry. The total diffusion is the sum of these two contributions plus the diffusion originating from the fluctuations of the forces due to the coupling to the vacuum modes other than the cavity mode (the so-called spontaneous emission term). Examples are given that help to evaluate the heating rates induced by an optical cavity for experiments operating at low atomic saturation. We also point out intriguing situations where the atom is heated although it cannot scatter light
Bildirici, Melike; Sonustun, Fulya Ozaksoy; Sonustun, Bahri
2018-01-01
In the regards of chaos theory, new concepts such as complexity, determinism, quantum mechanics, relativity, multiple equilibrium, complexity, (continuously) instability, nonlinearity, heterogeneous agents, irregularity were widely questioned in economics. It is noticed that linear models are insufficient for analyzing unpredictable, irregular and noncyclical oscillations of economies, and for predicting bubbles, financial crisis, business cycles in financial markets. Therefore, economists gave great consequence to use appropriate tools for modelling non-linear dynamical structures and chaotic behaviors of the economies especially in macro and the financial economy. In this paper, we aim to model the chaotic structure of exchange rates (USD-TL and EUR-TL). To determine non-linear patterns of the selected time series, daily returns of the exchange rates were tested by BDS during the period from January 01, 2002 to May 11, 2017 which covers after the era of the 2001 financial crisis. After specifying the non-linear structure of the selected time series, it was aimed to examine the chaotic characteristic for the selected time period by Lyapunov Exponents. The findings verify the existence of the chaotic structure of the exchange rate returns in the analyzed time period.
Chaotic dynamics dependence on doping density in weakly coupled GaAs/AlAs superlattices
International Nuclear Information System (INIS)
Yang Gui; Zhang Fengying; Li Yuanhong; Li Yuqi
2012-01-01
A discrete sequential tunneling model is used for studying the influence of the doping density on the dynamical behaviors in weakly coupled GaAs/AlAs superlattices. Driven by the DC bias, the system exhibits self-sustained current oscillations induced by the period motion of the unstable electric field domain, and an electrical hysteresis in the loop of current density voltage curve is deduced. It is found that the hysteresis range strongly depends on the doping density, and the width of the hysteresis loop increases with increasing the doping density. By adding an external driving ac voltage, more complicated nonlinear behaviors are observed including quasiperiodicity, period-3, and the route of an inverse period-doubling to chaos when the driving frequency changes. (semiconductor physics)
Elementary modes of coupled oscillators as whispering-gallery microresonators
Banerjee, Rabin; Mukherjee, Pradip
2015-10-01
We obtain the elementary modes of a system of parity-time reversal (PT)-symmetric coupled oscillators with balanced loss and gain. These modes are used to give a physical picture of the phase transition recently reported [C. M. Bender, M. Gianfreda, B. Peng, S. K. Özdemir and L. Yang, Phys. Rev. A 88, 062111 (2013); L. Yang, S. K. Özdemir and B. Peng, 12th Int. Workshop and Conf. Pseudo-Hermitian Hamiltonians in Quantum Physics, Istanbul, Turkey, July 2013; B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender and L. Yang, Nat. Phys. 10, 394 (2014)] in experiments with whispering-gallery microresonators.
DEFF Research Database (Denmark)
Schäfer, Mirko; Greiner, Martin
2011-01-01
to chaotic strings. Inhomogeneous coupling weights as well as small-world perturbations of the ring-network structure are discussed. It is found that certain combinations of coupling and network disorder preserve the empirical relationship between chaotic strings and the weak and strong sector...
Higher dimensional models of cross-coupled oscillators and application to design
Elwakil, Ahmed S.; Salama, Khaled N.
2010-01-01
We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.
Higher dimensional models of cross-coupled oscillators and application to design
Elwakil, Ahmed S.
2010-06-01
We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described. © 2010 World Scientific Publishing Company.
International Nuclear Information System (INIS)
Pando L, C.L.; Doedel, E.J.
2004-07-01
We investigate the onset of chaotic dynamics of the one-dimensional discrete nonlinear Schroedinger equation (DNLSE) with periodic boundary conditions in the presence of a single on-site defect. This model describes a ring of weakly- coupled Bose-Einstein condensates. We focus on the transition to global stochasticity in three different scenarios as the defect is changed. We make use of a suitable Poincare section and continuation methods. Numerical continuation enables us to find different families of stationary solutions, where certain bifurcations lead to global stochasticity. The global stochasticity is characterized by chaotic symbolic synchronization between the population inversions of certain pairs of condensates. We have seen that the Poincare cycles are useful to gain insight in the dynamics of this problem. Indeed, the return maps of the Poincare cycles have been used successfully to follow the motion along the stochastic layers of different resonances in the chaotic self-trapping regime. Moreover, the time series of the Poincare cycles suggests that in the global stochasticity regime the dynamics is, to some extent, Markovian, in spite of the fact that the condensates are phase locked with almost the same phase. This phase locking induces a peculiar local interference of the matter waves of the condensates. (author)
Targeting engineering synchronization in chaotic systems
Bhowmick, Sourav K.; Ghosh, Dibakar
2016-07-01
A method of targeting engineering synchronization states in two identical and mismatch chaotic systems is explained in detail. The method is proposed using linear feedback controller coupling for engineering synchronization such as mixed synchronization, linear and nonlinear generalized synchronization and targeting fixed point. The general form of coupling design to target any desire synchronization state under unidirectional coupling with the help of Lyapunov function stability theory is derived analytically. A scaling factor is introduced in the coupling definition to smooth control without any loss of synchrony. Numerical results are done on two mismatch Lorenz systems and two identical Sprott oscillators.
Chimera states in two-dimensional networks of locally coupled oscillators
Kundu, Srilena; Majhi, Soumen; Bera, Bidesh K.; Ghosh, Dibakar; Lakshmanan, M.
2018-02-01
Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera
Nakao, Hiroya; Yasui, Sho; Ota, Masashi; Arai, Kensuke; Kawamura, Yoji
2018-04-01
A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations for phase sensitivity functions, which characterize the phase response of the collective oscillation to small perturbations applied to individual elements, is derived. Using the phase sensitivity functions, collective oscillation of the network under weak perturbation can be described approximately by a one-dimensional phase equation. As an example, mutual synchronization between a pair of collectively oscillating networks of excitable and oscillatory FitzHugh-Nagumo elements with random coupling is studied.
International Nuclear Information System (INIS)
Liu Dan-Feng; Wu Zhao-Yan; Ye Qing-Ling
2014-01-01
In this paper, structure identification of an uncertain network coupled with complex-variable chaotic systems is investigated. Both the topological structure and the system parameters can be unknown and need to be identified. Based on impulsive stability theory and the Lyapunov function method, an impulsive control scheme combined with an adaptive strategy is adopted to design effective and universal network estimators. The restriction on the impulsive interval is relaxed by adopting an adaptive strategy. Further, the proposed method can monitor the online switching topology effectively. Several numerical simulations are provided to illustrate the effectiveness of the theoretical results. (general)
Chaotic synchronization of vibrations of a coupled mechanical system consisting of a plate and beams
Directory of Open Access Journals (Sweden)
J. Awrejcewicz
Full Text Available In this paper mathematical model of a mechanical system consisting of a plate and either one or two beams is derived. Obtained PDEs are reduced to ODEs, and then studied mainly using the fast Fourier and wavelet transforms. A few examples of the chaotic synchronizations are illustrated and discussed.
Energy Technology Data Exchange (ETDEWEB)
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it [MR-Lab, Center for Mind/Brain Science, University of Trento, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2014-12-01
In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.
International Nuclear Information System (INIS)
Minati, Ludovico
2014-01-01
In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties
The Madden-Julian Oscillation in NCEP Coupled Model Simulation
Directory of Open Access Journals (Sweden)
Wanqiu Wang Kyong-Hwan Seo
2009-01-01
Full Text Available This study documents a detailed analysis on the Madden-Julian Oscillation (MJO simulated by the National Centers for Environmental Prediction (NCEP using the Global Forecast System (GFS model version 2003 coupled with the Climate Forecast System model (CFS consisting of the 2003 version of GFS and the Geophysical Fluid Dynamics Laboratory (GFDL Modular Ocean Model V.3 (MOM3. The analyses are based upon a 21-year simulation of AMIP-type with GFS and CMIP-type with CFS. It is found that air-sea coupling in CFS is shown to improve the coherence between convection and large-scale circulation associated with the MJO. The too fast propagation of convection from the Indian Ocean to the maritime continents and the western Pacific in GFS is improved (slowed down in CFS. Both GFS and CFS produce too strong intraseasonal convective heating and circulation anomalies in the central-eastern Pacific; further, the air-sea coupling in CFS enhances this unrealistic feature. The simulated mean slow phase speed of east ward propagating low-wavenumber components shown in the wavenumber-frequency spectra is due to the slow propagation in the central-eastern Pacific in both GFS and CFS. Errors in model climatology may have some effect upon the simulated MJO and two possible influences are: (i CFS fails to simulate the westerlies over maritime continents and western Pacific areas, resulting in an unrealistic representation of surface latent heat flux associated with the MJO; and (ii vertical easterly wind shear from the Indian Ocean to the western Pacific in CFS is much weaker than that in the observation and in GFS, which may adversely affect the eastward propagation of the simulated MJO.
Negative Resistance Circuit for Damping an Array of Coupled FitzHugh-Nagumo Oscillators
DEFF Research Database (Denmark)
Tamaševičius, Arūnas; Adomaitienė, Elena; Bumelienė, Skaidra
2015-01-01
An analog circuit, based on a negative impedance converter and a capacitor, for damping oscillations in an array of mean-field coupled neuronal FitzHugh–Nagumo (FHN) type oscillators is described. The circuit is essentially a two-terminal feedback controller. When coupled to an array of the FHN...
Amplitude death and spatiotemporal bifurcations in nonlocally delay-coupled oscillators
International Nuclear Information System (INIS)
Guo, Yuxiao; Niu, Ben
2015-01-01
Amplitude death and spatiotemporal oscillations are remarkable patterns in coupled systems. We consider a ring of n identical oscillators with distance-dependent couplings and time delay. The amplitude death region is the intersection of three stable regions. Employing the method of multiple scales and normal form theory, the stability and criticality of spatiotemporal oscillations are determined. Around the amplitude death boundary there exist one branch of synchronized oscillations, n − 3 branches of co-existing phase-locked oscillations, n branches of mirror-reflecting oscillations, n branches of standing-wave oscillations, one branch of quasiperiodic oscillations and two branches of co-existing synchronized oscillations. It is proved that amplitude death is robust to small inhomogeneity of couplings, and the stability of synchronized or phase-locked oscillations inherits that of the individual decoupled oscillator. For the arbitrary form of coupling functions, some general results are also obtained for the thermodynamic limit. Finally, two examples are given to support the main results. (paper)
Stable amplitude chimera states in a network of locally coupled Stuart-Landau oscillators
Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2018-03-01
We investigate the occurrence of collective dynamical states such as transient amplitude chimera, stable amplitude chimera, and imperfect breathing chimera states in a locally coupled network of Stuart-Landau oscillators. In an imperfect breathing chimera state, the synchronized group of oscillators exhibits oscillations with large amplitudes, while the desynchronized group of oscillators oscillates with small amplitudes, and this behavior of coexistence of synchronized and desynchronized oscillations fluctuates with time. Then, we analyze the stability of the amplitude chimera states under various circumstances, including variations in system parameters and coupling strength, and perturbations in the initial states of the oscillators. For an increase in the value of the system parameter, namely, the nonisochronicity parameter, the transient chimera state becomes a stable chimera state for a sufficiently large value of coupling strength. In addition, we also analyze the stability of these states by perturbing the initial states of the oscillators. We find that while a small perturbation allows one to perturb a large number of oscillators resulting in a stable amplitude chimera state, a large perturbation allows one to perturb a small number of oscillators to get a stable amplitude chimera state. We also find the stability of the transient and stable amplitude chimera states and traveling wave states for an appropriate number of oscillators using Floquet theory. In addition, we also find the stability of the incoherent oscillation death states.
International Nuclear Information System (INIS)
Chung, N. N.; Chew, L. Y.
2007-01-01
We have generalized the two-step approach to the solution of systems of N coupled quantum anharmonic oscillators. By using the squeezed vacuum state of each individual oscillator, we construct the tensor product state, and obtain the optimal squeezed vacuum product state through energy minimization. We then employ this optimal state and its associated bosonic operators to define a basis set to construct the Heisenberg matrix. The diagonalization of the matrix enables us to obtain the energy eigenvalues of the coupled oscillators. In particular, we have applied our formalism to determine the eigenenergies of systems of two coupled quantum anharmonic oscillators perturbed by a general polynomial potential, as well as three and four coupled systems. Furthermore, by performing a first-order perturbation analysis about the optimal squeezed vacuum product state, we have also examined into the squeezing properties of two coupled oscillator systems
Radwan, Ahmed Gomaa
2014-06-18
This paper presents a digital implementation of a 3rd order chaotic system using the Euler approximation. Short-term predictability is studied in relation to system precision, Euler step size and attractor size and optimal parameters for maximum performance are derived. Defective bits from the native chaotic output are neglected and the remaining pass the NIST SP. 800-22 tests without post-processing. The resulting optimized pseudorandom number generator has throughput up to 17.60 Gbits/s for a 64-bit design experimentally verified on a Xilinx Virtex 4 FPGA with logic utilization less than 1.85%.
Radwan, Ahmed Gomaa; Mansingka, Abhinav S.; Salama, Khaled N.; Zidan, Mohammed A.
2014-01-01
This paper presents a digital implementation of a 3rd order chaotic system using the Euler approximation. Short-term predictability is studied in relation to system precision, Euler step size and attractor size and optimal parameters for maximum performance are derived. Defective bits from the native chaotic output are neglected and the remaining pass the NIST SP. 800-22 tests without post-processing. The resulting optimized pseudorandom number generator has throughput up to 17.60 Gbits/s for a 64-bit design experimentally verified on a Xilinx Virtex 4 FPGA with logic utilization less than 1.85%.
International Nuclear Information System (INIS)
Raghavan, S.; Smerzi, A.; Fantoni, S.; Shenoy, S.R.
2001-03-01
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to π (π-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of 3 He-B and the internal Josephson effect in 3 He-A are also discussed. (author)
Collective motions of globally coupled oscillators and some probability distributions on circle
Energy Technology Data Exchange (ETDEWEB)
Jaćimović, Vladimir [Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put, bb., 81000 Podgorica (Montenegro); Crnkić, Aladin, E-mail: aladin.crnkic@hotmail.com [Faculty of Technical Engineering, University of Bihać, Ljubijankićeva, bb., 77000 Bihać, Bosnia and Herzegovina (Bosnia and Herzegovina)
2017-06-28
In 2010 Kato and Jones described a new family of probability distributions on circle, obtained as Möbius transformation of von Mises distribution. We present the model demonstrating that these distributions appear naturally in study of populations of coupled oscillators. We use this opportunity to point out certain relations between Directional Statistics and collective motion of coupled oscillators. - Highlights: • We specify probability distributions on circle that arise in Kuramoto model. • We study how the mean-field coupling affects the shape of distribution of phases. • We discuss potential applications in some experiments on cell cycle. • We apply Directional Statistics to study collective dynamics of coupled oscillators.
Collective oscillations and coupled modes in confined microfluidic droplet arrays
Schiller, Ulf D.; Fleury, Jean-Baptiste; Seemann, Ralf; Gompper, Gerhard
Microfluidic droplets have a wide range of applications ranging from analytic assays in cellular biology to controlled mixing in chemical engineering. Ensembles of microfluidic droplets are interesting model systems for non-equilibrium many-body phenomena. When flowing in a microchannel, trains of droplets can form microfluidic crystals whose dynamics are governed by long-range hydrodynamic interactions and boundary effects. In this contribution, excitation mechanisms for collective waves in dense and confined microfluidic droplet arrays are investigated by experiments and computer simulations. We demonstrate that distinct modes can be excited by creating specific `defect' patterns in flowing droplet trains. While longitudinal modes exhibit a short-lived cascade of pairs of laterally displacing droplets, transversely excited modes form propagating waves that behave like microfluidic phonons. We show that the confinement induces a coupling between longitudinal and transverse modes. We also investigate the life time of the collective oscillations and discuss possible mechanisms for the onset of instabilities. Our results demonstrate that microfluidic phonons can exhibit effects beyond the linear theory, which can be studied particularly well in dense and confined systems. This work was supported by Deutsche Forschungsgemeinschaft under Grant No. SE 1118/4.
Transient chaos in a globally coupled system of nearly conservative Hamiltonian Duffing oscillators
International Nuclear Information System (INIS)
Sabarathinam, S.; Thamilmaran, K.
2015-01-01
Highlights: •We have examined transient chaos in globally coupled oscillators. •We analyze transient chaos using new techniques. •We give experimental confirmation of transient chaos. -- Abstract: In this work, transient chaos in a ring and globally coupled system of nearly conservative Hamiltonian Duffing oscillators is reported. The networks are formed by coupling of three, four and six Duffing oscillators. The nearly conservative Hamiltonian nature of the coupled system is proved by stability analysis. The transient phenomenon is confirmed through various numerical investigations such as recurrence analysis, 0–1 test and Finite Time Lyapunov Exponents. Further, the effect of damping and the average transient lifetime of three, four and six coupled schemes for randomly generated initial conditions have been analyzed. The experimental confirmation of transient chaos in an illustrative system of three ringly coupled Duffing oscillators is also presented
Implication of two-coupled differential Van der Pol Duffing oscillator in weak signal detection
International Nuclear Information System (INIS)
Peng Hanghang; Xu Xuemei; Yang Bingchu; Yin Linzi
2016-01-01
The principle of the Van der Pol Duffing oscillator for state transition and for determining critical value is described, which has been studied to indicate that the application of the Van der Pol Duffing oscillator in weak signal detection is feasible. On the basis of this principle, an improved two-coupled differential Van der Pol Duffing oscillator is proposed which can identify signals under any frequency and ameliorate signal-to-noise ratio (SNR). The analytical methods of the proposed model and the construction of the proposed oscillator are introduced in detail. Numerical experiments on the properties of the proposed oscillator compared with those of the Van der Pol Duffing oscillator are carried out. Our numerical simulations have confirmed the analytical treatment. The results demonstrate that this novel oscillator has better detection performance than the Van der Pol Duffing oscillator. (author)
Implication of Two-Coupled Differential Van der Pol Duffing Oscillator in Weak Signal Detection
Peng, Hang-hang; Xu, Xue-mei; Yang, Bing-chu; Yin, Lin-zi
2016-04-01
The principle of the Van der Pol Duffing oscillator for state transition and for determining critical value is described, which has been studied to indicate that the application of the Van der Pol Duffing oscillator in weak signal detection is feasible. On the basis of this principle, an improved two-coupled differential Van der Pol Duffing oscillator is proposed which can identify signals under any frequency and ameliorate signal-to-noise ratio (SNR). The analytical methods of the proposed model and the construction of the proposed oscillator are introduced in detail. Numerical experiments on the properties of the proposed oscillator compared with those of the Van der Pol Duffing oscillator are carried out. Our numerical simulations have confirmed the analytical treatment. The results demonstrate that this novel oscillator has better detection performance than the Van der Pol Duffing oscillator.
Infinite-time and finite-time synchronization of coupled harmonic oscillators
International Nuclear Information System (INIS)
Cheng, S; Ji, J C; Zhou, J
2011-01-01
This paper studies the infinite-time and finite-time synchronization of coupled harmonic oscillators with distributed protocol in the scenarios with and without a leader. In the absence of a leader, the convergence conditions and the final trajectories that each harmonic oscillator follows are developed. In the presence of a leader, it is shown that all harmonic oscillators can achieve the trajectory of the leader in finite time. Numerical simulations of six coupled harmonic oscillators are given to show the effects of the interaction function parameter, algebraic connectivity and initial conditions on the convergence time.
International Nuclear Information System (INIS)
Wang, C M; Lei, X L
2014-01-01
We study dc-current effects on the magnetoresistance oscillation in a two-dimensional electron gas with Rashba spin-orbit coupling, using the balance-equation approach to nonlinear magnetotransport. In the weak current limit the magnetoresistance exhibits periodical Shubnikov-de Haas oscillation with changing Rashba coupling strength for a fixed magnetic field. At finite dc bias, the period of the oscillation halves when the interbranch contribution to resistivity dominates. With further increasing current density, the oscillatory resistivity exhibits phase inversion, i.e., magnetoresistivity minima (maxima) invert to maxima (minima) at certain values of the dc bias, which is due to the current-induced magnetoresistance oscillation. (paper)
Synchronization of identical chaotic systems through external chaotic driving
International Nuclear Information System (INIS)
Patidar, V.; Sud, K.K.
2005-11-01
In recent years, the study of synchronization of identical chaotic systems subjected to a common fluctuating random driving signal has drawn considerable interest. In this communication, we report that it is possible to achieve synchronization between two identical chaotic systems, which are not coupled directly but subjected to an external chaotic signal. The external chaotic signal may be obtained from any chaotic system identical or non-identical to both identical chaotic systems. Results of numerical simulations on well known Roessler and jerk dynamical systems have been presented. (author)
Aydiner, Ekrem
2018-01-15
In this study, we consider nonlinear interactions between components such as dark energy, dark matter, matter and radiation in the framework of the Friedman-Robertson-Walker space-time and propose a simple interaction model based on the time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra type equations. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for 0 > w de >-1, w dm ≥ 0, w m ≥ 0 and w r ≥ 0 values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in the time evolution of the densities. These results provide that the time evolution of the universe is chaotic. The present model may have potential to solve some of the cosmological problems such as the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, the emergence of the galaxies, matter distribution and large-scale organization of the universe. The model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe and offers a new perspective and a new different scenario for the universe evolution.
Synchronization of chaotic systems
International Nuclear Information System (INIS)
Pecora, Louis M.; Carroll, Thomas L.
2015-01-01
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators
Lai, Yi Ming
2013-07-09
We study ensembles of globally coupled, nonidentical phase oscillators subject to correlated noise, and we identify several important factors that cause noise and coupling to synchronize or desynchronize a system. By introducing noise in various ways, we find an estimate for the onset of synchrony of a system in terms of the coupling strength, noise strength, and width of the frequency distribution of its natural oscillations. We also demonstrate that noise alone can be sufficient to synchronize nonidentical oscillators. However, this synchrony depends on the first Fourier mode of a phase-sensitivity function, through which we introduce common noise into the system. We show that higher Fourier modes can cause desynchronization due to clustering effects, and that this can reinforce clustering caused by different forms of coupling. Finally, we discuss the effects of noise on an ensemble in which antiferromagnetic coupling causes oscillators to form two clusters in the absence of noise. © 2013 American Physical Society.
Aging transition in systems of oscillators with global distributed-delay coupling.
Rahman, B; Blyuss, K B; Kyrychko, Y N
2017-09-01
We consider a globally coupled network of active (oscillatory) and inactive (nonoscillatory) oscillators with distributed-delay coupling. Conditions for aging transition, associated with suppression of oscillations, are derived for uniform and gamma delay distributions in terms of coupling parameters and the proportion of inactive oscillators. The results suggest that for the uniform distribution increasing the width of distribution for the same mean delay allows aging transition to happen for a smaller coupling strength and a smaller proportion of inactive elements. For gamma distribution with sufficiently large mean time delay, it may be possible to achieve aging transition for an arbitrary proportion of inactive oscillators, as long as the coupling strength lies in a certain range.
Stages of chaotic synchronization.
Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.
1998-09-01
In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.
On the dynamics of traveling phase-oscillators with positive and negative couplings
International Nuclear Information System (INIS)
Choi, Jungzae; Choi, Mooyoung; Yoon, Byunggook
2014-01-01
We investigate numerically the dynamics of traveling clusters in systems of phase oscillators, some of which possess positive couplings and others negative couplings. The phase distribution, speed of traveling, and average separation between clusters, as well as the order parameters for positive and negative oscillators, are computed as the ratio of the two coupling constants and the fraction of positive oscillators are varied. The dependence of the traveling speed on these parameters is obtained and is observed to fit well with the numerical data of the systems. With the help of this, we describe the conditions for the traveling state to appear in the systems with and without a periodic driving field.
Ge, Li; Zhao, Nan
2018-04-01
We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is dominated by the quadratic coupling strength g 2. The coherence decays and revives at a period , with the width of coherence peak decreasing as the temperature increases, hence providing a way to measure g 2 precisely without cooling. Unlike the case of linear coupling, here the coherence dynamics never reduces to the classical limit in which the oscillator is classical. Finally, the validity of linear coupling approximation is discussed and the coherence under Hahn-echo is evaluated.
Cross-frequency coupling of brain oscillations in studying motivation and emotion.
Schutter, Dennis J L G; Knyazev, Gennady G
2012-03-01
Research has shown that brain functions are realized by simultaneous oscillations in various frequency bands. In addition to examining oscillations in pre-specified bands, interactions and relations between the different frequency bandwidths is another important aspect that needs to be considered in unraveling the workings of the human brain and its functions. In this review we provide evidence that studying interdependencies between brain oscillations may be a valuable approach to study the electrophysiological processes associated with motivation and emotional states. Studies will be presented showing that amplitude-amplitude coupling between delta-alpha and delta-beta oscillations varies as a function of state anxiety and approach-avoidance-related motivation, and that changes in the association between delta-beta oscillations can be observed following successful psychotherapy. Together these studies suggest that cross-frequency coupling of brain oscillations may contribute to expanding our understanding of the neural processes underlying motivation and emotion.
Induction of Hopf bifurcation and oscillation death by delays in coupled networks
International Nuclear Information System (INIS)
Cheng, C.-Y.
2009-01-01
This work explores a system of two coupled networks that each has four nodes. Delayed effects of short-cuts in each network and the coupling between the two groups are considered. When the short-cut delay is fixed, the arising and death of oscillations are caused by the variational coupling delay.
Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?
Wit, Hero P.; van Dijk, Pim
Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of
Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?
Wit, Hero P; van Dijk, Pim
2012-08-01
Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of SOAEs.
How the self-coupled neuron can affect the chaotic synchronization of network
International Nuclear Information System (INIS)
Jia Chenhui; Wang Jiang; Deng, Bin
2009-01-01
We have calculated 34 kinds of three-cell neuron networks' minimum coupling strength, from the result; we find that a self-coupled neuron can have some effect on the synchronization of the network. The reason is the self-coupled neurons make the number of neurons looks 'decrease', and they decrease the coupling strength of the other neurons which are coupled with them.
Coordination of the Walking Stick Insect Using a System of Nonlinear Coupled Oscillators
National Research Council Canada - National Science Library
Marvin, Daryl J
1992-01-01
The area of walking machines is investigated. A design for a central pattern generator composed of nonlinear coupled oscillators which generates the characteristic gaits of the walking stick insect is presented...
Amplification through chaotic synchronization in spatially extended beam-plasma systems
Moskalenko, Olga I.; Frolov, Nikita S.; Koronovskii, Alexey A.; Hramov, Alexander E.
2017-12-01
In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems. We have also provided the numerical study of physical processes in the chain of beam-plasma systems leading to the chaotic synchronization and the amplification of microwave oscillations power, respectively.
Stability of The Synchronization Manifold in An All-To-All Time LAG- Diffusively Coupled Oscillators
Directory of Open Access Journals (Sweden)
Adu A.M. Wasike
2009-06-01
Full Text Available we consider a lattice system of identical oscillators that are all coupled to one another with a diffusive coupling that has a time lag. We use the natural splitting of the system into synchronized manifold and transversal manifold to estimate the value of the time lag for which the stability of the system follows from that without a time lag. Each oscillator has a unique periodic solution that is attracting.
Stable integrated hyper-parametric oscillator based on coupled optical microcavities.
Armaroli, Andrea; Feron, Patrice; Dumeige, Yannick
2015-12-01
We propose a flexible scheme based on three coupled optical microcavities that permits us to achieve stable oscillations in the microwave range, the frequency of which depends only on the cavity coupling rates. We find that the different dynamical regimes (soft and hard excitation) affect the oscillation intensity, but not their periods. This configuration may permit us to implement compact hyper-parametric sources on an integrated optical circuit with interesting applications in communications, sensing, and metrology.
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode.
Verhagen, E; Deléglise, S; Weis, S; Schliesser, A; Kippenberg, T J
2012-02-01
Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.
Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling.
Ryu, Jung-Wan; Kim, Jong-Ho; Son, Woo-Sik; Hwang, Dong-Uk
2017-08-01
We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.
Synchronization and desynchronization in a network of locally coupled Wilson-Cowan oscillators.
Campbell, S; Wang, D
1996-01-01
A network of Wilson-Cowan (WC) oscillators is constructed, and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis. The network is a 2D matrix, where each oscillator is coupled only to its neighbors. We show analytically that a chain of locally coupled oscillators (the piecewise linear approximation to the WC oscillator) synchronizes, and we present a technique to rapidly entrain finite numbers of oscillators. The coupling strengths change on a fast time scale based on a Hebbian rule. A global separator is introduced which receives input from and sends feedback to each oscillator in the matrix. The global separator is used to desynchronize different oscillator groups. Unlike many other models, the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding Gestalt principles of feature grouping. The ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure/ground segregation based on oscillatory correlation.
He, Yong
2017-06-23
We utilize the surface plasmon field of a metal nanoparticle (MNP) to show strain-mediated coupling in a quantum dot-mechanical resonator hybrid system including a quantum dot (QD) embedded within a conical nanowire (NW) and a MNP in the presence of an external field. Based on the numerical solutions of the master equation, we find that a slow oscillation, originating from the strain-mediated coupling between the QD and the NW, appears in the time evolution of the plasmon field enhancement. The results show that the period (about [Formula: see text]) of the slow oscillation is equal to that of the mechanical resonator of NW, which suggests that the time-resolved measurement of the plasmon field enhancement can be easily achieved based on the current experimental conditions. Its amplitude increases with the increasing strain-mediated coupling strength, and under certain conditions there is a linear relationship between them. The slow oscillation of the plasmon field enhancement provides valuable tools for measurements of the mechanical frequency and the strain-mediated coupling strength.
Phase correlation and clustering of a nearest neighbour coupled oscillators system
International Nuclear Information System (INIS)
EI-Nashar, Hassan F.
2002-09-01
We investigated the phases in a system of nearest neighbour coupled oscillators before complete synchronization in frequency occurs. We found that when oscillators under the influence of coupling form a cluster of the same time-average frequency, their phases start to correlate. An order parameter, which measures this correlation, starts to grow at this stage until it reaches maximum. This means that a time-average phase locked state is reached between the oscillators inside the cluster of the same time- average frequency. At this strength the cluster attracts individual oscillators or a cluster to join in. We also observe that clustering in averaged frequencies orders the phases of the oscillators. This behavior is found at all the transition points studied. (author)
Phase correlation and clustering of a nearest neighbour coupled oscillators system
Ei-Nashar, H F
2002-01-01
We investigated the phases in a system of nearest neighbour coupled oscillators before complete synchronization in frequency occurs. We found that when oscillators under the influence of coupling form a cluster of the same time-average frequency, their phases start to correlate. An order parameter, which measures this correlation, starts to grow at this stage until it reaches maximum. This means that a time-average phase locked state is reached between the oscillators inside the cluster of the same time- average frequency. At this strength the cluster attracts individual oscillators or a cluster to join in. We also observe that clustering in averaged frequencies orders the phases of the oscillators. This behavior is found at all the transition points studied.
Measure synchronization in a coupled Hamiltonian associated with ...
African Journals Online (AJOL)
We report here, the existence of measure synchronization (MS) in a coupled Hamiltonian system associated with the motion of particles in a periodic potential of the pendulum type. We show that the oscillators can assume chaotic MS stares vis quasiperiodic measure desynchrononized state. In the chaotic MS state, the ...
Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Ghesquière, Anne, E-mail: Anne.Ghesquiere@nithep.ac.za; Sinayskiy, Ilya, E-mail: sinayskiy@ukzn.ac.za; Petruccione, Francesco, E-mail: petruccione@ukzn.ac.za
2013-10-15
A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.
Quantum effects in amplitude death of coupled anharmonic self-oscillators
Amitai, Ehud; Koppenhöfer, Martin; Lörch, Niels; Bruder, Christoph
2018-05-01
Coupling two or more self-oscillating systems may stabilize their zero-amplitude rest state, therefore quenching their oscillation. This phenomenon is termed "amplitude death." Well known and studied in classical self-oscillators, amplitude death was only recently investigated in quantum self-oscillators [Ishibashi and Kanamoto, Phys. Rev. E 96, 052210 (2017), 10.1103/PhysRevE.96.052210]. Quantitative differences between the classical and quantum descriptions were found. Here, we demonstrate that for quantum self-oscillators with anharmonicity in their energy spectrum, multiple resonances in the mean phonon number can be observed. This is a result of the discrete energy spectrum of these oscillators, and is not present in the corresponding classical model. Experiments can be realized with current technology and would demonstrate these genuine quantum effects in the amplitude death phenomenon.
Correlations in a chain of three oscillators with nearest neighbour coupling
Idrus, B.; Konstadopoulou, A.; Spiller, T.; Vourdas, A.
2010-04-01
A chain of three oscillators A, B, C with nearest neighbour coupling, is considered. It is shown that the correlations between A, C (which are not coupled directly) can be stronger than the correlations between A, B. Also in some cases various witnesses of entanglement show that A, C are entangled but they cannot lead to any conclusion about A, B.
Interaction of chimera states in a multilayered network of nonlocally coupled oscillators
Goremyko, M. V.; Maksimenko, V. A.; Makarov, V. V.; Ghosh, D.; Bera, B.; Dana, S. K.; Hramov, A. E.
2017-08-01
The processes of formation and evolution of chimera states in the model of a multilayered network of nonlinear elements with complex coupling topology are studied. A two-layered network of nonlocally intralayer-coupled Kuramoto-Sakaguchi phase oscillators is taken as the object of investigation. Different modes implemented in this system upon variation of the degree of interlayer interaction are demonstrated.
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...
Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle
C. Feillet (Céline); C.A. Krusche; F. Tamanini (Filippo); R. Janssens (Roel); R.A. Downey (Roger); P. Martin (Patrick); J.L. Teboul (Jean Louis); S. Saito (Seiji); F.A. Lévi (Francis); T. Bretschneider (Till); G.T.J. van der Horst (Gijsbertus); F. Delaunay (Franck); D.A. Rand (David)
2014-01-01
textabstractDaily synchronous rhythms of cell division at the tissue or organism level are observed in many species and suggest that the circadian clock and cell cycle oscillators are coupled. For mammals, despite known mechanistic interactions, the effect of such coupling on clock and cell cycle
Chaotic exploration and learning of locomotion behaviors.
Shim, Yoonsik; Husbands, Phil
2012-08-01
We present a general and fully dynamic neural system, which exploits intrinsic chaotic dynamics, for the real-time goal-directed exploration and learning of the possible locomotion patterns of an articulated robot of an arbitrary morphology in an unknown environment. The controller is modeled as a network of neural oscillators that are initially coupled only through physical embodiment, and goal-directed exploration of coordinated motor patterns is achieved by chaotic search using adaptive bifurcation. The phase space of the indirectly coupled neural-body-environment system contains multiple transient or permanent self-organized dynamics, each of which is a candidate for a locomotion behavior. The adaptive bifurcation enables the system orbit to wander through various phase-coordinated states, using its intrinsic chaotic dynamics as a driving force, and stabilizes on to one of the states matching the given goal criteria. In order to improve the sustainability of useful transient patterns, sensory homeostasis has been introduced, which results in an increased diversity of motor outputs, thus achieving multiscale exploration. A rhythmic pattern discovered by this process is memorized and sustained by changing the wiring between initially disconnected oscillators using an adaptive synchronization method. Our results show that the novel neurorobotic system is able to create and learn multiple locomotion behaviors for a wide range of body configurations and physical environments and can readapt in realtime after sustaining damage.
DEFF Research Database (Denmark)
Granados, Albert
2017-01-01
Energy harvesting systems based on oscillators aim to capture energy from mechanical oscillations and convert it into electrical energy. Widely extended are those based on piezoelectric materials, whose dynamics are Hamiltonian submitted to different sources of dissipation: damping and coupling...... in Hamiltonian systems and hence could be very useful in energy harvesting applications. This article is a first step towards this goal. We consider two piezoelectric beams submitted to a small forcing and coupled through an electric circuit. By considering the coupling, damping and forcing as perturbations, we...
Controlled perturbation-induced switching in pulse-coupled oscillator networks
International Nuclear Information System (INIS)
Schittler Neves, Fabio; Timme, Marc
2009-01-01
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may in principle support switching processes in these networks and enable novel kinds of neural computations. For small networks of coupled oscillators, we here investigate under which conditions and how system symmetry enforces or forbids certain switching transitions that may be induced by perturbations. For networks of five oscillators, we derive explicit transition rules that for two cluster symmetries deviate from those known from oscillators coupled continuously in time. A third symmetry yields heteroclinic networks that consist of sets of all unstable attractors with that symmetry and the connections between them. Our results indicate that pulse-coupled systems can reliably generate well-defined sets of complex spatiotemporal patterns that conform to specific transition rules. We briefly discuss possible implications for computation with spiking neural systems.
Controlled perturbation-induced switching in pulse-coupled oscillator networks
Energy Technology Data Exchange (ETDEWEB)
Schittler Neves, Fabio; Timme, Marc [Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization, Goettingen, D-37073 (Germany); Bernstein Center for Computational Neuroscience (BCCN), Goettingen (Germany)], E-mail: neves@nld.ds.mpg.de, E-mail: timme@nld.ds.mpg.de
2009-08-28
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may in principle support switching processes in these networks and enable novel kinds of neural computations. For small networks of coupled oscillators, we here investigate under which conditions and how system symmetry enforces or forbids certain switching transitions that may be induced by perturbations. For networks of five oscillators, we derive explicit transition rules that for two cluster symmetries deviate from those known from oscillators coupled continuously in time. A third symmetry yields heteroclinic networks that consist of sets of all unstable attractors with that symmetry and the connections between them. Our results indicate that pulse-coupled systems can reliably generate well-defined sets of complex spatiotemporal patterns that conform to specific transition rules. We briefly discuss possible implications for computation with spiking neural systems.
Beam splitter coupled CdSe optical parametric oscillator
International Nuclear Information System (INIS)
Levinos, N.J.; Arnold, G.P.
1980-01-01
An optical parametric oscillator is disclosed in which the resonant radiation is separated from the pump and output radiation so that it can be manipulated without interfering with them. Thus, for example, very narrow band output may readily be achieved by passing the resonant radiation through a line narrowing device which does not in itself interfere with either the pump radiation or the output radiation
Direction of Coupling from Phases of Interacting Oscillators: A Permutation Information Approach
Bahraminasab, A.; Ghasemi, F.; Stefanovska, A.; McClintock, P. V. E.; Kantz, H.
2008-02-01
We introduce a directionality index for a time series based on a comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well as reveal and quantify asymmetry in bidirectional coupling. It is tested on a numerical model of coupled van der Pol oscillators, and applied to cardiorespiratory data from healthy subjects. There is no need for preprocessing and fine-tuning the parameters, which makes the method very simple, computationally fast and robust.
Chimera states in an ensemble of linearly locally coupled bistable oscillators
Shchapin, D. S.; Dmitrichev, A. S.; Nekorkin, V. I.
2017-11-01
Chimera states in a system with linear local connections have been studied. The system is a ring ensemble of analog bistable self-excited oscillators with a resistive coupling. It has been shown that the existence of chimera states is not due to the nonidentity of oscillators and noise, which is always present in real experiments, but is due to the nonlinear dynamics of the system on invariant tori with various dimensions.
Uwate, Y; Nishio, Y; Stoop, R
2009-01-01
We explore the synchronization and switching behavior of a system of two identical van der Pol oscillators coupled by a stochastically timevarying resistor. Triggered by the time-varying resistor, the system of oscillators switches between synchronized and anti-synchronized behavior. We find that the preference of the synchronized/antisynchronized state is determined by the ratio of the probabilities of the two resistor states. The length of the phases of maintained resistor states, however, ...
Zhu, Yenan; Hsieh, Yee-Hsee; Dhingra, Rishi R.; Dick, Thomas E.; Jacono, Frank J.; Galán, Roberto F.
2013-02-01
Interactions between oscillators can be investigated with standard tools of time series analysis. However, these methods are insensitive to the directionality of the coupling, i.e., the asymmetry of the interactions. An elegant alternative was proposed by Rosenblum and collaborators [M. G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.65.041909 65, 041909 (2002); M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.64.045202 64, 045202 (2001)] which consists in fitting the empirical phases to a generic model of two weakly coupled phase oscillators. This allows one to obtain the interaction functions defining the coupling and its directionality. A limitation of this approach is that a solution always exists in the least-squares sense, even in the absence of coupling. To preclude spurious results, we propose a three-step protocol: (1) Determine if a statistical dependency exists in the data by evaluating the mutual information of the phases; (2) if so, compute the interaction functions of the oscillators; and (3) validate the empirical oscillator model by comparing the joint probability of the phases obtained from simulating the model with that of the empirical phases. We apply this protocol to a model of two coupled Stuart-Landau oscillators and show that it reliably detects genuine coupling. We also apply this protocol to investigate cardiorespiratory coupling in anesthetized rats. We observe reciprocal coupling between respiration and heartbeat and that the influence of respiration on the heartbeat is generally much stronger than vice versa. In addition, we find that the vagus nerve mediates coupling in both directions.
Energy Technology Data Exchange (ETDEWEB)
Márquez, Bicky A., E-mail: bmarquez@ivic.gob.ve; Suárez-Vargas, José J., E-mail: jjsuarez@ivic.gob.ve; Ramírez, Javier A. [Centro de Física, Instituto Venezolano de Investigaciones Científicas, km. 11 Carretera Panamericana, Caracas 1020-A (Venezuela, Bolivarian Republic of)
2014-09-01
Controlled transitions between a hierarchy of n-scroll attractors are investigated in a nonlinear optoelectronic oscillator. Using the system's feedback strength as a control parameter, it is shown experimentally the transition from Van der Pol-like attractors to 6-scroll, but in general, this scheme can produce an arbitrary number of scrolls. The complexity of every state is characterized by Lyapunov exponents and autocorrelation coefficients.
DEFF Research Database (Denmark)
Thoke, Henrik Seir; Tobiesen, Asger; Brewer, Jonathan R.
2015-01-01
We detected very strong coupling between the oscillating concentration of ATP and the dynamics of intracellular water during glycolysis in Saccharomyces cerevisiae. Our results indicate that: i) dipolar relaxation of intracellular water is heterogeneous within the cell and different from dilute...... conditions, ii) water dipolar relaxation oscillates with glycolysis and in phase with ATP concentration, iii) this phenomenon is scale-invariant from the subcellular to the ensemble of synchronized cells and, iv) the periodicity of both glycolytic oscillations and dipolar relaxation are equally affected by D...
International Nuclear Information System (INIS)
Donko, Z.; Schulze, J.; Czarnetzki, U.; Luggenhoelscher, D.
2009-01-01
At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies
Sinusoidal visuomotor tracking: intermittent servo-control or coupled oscillations?
Russell, D M; Sternad, D
2001-12-01
In visuomotor tasks that involve accuracy demands, small directional changes in the trajectories have been taken as evidence of feedback-based error corrections. In the present study variability, or intermittency, in visuomanual tracking of sinusoidal targets was investigated. Two lines of analyses were pursued: First, the hypothesis that humans fundamentally act as intermittent servo-controllers was re-examined, probing the question of whether discontinuities in the movement trajectory directly imply intermittent control. Second, an alternative hypothesis was evaluated: that rhythmic tracking movements are generated by entrainment between the oscillations of the target and the actor, such that intermittency expresses the degree of stability. In 2 experiments, participants (N = 6 in each experiment) swung 1 of 2 different hand-held pendulums, tracking a rhythmic target that oscillated at different frequencies with a constant amplitude. In 1 line of analyses, the authors tested the intermittency hypothesis by using the typical kinematic error measures and spectral analysis. In a 2nd line, they examined relative phase and its variability, following analyses of rhythmic interlimb coordination. The results showed that visually guided corrective processes play a role, especially for slow movements. Intermittency, assessed as frequency and power components of the movement trajectory, was found to change as a function of both target frequency and the manipulandum's inertia. Support for entrainment was found in conditions in which task frequency was identical to or higher than the effector's eigenfrequency. The results suggest that it is the symmetry between task and effector that determines which behavioral regime is dominant.
Effect of parameter mismatch on the dynamics of strongly coupled self sustained oscillators.
Chakrabarty, Nilaj; Jain, Aditya; Lal, Nijil; Das Gupta, Kantimay; Parmananda, Punit
2017-01-01
In this paper, we present an experimental setup and an associated mathematical model to study the synchronization of two self-sustained, strongly coupled, mechanical oscillators (metronomes). The effects of a small detuning in the internal parameters, namely, damping and frequency, have been studied. Our experimental system is a pair of spring wound mechanical metronomes; coupled by placing them on a common base, free to move along a horizontal direction. We designed a photodiode array based non-contact, non-magnetic position detection system driven by a microcontroller to record the instantaneous angular displacement of each oscillator and the small linear displacement of the base, coupling the two. In our system, the mass of the oscillating pendula forms a significant fraction of the total mass of the system, leading to strong coupling of the oscillators. We modified the internal mechanism of the spring-wound "clockwork" slightly, such that the natural frequency and the internal damping could be independently tuned. Stable synchronized and anti-synchronized states were observed as the difference in the parameters was varied in the experiments. The simulation results showed a rapid increase in the phase difference between the two oscillators beyond a certain threshold of parameter mismatch. Our simple model of the escapement mechanism did not reproduce a complete 180° out of phase state. However, the numerical simulations show that increased mismatch in parameters leads to a synchronized state with a large phase difference.
International Nuclear Information System (INIS)
Franzosi, Roberto; Penna, Vittorio
2003-01-01
The dynamics of the three coupled bosonic wells (trimer) containing N bosons is investigated within a standard (mean-field) semiclassical picture based on the coherent-state method. Various periodic solutions (configured as π-like, dimerlike, and vortex states) representing collective modes are obtained analytically when the fixed points of trimer dynamics are identified on the N=const submanifold in the phase space. Hyperbolic, maximum and minimum points are recognized in the fixed-point set by studying the Hessian signature of the trimer Hamiltonian. The system dynamics in the neighborhood of periodic orbits (associated with fixed points) is studied via numeric integration of trimer motion equations, thus revealing a diffused chaotic behavior (not excluding the presence of regular orbits), macroscopic effects of population inversion, and self-trapping. In particular, the behavior of orbits with initial conditions close to the dimerlike periodic orbits shows how the self-trapping effect of dimerlike integrable subregimes is destroyed by the presence of chaos
Li, Jiafu; Xiang, Shuiying; Wang, Haoning; Gong, Junkai; Wen, Aijun
2018-03-01
In this paper, a novel image encryption algorithm based on synchronization of physical random bit generated in a cascade-coupled semiconductor ring lasers (CCSRL) system is proposed, and the security analysis is performed. In both transmitter and receiver parts, the CCSRL system is a master-slave configuration consisting of a master semiconductor ring laser (M-SRL) with cross-feedback and a solitary SRL (S-SRL). The proposed image encryption algorithm includes image preprocessing based on conventional chaotic maps, pixel confusion based on control matrix extracted from physical random bit, and pixel diffusion based on random bit stream extracted from physical random bit. Firstly, the preprocessing method is used to eliminate the correlation between adjacent pixels. Secondly, physical random bit with verified randomness is generated based on chaos in the CCSRL system, and is used to simultaneously generate the control matrix and random bit stream. Finally, the control matrix and random bit stream are used for the encryption algorithm in order to change the position and the values of pixels, respectively. Simulation results and security analysis demonstrate that the proposed algorithm is effective and able to resist various typical attacks, and thus is an excellent candidate for secure image communication application.
Network synchronization in a population of star-coupled fractional nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Wang Junwei, E-mail: wangjunweilj@yahoo.com.c [School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006 (China); Zhang Yanbin [School of Computer Science, Hangzhou Dianzi University, Hangzhou 310018 (China)
2010-03-29
The topic of fractional calculus is enjoying growing interest among mathematicians, physicists and engineers in recent years. For complex network consisting of more than two fractional-order systems, however, it is difficult to establish its synchronization behavior. In this Letter, we study the synchronized motions in a star network of coupled fractional-order systems in which the major element is coupled to each of the noninteracting individual elements. On the basis of the stability theory of linear fractional-order differential equations, we derive a sufficient condition for the stability of the synchronization behavior in such a network. Furthermore, we verify our theoretical results by numerical simulations of star-coupled network with fractional-order chaotic nodes.
International Nuclear Information System (INIS)
Wang Peng-Fei; Xu Zhong-Bin; Ruan Xiao-Dong; Fu Xin
2015-01-01
The Hong–Strogatz (HS) model of globally coupled phase oscillators with attractive and repulsive interactions reflects the fact that each individual (oscillator) has its own attitude (attractive or repulsive) to the same environment (mean field). Previous studies on HS model focused mainly on the stable states on Ott–Antonsen (OA) manifold. In this paper, the eigenvalues of the Jacobi matrix of each fixed point in HS model are explicitly derived, with the aim to understand the local dynamics around each fixed point. Phase transitions are described according to relative population and coupling strength. Besides, the dynamics off OA manifold is studied. (paper)
Generating macroscopic chaos in a network of globally coupled phase oscillators
So, Paul; Barreto, Ernest
2011-01-01
We consider an infinite network of globally coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when the coupling strength varies periodically in time. We identify period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for the macroscopic mean field. Based on recent work that clarified the bifurcation structure of the static bimodal Kuramoto system, we qualitatively describe the mechanism for the generation of such complicated behavior in the time varying case. PMID:21974662
Synchronization scenarios in the Winfree model of coupled oscillators
Gallego, Rafael; Montbrió, Ernest; Pazó, Diego
2017-10-01
Fifty years ago Arthur Winfree proposed a deeply influential mean-field model for the collective synchronization of large populations of phase oscillators. Here we provide a detailed analysis of the model for some special, analytically tractable cases. Adopting the thermodynamic limit, we derive an ordinary differential equation that exactly describes the temporal evolution of the macroscopic variables in the Ott-Antonsen invariant manifold. The low-dimensional model is then thoroughly investigated for a variety of pulse types and sinusoidal phase response curves (PRCs). Two structurally different synchronization scenarios are found, which are linked via the mutation of a Bogdanov-Takens point. From our results, we infer a general rule of thumb relating pulse shape and PRC offset with each scenario. Finally, we compare the exact synchronization threshold with the prediction of the averaging approximation given by the Kuramoto-Sakaguchi model. At the leading order, the discrepancy appears to behave as an odd function of the PRC offset.
Synchronization of complex chaotic systems in series expansion form
International Nuclear Information System (INIS)
Ge Zhengming; Yang Chenghsiung
2007-01-01
This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy
Partial synchronization in diffusively time-delay coupled oscillator networks
Steur, E.; Oguchi, T.; Leeuwen, van C.; Nijmeijer, H.
2012-01-01
We study networks of diffusively time-delay coupled oscillatory units and we show that networks with certain symmetries can exhibit a form of incomplete synchronization called partial synchronization. We present conditions for the existence and stability of partial synchronization modes in networks
Synchronization and basin bifurcations in mutually coupled oscillators
Indian Academy of Sciences (India)
its motivation from its role in understanding the basic features of coupled nonlinear systems and in view of potential applications in communication systems, time ..... [21] U E Vincent, A N Njah, O Akinlade and A R T Solarin, Physica A360, 186 (2006). [22] U E Vincent, A N Njah, O Akinlade and A R T Solarin, Chaos 14, 1018 ...
Pulse-coupled mixed-mode oscillators: Cluster states and extreme noise sensitivity
Karamchandani, Avinash J.; Graham, James N.; Riecke, Hermann
2018-04-01
Motivated by rhythms in the olfactory system of the brain, we investigate the synchronization of all-to-all pulse-coupled neuronal oscillators exhibiting various types of mixed-mode oscillations (MMOs) composed of sub-threshold oscillations (STOs) and action potentials ("spikes"). We focus particularly on the impact of the delay in the interaction. In the weak-coupling regime, we reduce the system to a Kuramoto-type equation with non-sinusoidal phase coupling and the associated Fokker-Planck equation. Its linear stability analysis identifies the appearance of various cluster states. Their type depends sensitively on the delay and the width of the pulses. Interestingly, long delays do not imply slow population rhythms, and the number of emerging clusters only loosely depends on the number of STOs. Direct simulations of the oscillator equations reveal that for quantitative agreement of the weak-coupling theory the coupling strength and the noise have to be extremely small. Even moderate noise leads to significant skipping of STO cycles, which can enhance the diffusion coefficient in the Fokker-Planck equation by two orders of magnitude. Introducing an effective diffusion coefficient extends the range of agreement significantly. Numerical simulations of the Fokker-Planck equation reveal bistability and solutions with oscillatory order parameters that result from nonlinear mode interactions. These are confirmed in simulations of the full spiking model.
Synchronization of vortex-based spin torque nano-oscillators by magnetostatic coupling
Energy Technology Data Exchange (ETDEWEB)
Zaspel, C.E., E-mail: craig.zaspel@umwestern.edu
2015-12-15
Synchronization of two nanopillar oscillators driven by spin torque and coupled through the magnetic dipolar interaction. The dominant mode in each oscillator is gyrotropic motion of the vortex core in an elliptical orbit about the free layer disk center. The dynamic properties of this mode is investigated by solution the coupled Thiele equations with both nanopillar oscillators having identical dimensions, but with a current mismatch. It is noticed that there is a range in the current difference where the oscillators will be synchronized where the vortex gyrotropic motion will be frequency-locked with the radii of gyrotropic motion equal for both disks. There is, however, a phase shift between the gyrotropic motion with the smaller current disk lagging the higher current disk by a few degrees. - Highlights: • Vortex-based nanopillar oscillators re synchronized by the dipolar interaction. • There is a range of frequencies where both oscillators will frequency-locked. • There are upper and lower critical currents defining a locking range.
Study of λφ4 theory in the coupled independent double-oscillator approximation
International Nuclear Information System (INIS)
Bray, H.; Stevenson, P.M.
1992-01-01
A scalar field can be viewed as an infinite set of coupled oscillators, one at each lattice point in space, as the lattice spacing goes to zero. Λφ 4 theory considers the case when each oscillator is given a potential of the form V(φ) = 1/2m 2 φ 2 + λφ 4 . The question the authors wish to investigate is whether or not such a potential can cause spontaneous symmetry breaking. They approach this problem by defining an open-quotes effective potentialclose quotes which takes into account the quantum effects of the oscillators. This is useful because a double well effective potential would imply spontaneous symmetry breaking. They consider a variational calculation with a trial wavefunctional that is a product of independent double-oscillator wavefunctions. Each double-oscillator wavefunction is defined to be the sum of two Gaussians with the same widths, centered around φ o . They then define the effective potential at φ o to be the energy density resulting from this variational calculation, where the separation and the width of the Gaussians are the parameters which are allowed to vary. They call this the open-quotes Coupled Independent Double-Oscillator Approximation.close quotes The goal of this research is to compute this effective potential, renormalize the variables, and to gain additional insight into whether or not spontaneous symmetry breaking occurs
Energy Technology Data Exchange (ETDEWEB)
Emenheiser, Jeffrey [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Chapman, Airlie; Mesbahi, Mehran [William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States); Pósfai, Márton [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Crutchfield, James P. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); D' Souza, Raissa M. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States)
2016-09-15
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.
The Coupling between Gamma and Theta Oscillation and Visuotactile Integration Process
Directory of Open Access Journals (Sweden)
Noriaki Kanayama
2011-10-01
Full Text Available Some researches revealed the relationship between multisensory integration and EEG oscillations. Previous studies revealed that the visuotactile integration process could be explained by gamma and theta band oscillation. In addition, recent studies have showed the possibility that a coupling between oscillations at the different frequency bands plays an important role on the multisensory integration system. This study aimed to investigate whether the gamma and theta oscillations show the coupling during the visuotactile integration. Using congruency effect paradigm only for left hand, we measured scalp EEG during simultaneous presentation of “spatially congruent” or “spatially incongruent” visuotactile stimuli. In Experiment 1, the proportion of the spatially congruent trials (80% vs 20% was changed across the experimental blocks. The results showed that the relationship between gamma power and theta phase at the parietal area was modulated by the proportion. In Experiment 2, the saliency of the vibration stimulus (0dB vs −20dB was changed across trials. The results showed that the relationship between gamma power and theta phase was immune to the saliency. These results suggest that multisensory integration process has a plasticity, which is modulated by the proportion of congruent trial, and the process could be explained by the coupling between gamma/theta oscillations.
Tuning the synchronization of a network of weakly coupled self-oscillating gels via capacitors
Fang, Yan; Yashin, Victor V.; Dickerson, Samuel J.; Balazs, Anna C.
2018-05-01
We consider a network of coupled oscillating units, where each unit comprises a self-oscillating polymer gel undergoing the Belousov-Zhabotinsky (BZ) reaction and an overlaying piezoelectric (PZ) cantilever. Through chemo-mechano-electrical coupling, the oscillations of the networked BZ-PZ units achieve in-phase or anti-phase synchronization, enabling, for example, the storage of information within the system. Herein, we develop numerical and computational models to show that the introduction of capacitors into the BZ-PZ system enhances the dynamical behavior of the oscillating network by yielding additional stable synchronization modes. We specifically show that the capacitors lead to a redistribution of charge in the system and alteration of the force that the PZ cantilevers apply to the underlying gel. Hence, the capacitors modify the strength of the coupling between the oscillators in the network. We utilize a linear stability analysis to determine the phase behavior of BZ-PZ networks encompassing different capacitances, force polarities, and number of units and then verify our findings with numerical simulations. Thus, through analytical calculations and numerical simulations, we determine the impact of the capacitors on the existence of the synchronization modes, their stability, and the rate of synchronization within these complex dynamical systems. The findings from our study can be used to design robotic materials that harness the materials' intrinsic, responsive properties to perform such functions as sensing, actuation, and information storage.
Mansingka, Abhinav S.
2014-06-18
This paper introduces fully digital implementations of four di erent systems in the 3rd order jerk-equation based chaotic family using the Euler approximation. The digitization approach enables controllable chaotic systems that reliably provide sinusoidal or chaotic output based on a selection input. New systems are introduced, derived using logical and arithmetic operations between two system implementations of different bus widths, with up to 100x higher maximum Lyapunov exponent than the original jerkequation based chaotic systems. The resulting chaotic output is shown to pass the NIST sp. 800-22 statistical test suite for pseudorandom number generators without post-processing by only eliminating the statistically defective bits. The systems are designed in Verilog HDL and experimentally verified on a Xilinx Virtex 4 FPGA for a maximum throughput of 15.59 Gbits/s for the native chaotic output and 8.77 Gbits/s for the resulting pseudo-random number generators.
Phase models and clustering in networks of oscillators with delayed coupling
Campbell, Sue Ann; Wang, Zhen
2018-01-01
We consider a general model for a network of oscillators with time delayed coupling where the coupling matrix is circulant. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to determine model independent existence and stability results for symmetric cluster solutions. Our results extend previous work to systems with time delay and a more general coupling matrix. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies.
Influences of adding negative couplings between cliques of Kuramoto-like oscillators
Yang, Li-xin; Lin, Xiao-lin; Jiang, Jun
2018-06-01
We study the dynamics in a clustered network of coupled oscillators by considering positive and negative coupling schemes. Second order oscillators can be interpreted as a model of consumers and generators working in a power network. Numerical results indicate that coupling strategies play an important role in the synchronizability of the clustered power network. It is found that the synchronizability can be enhanced as the positive intragroup connections increase. Meanwhile, when the intragroup interactions are positive and the probability p that two nodes belonging to different clusters are connected is increased, the synchronization has better performance. Besides, when the intragroup connections are negative, it is observed that the power network has poor synchronizability as the probability p increases. Our simulation results can help us understand the collective behavior of the power network with positive and negative couplings.
Coupled oscillators in identification of nonlinear damping of a real parametric pendulum
Olejnik, Paweł; Awrejcewicz, Jan
2018-01-01
A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.
Thermal coupling and effect of subharmonic synchronization in a system of two VO2 based oscillators
Velichko, Andrey; Belyaev, Maksim; Putrolaynen, Vadim; Perminov, Valentin; Pergament, Alexander
2018-03-01
We explore a prototype of an oscillatory neural network (ONN) based on vanadium dioxide switching devices. The model system under study represents two oscillators based on thermally coupled VO2 switches. Numerical simulation shows that the effective action radius RTC of coupling depends both on the total energy released during switching and on the average power. It is experimentally and numerically proved that the temperature change ΔT commences almost synchronously with the released power peak and T-coupling reveals itself up to a frequency of about 10 kHz. For the studied switching structure configuration, the RTC value varies over a wide range from 4 to 45 μm, depending on the external circuit capacitance C and resistance Ri, but the variation of Ri is more promising from the practical viewpoint. In the case of a "weak" coupling, synchronization is accompanied by attraction effect and decrease of the main spectra harmonics width. In the case of a "strong" coupling, the number of effects increases, synchronization can occur on subharmonics resulting in multilevel stable synchronization of two oscillators. An advanced algorithm for synchronization efficiency and subharmonic ratio calculation is proposed. It is shown that of the two oscillators the leading one is that with a higher main frequency, and, in addition, the frequency stabilization effect is observed. Also, in the case of a strong thermal coupling, the limit of the supply current parameters, for which the oscillations exist, expands by ∼10%. The obtained results have a universal character and open up a new kind of coupling in ONNs, namely, T-coupling, which allows for easy transition from 2D to 3D integration. The effect of subharmonic synchronization hold promise for application in classification and pattern recognition.
Electron screening and kinetic-energy oscillations in a strongly coupled plasma
International Nuclear Information System (INIS)
Chen, Y.C.; Simien, C.E.; Laha, S.; Gupta, P.; Martinez, Y.N.; Mickelson, P.G.; Nagel, S.B.; Killian, T.C.
2004-01-01
We study equilibration of strongly coupled ions in an ultracold neutral plasma produced by photoionizing laser-cooled and trapped atoms. By varying the electron temperature, we show that electron screening modifies the equilibrium ion temperature. Even with few electrons in a Debye sphere, the screening is well described by a model using a Yukawa ion-ion potential. We also observe damped oscillations of the ion kinetic energy that are a unique feature of equilibration of a strongly coupled plasma
Numerical study of unsteady flows past oscillating airfoils using direct zonal coupling method
International Nuclear Information System (INIS)
Zhang, F.; Khalid, M.
2005-01-01
A direct zonal coupling method was proposed for solving the flows past oscillating airfoils in this study. The entire computational domain was divided into inner and outer zones. The grid in the inner zone is moving with the oscillation of the airfoil, whereas the grid in the outer zone is artificially adjusted to the position consistent with the inner zone grid. The governing equations in the moving frame (the rotation potential energy is included) and those under the stationary frame were applied to inner and outer zones, respectively. By using this kind of treatment, the grid on the zonal interface is 1-to-1 matched. The coupling between the two zones is direct. Both the geometric and flow conservations are entirely satisfied. The NACA0012 and NLR7301 airfoils with oscillations were used as the test cases. The accuracy of the proposed method was demonstrated by the computational results compared with the experimental data.(author)
Du, Lei; Fan, Chu-Hui; Zhang, Han-Xiao; Wu, Jin-Hui
2017-11-20
We study the synchronization behaviors of two indirectly coupled mechanical oscillators of different frequencies in a doublecavity optomechanical system. It is found that quantum synchronization is roughly vanishing though classical synchronization seems rather good when each cavity mode is driven by an external field in the absence of temporal modulations. By periodically modulating cavity detunings or driving amplitudes, however, it is possible to observe greatly enhanced quantum synchronization accompanied with nearly perfect classical synchronization. The level of quantum synchronization observed here is, in particular, much higher than that for two directly coupled mechanical oscillators. Note also that the modulation on cavity detunings is more appealing than that on driving amplitudes when the robustness of quantum synchronization is examined against the bath's mean temperature or the oscillators' frequency difference.
Coupled Josephson local oscillator and detector experiments in the terahertz regime
International Nuclear Information System (INIS)
Robertazzi, R.P.; Hallen, H.D.; Buhrman, R.A.
1988-01-01
Recent coupled Josephson junction experiments in the authors' laboratory have demonstrated that high critical current density tunnel junctions can serve as effective local oscillators at frequencies up to and in excess of the gap sum frequency of the junction, i.e. well above 1 Terahertz for a niobium or niobium compound tunnel junction. While the details of the behavior of such a THz. oscillator were found not to be in accord with the predictions of the accepted theory of the A.C. Josephson effect in the gap region significant radiation could be capacitively coupled from the oscillator junction to an adjacent junction, sufficient for SIS mixer experiments at Terahertz frequencies. Research efforts are now under way to further extend and expand these studies. A high critical current density all NbN tunnel junction system is now under development for Terahertz applications and a new set of coupled Josephson oscillator - SIS detector experiments is being initiated using NbN tunnel junctions. In this paper the authors review the original coupled junction high frequency experiments and report on the recent progress of the current NbN tunnel junction experiments
Statistical properties of multiphoton time-dependent three-boson coupled oscillators
Czech Academy of Sciences Publication Activity Database
Abdalla, M. S.; Peřina, Jan; Křepelka, Jaromír
2006-01-01
Roč. 23, č. 6 (2006), s. 1146-1160 ISSN 0740-3224 R&D Projects: GA MŠk(CZ) OC P11.003 Institutional research plan: CEZ:AV0Z10100522 Keywords : quantum statistic * coupled oscillators * multiphoton Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.002, year: 2006
Two Coupled Oscillators : Simulations of the Circadian Pacemaker in Mammalian Activity Rhythms
Daan, Serge; Berde, Charles
1978-01-01
In the activity rhythms of captive small mammals a variety of features, most notably “splitting”, sugges that two coupled oscillators may constitute the pacemaker system which underlies the rhythms. A proposed phenomenological model is developed and expanded here using an explicit quantitative
Ueki, Takeshi; Yoshida, Ryo
2014-06-14
Herein, we summarise the recent developments in self-oscillating polymeric materials based on the concepts of supramolecular chemistry, where aggregates of molecular building blocks with non-covalent bonds evolve the temporal or spatiotemporal structure. By utilising the rhythmic oscillation of the association/dissociation of molecular aggregates coupled with the redox oscillation by the BZ reaction, novel soft materials that express similar functions as those of living matter will be achieved. Further, from the viewpoint of materials science, our recent approach to prepare self-oscillating materials that operate long-term under mild conditions will be introduced.
Mathematical structure of Rabi oscillations in the strong coupling regime
International Nuclear Information System (INIS)
Fujii, Kazuyuki
2003-01-01
In this paper, we generalize the Jaynes-Cummings Hamiltonian by making use of some operators based on Lie algebras su(1, 1) and su(2), and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators (Fujii K 2002 Preprint quant-ph/0202081) under the rotating-wave approximation. In the first half, we make a general review of coherent operators and generalized coherent ones based on Lie algebras su(1, 1) and su(2). In the latter half, we carry out a detailed examination of Frasca (Frasca M 2001 Preprint quant-ph/0111134) and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in quantum computation. Lastly, we make a brief comment on application to holonomic quantum computation
Connection adaption for control of networked mobile chaotic agents.
Zhou, Jie; Zou, Yong; Guan, Shuguang; Liu, Zonghua; Xiao, Gaoxi; Boccaletti, S
2017-11-22
In this paper, we propose a strategy for the control of mobile chaotic oscillators by adaptively rewiring connections between nearby agents with local information. In contrast to the dominant adaptive control schemes where coupling strength is adjusted continuously according to the states of the oscillators, our method does not request adaption of coupling strength. As the resulting interaction structure generated by this proposed strategy is strongly related to unidirectional chains, by investigating synchronization property of unidirectional chains, we reveal that there exists a certain coupling range in which the agents could be controlled regardless of the length of the chain. This feature enables the adaptive strategy to control the mobile oscillators regardless of their moving speed. Compared with existing adaptive control strategies for networked mobile agents, our proposed strategy is simpler for implementation where the resulting interaction networks are kept unweighted at all time.
Synchronization ability of coupled cell-cycle oscillators in changing environments
2012-01-01
Background The biochemical oscillator that controls periodic events during the Xenopus embryonic cell cycle is centered on the activity of CDKs, and the cell cycle is driven by a protein circuit that is centered on the cyclin-dependent protein kinase CDK1 and the anaphase-promoting complex (APC). Many studies have been conducted to confirm that the interactions in the cell cycle can produce oscillations and predict behaviors such as synchronization, but much less is known about how the various elaborations and collective behavior of the basic oscillators can affect the robustness of the system. Therefore, in this study, we investigate and model a multi-cell system of the Xenopus embryonic cell cycle oscillators that are coupled through a common complex protein, and then analyze their synchronization ability under four different external stimuli, including a constant input signal, a square-wave periodic signal, a sinusoidal signal and a noise signal. Results Through bifurcation analysis and numerical simulations, we obtain synchronization intervals of the sensitive parameters in the individual oscillator and the coupling parameters in the coupled oscillators. Then, we analyze the effects of these parameters on the synchronization period and amplitude, and find interesting phenomena, e.g., there are two synchronization intervals with activation coefficient in the Hill function of the activated CDK1 that activates the Plk1, and different synchronization intervals have distinct influences on the synchronization period and amplitude. To quantify the speediness and robustness of the synchronization, we use two quantities, the synchronization time and the robustness index, to evaluate the synchronization ability. More interestingly, we find that the coupled system has an optimal signal strength that maximizes the synchronization index under different external stimuli. Simulation results also show that the ability and robustness of the synchronization for the square
Sato, Katsuhiko; Shima, Shin-ichiro
2015-10-01
We investigate a phase model that includes both locally attractive and globally repulsive coupling in one dimension. This model exhibits nontrivial spatiotemporal patterns that have not been observed in systems that contain only local or global coupling. Depending on the relative strengths of the local and global coupling and on the form of global coupling, the system can show a spatially uniform state (in-phase synchronization), a monotonically increasing state (traveling wave), and three types of oscillations of relative phase difference. One of the oscillations of relative phase difference has the characteristic of being locally unstable but globally attractive. That is, any small perturbation to the periodic orbit in phase space destroys its periodic motion, but after a long time the system returns to the original periodic orbit. This behavior is closely related to the emergence of saddle two-cluster states for global coupling only, which are connected to each other by attractive heteroclinic orbits. The mechanism of occurrence of this type of oscillation is discussed.
Identical synchronization of coupled Rossler systems
DEFF Research Database (Denmark)
Yanchuk, S.; Maistrenko, Y.; Mosekilde, Erik
1999-01-01
Analyzing the transverse stability of low periodic orbits embedded in the synchronized chaotic state for a system of two coupled Rössler oscillators, we obtain the conditions for synchronization and determine the coupling parameters for which riddled basins of attraction may arise. It is shown how...
Synchronization in slowly switching networks of coupled oscillators
Zhou, Jie; Zou, Yong; Guan, Shuguang; Liu, Zonghua; Boccaletti, S.
2016-01-01
Networks whose structure of connections evolves in time constitute a big challenge in the study of synchronization, in particular when the time scales for the evolution of the graph topology are comparable with (or even longer than) those pertinent to the units’ dynamics. We here focus on networks with a slow-switching structure, and show that the necessary conditions for synchronization, i.e. the conditions for which synchronization is locally stable, are determined by the time average of the largest Lyapunov exponents of transverse modes of the switching topologies. Comparison between fast- and slow-switching networks allows elucidating that slow-switching processes prompt synchronization in the cases where the Master Stability Function is concave, whereas fast-switching schemes facilitate synchronization for convex curves. Moreover, the condition of slow-switching enables the introduction of a control strategy for inducing synchronization in networks with arbitrary structure and coupling strength, which is of evident relevance for broad applications in real world systems. PMID:27779253
Williams, Caitlin R. S.; Sorrentino, Francesco; Murphy, Thomas E.; Roy, Rajarshi
2013-12-01
We experimentally study the complex dynamics of a unidirectionally coupled ring of four identical optoelectronic oscillators. The coupling between these systems is time-delayed in the experiment and can be varied over a wide range of delays. We observe that as the coupling delay is varied, the system may show different synchronization states, including complete isochronal synchrony, cluster synchrony, and two splay-phase states. We analyze the stability of these solutions through a master stability function approach, which we show can be effectively applied to all the different states observed in the experiment. Our analysis supports the experimentally observed multistability in the system.
Mean-field behavior in coupled oscillators with attractive and repulsive interactions.
Hong, Hyunsuk; Strogatz, Steven H
2012-05-01
We consider a variant of the Kuramoto model of coupled oscillators in which both attractive and repulsive pairwise interactions are allowed. The sign of the coupling is assumed to be a characteristic of a given oscillator. Specifically, some oscillators repel all the others, thus favoring an antiphase relationship with them. Other oscillators attract all the others, thus favoring an in-phase relationship. The Ott-Antonsen ansatz is used to derive the exact low-dimensional dynamics governing the system's long-term macroscopic behavior. The resulting analytical predictions agree with simulations of the full system. We explore the effects of changing various parameters, such as the width of the distribution of natural frequencies and the relative strengths and proportions of the positive and negative interactions. For the particular model studied here we find, unexpectedly, that the mixed interactions produce no new effects. The system exhibits conventional mean-field behavior and displays a second-order phase transition like that found in the original Kuramoto model. In contrast to our recent study of a different model with mixed interactions [Phys. Rev. Lett. 106, 054102 (2011)], the π state and traveling-wave state do not appear for the coupling type considered here.
Spatiotemporal coding of inputs for a system of globally coupled phase oscillators
Wordsworth, John; Ashwin, Peter
2008-12-01
We investigate the spatiotemporal coding of low amplitude inputs to a simple system of globally coupled phase oscillators with coupling function g(ϕ)=-sin(ϕ+α)+rsin(2ϕ+β) that has robust heteroclinic cycles (slow switching between cluster states). The inputs correspond to detuning of the oscillators. It was recently noted that globally coupled phase oscillators can encode their frequencies in the form of spatiotemporal codes of a sequence of cluster states [P. Ashwin, G. Orosz, J. Wordsworth, and S. Townley, SIAM J. Appl. Dyn. Syst. 6, 728 (2007)]. Concentrating on the case of N=5 oscillators we show in detail how the spatiotemporal coding can be used to resolve all of the information that relates the individual inputs to each other, providing that a long enough time series is considered. We investigate robustness to the addition of noise and find a remarkable stability, especially of the temporal coding, to the addition of noise even for noise of a comparable magnitude to the inputs.
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
International Nuclear Information System (INIS)
Kao, Jhih-Yuan; Chou, Chung-Hsien
2016-01-01
We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number. (paper)
Characterization of chaotic electroconvection near flat electrodes under oscillatory voltages
Kim, Jeonglae; Davidson, Scott; Mani, Ali
2017-11-01
Onset of hydrodynamic instability and chaotic electroconvection in aqueous systems are studied by directly solving the two-dimensional coupled Poisson-Nernst-Planck and Navier-Stokes equations. An aqueous binary electrolyte is bounded by two planar electrodes where time-harmonic voltage is applied at a constant oscillation frequency. The governing equations are solved using a fully-conservative second-order-accurate finite volume discretization and a second-order implicit Euler time advancement. At a sufficiently high amplitude of applied voltage, the system exhibits chaotic behaviors involving strong hydrodynamic mixing and enhanced electroconvection. The system responses are characterized as a function of oscillation frequency, voltage magnitude, and the ratio of diffusivities of two ion species. Our results indicate that electroconvection is most enhanced for frequencies on the order of inverse system RC time scale. We will discuss the dependence of this optimal frequency on the asymmetry of the diffusion coefficients of ionic species. Supported by the Stanford's Precourt Institute.
Plexcitons: The Role of Oscillator Strengths and Spectral Widths in Determining Strong Coupling
Energy Technology Data Exchange (ETDEWEB)
Thomas, Reshmi [School; Thomas, Anoop [School; Pullanchery, Saranya [School; Joseph, Linta [School; Somasundaran, Sanoop Mambully [School; Swathi, Rotti Srinivasamurthy [School; Gray, Stephen K. [Center; Thomas, K. George [School
2018-01-05
Strong coupling interactions between plasmon and exciton-based excitations have been proposed to be useful in the design of optoelectronic systems. However, the role of various optical parameters dictating the plasmon-exciton (plexciton) interactions is less understood. Herein, we propose an inequality for achieving strong coupling between plasmons and excitons through appropriate variation of their oscillator strengths and spectral widths. These aspects are found to be consistent with experiments on two sets of free-standing plexcitonic systems obtained by (i) linking fluorescein isothiocyanate on Ag nanoparticles of varying sizes through silane coupling and (ii) electrostatic binding of cyanine dyes on polystyrenesulfonate-coated Au nanorods of varying aspect ratios. Being covalently linked on Ag nanoparticles, fluorescein isothiocyanate remains in monomeric state, and its high oscillator strength and narrow spectral width enable us to approach the strong coupling limit. In contrast, in the presence of polystyrenesulfonate, monomeric forms of cyanine dyes exist in equilibrium with their aggregates: Coupling is not observed for monomers and H-aggregates whose optical parameters are unfavorable. The large aggregation number, narrow spectral width, and extremely high oscillator strength of J-aggregates of cyanines permit effective delocalization of excitons along the linear assembly of chromophores, which in turn leads to efficient coupling with the plasmons. Further, the results obtained from experiments and theoretical models are jointly employed to describe the plexcitonic states, estimate the coupling strengths, and rationalize the dispersion curves. The experimental results and the theoretical analysis presented here portray a way forward to the rational design of plexcitonic systems attaining the strong coupling limits.
Volcanic CO2 Emissions and Glacial Cycles: Coupled Oscillations
Burley, J. M.; Huybers, P. J.; Katz, R. F.
2016-12-01
Following the mid-Pleistocene transition, the dominant period of glacial cycles changed from 40 ka to 100 ka. It is broadly accepted that the 40 ka glacial cycles were driven by cyclical changes in obliquity. However, this forcing does not explain the 100 ka glacial cycles. Mechanisms proposed for 100 ka cycles include isostatic bed depression and proglacial lakes destabilising the Laurentide ice sheet, non-linear responses to orbital eccentricity, and Antarctic ice sheets influencing deep-ocean stratification. None of these are universally accepted. Here we investigate the hypothesis that variations in volcanic CO2 emissions can cause 100 ka glacial cycles. Any proposed mechanism for 100 ka glacial cycles must give the Earth's climate system a memory of 10^4 - 10^5years. This timescale is difficult to achieve for surface processes, however it is possible for the solid Earth. Recent work suggests volcanic CO2 emissions change in response to glacial cycles [1] and that there could be a 50 ka delay in that response [2]. Such a lagged response could drive glacial cycles from 40 ka cycles to an integer multiple of the forcing period. Under what conditions could the climate system admit such a response? To address this, we use a simplified climate model modified from Huybers and Tziperman [3]. Our version comprises three component models for energy balance, ice sheet growth and atmospheric CO2 concentration. The model is driven by insolation alone with other components varying according to a system of coupled, differential equations. The model is run for 500 ka to produce several glacial cycles and the resulting changes in global ice volume and atmospheric CO2 concentration.We obtain a switch from 40 ka to 100 ka cycles as the volcanic CO2 response to glacial cycles is increased. These 100 ka cycles are phase-locked to obliquity, lasting 80 or 120 ka. Whilst the MOR response required (in this model) is larger than plausible estimates based on [2], it illustrates the
Synchronization of hyperchaotic oscillators
DEFF Research Database (Denmark)
Tamasevicius, A.; Cenys, A.; Mykolaitis, G.
1997-01-01
Synchronization of chaotic oscillators is believed to have promising applications in secure communications. Hyperchaotic systems with multiple positive Lyapunov exponents (LEs) have an advantage over common chaotic systems with only one positive LE. Three different types of hyperchaotic electronic...... oscillators are investigated demonstrating synchronization by means of only one properly selected variable....
Duggento, Andrea; Stankovski, Tomislav; McClintock, Peter V. E.; Stefanovska, Aneta
2012-12-01
Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.024101 109, 024101 (2012)] introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time-evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically generated data, data from an analog electronic circuit, and cardiorespiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.
Dynamical bifurcation in a system of coupled oscillators with slowly varying parameters
Directory of Open Access Journals (Sweden)
Igor Parasyuk
2016-08-01
Full Text Available This paper deals with a fast-slow system representing n nonlinearly coupled oscillators with slowly varying parameters. We find conditions which guarantee that all omega-limit sets near the slow surface of the system are equilibria and invariant tori of all dimensions not exceeding n, the tori of dimensions less then n being hyperbolic. We show that a typical trajectory demonstrates the following transient process: while its slow component is far from the stationary points of the slow vector field, the fast component exhibits damping oscillations; afterwards, the former component enters and stays in a small neighborhood of some stationary point, and the oscillation amplitude of the latter begins to increase; eventually the trajectory is attracted by an n-dimesional invariant torus and a multi-frequency oscillatory regime is established.
Two-step approach to the dynamics of coupled anharmonic oscillators
International Nuclear Information System (INIS)
Chung, N. N.; Chew, L. Y.
2009-01-01
We have further extended the two-step approach developed by Chung and Chew [N. N. Chung and L. Y. Chew, Phys. Rev. A 76, 032113 (2007)] to the solution of the quantum dynamics of general systems of N-coupled anharmonic oscillators. The idea is to employ an optimized basis set to represent the dynamical quantum states of these oscillator systems. The set is generated via the action of the optimized Bogoliubov transformed bosonic operators on the optimal squeezed vacuum product state. The procedure requires (i) applying the two-step approach to the eigendecomposition of the time evolution operator and (ii) transforming the representation of the initial state from the original to the optimal bases. We have applied the formalism to examine the dynamics of squeezing and entanglement of several anharmonic oscillator systems.
International Nuclear Information System (INIS)
Gudkov, V.V.; Zhevstovskikh, I.V.; Zimbovskaya, N.A.; Okulov, V.I.
1991-01-01
The quantum oscillations are studied of ellipcity, the rotation angle of the ultrasound polarization plane, the velocity and absorption of waves polarized circularly at the 196 MHz frequency in a tungsten single crystal in magnetic field of 30-80 kOe at temperature 1,8 K. The oscillation amplitudes of ellipticity and rotation angle of the ultrasound polarization plane beyond the Doppler-shifted cyclotron resonance are found to vary nonmonotonously with field and to be large enough, so that they are not described by the simple expressions for high fields. The explanation for the oscillation amplification of the polarization parameters is given within the theory involving the ultrasound-spiral wave coupling predicted by Kaner and Skobov. The quantitative comparison in details demonstrates a good agreement in the theory and experimental data and allows to find the numerical values of new parameters characterizing the Fermi surface, electron relaxation frequency, and deformation potential
Time-delay-induced amplitude death in chaotic map lattices and its avoiding control
International Nuclear Information System (INIS)
Konishi, Keiji; Kokame, Hideki
2007-01-01
The present Letter deals with amplitude death in chaotic map lattices coupled with a diffusive delay connection. It is shown that if a fixed point of the individual map satisfies an odd-number property, then amplitude death never occurs at the fixed point for any number of the maps, coupling strength, and delay time. From the viewpoint of engineering applications that utilize oscillatory behavior in coupled oscillators, death would be undesirable. This Letter proposes a feedback controller, which is added to each chaotic map, such that the fixed point of the individual map satisfies the odd-number property. Accordingly, it is guaranteed that death never occurs in the controlled chaotic-map-lattice. It is verified that the proposed controller works well in numerical simulations
Spiral wave chimera states in large populations of coupled chemical oscillators
Totz, Jan Frederik; Rode, Julian; Tinsley, Mark R.; Showalter, Kenneth; Engel, Harald
2018-03-01
The coexistence of coherent and incoherent dynamics in a population of identically coupled oscillators is known as a chimera state1,2. Discovered in 20023, this counterintuitive dynamical behaviour has inspired extensive theoretical and experimental activity4-15. The spiral wave chimera is a particularly remarkable chimera state, in which an ordered spiral wave rotates around a core consisting of asynchronous oscillators. Spiral wave chimeras were theoretically predicted in 200416 and numerically studied in a variety of systems17-23. Here, we report their experimental verification using large populations of nonlocally coupled Belousov-Zhabotinsky chemical oscillators10,18 in a two-dimensional array. We characterize previously unreported spatiotemporal dynamics, including erratic motion of the asynchronous spiral core, growth and splitting of the cores, as well as the transition from the chimera state to disordered behaviour. Spiral wave chimeras are likely to occur in other systems with long-range interactions, such as cortical tissues24, cilia carpets25, SQUID metamaterials26 and arrays of optomechanical oscillators9.
Coupled-oscillator theory of dispersion and Casimir-Polder interactions
Energy Technology Data Exchange (ETDEWEB)
Berman, P. R.; Ford, G. W. [Physics Department, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109-1040 (United States); Milonni, P. W. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (United States)
2014-10-28
We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength. However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r{sup −4}, a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called “remarkable formula” for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented.
Coupled-oscillator theory of dispersion and Casimir-Polder interactions
International Nuclear Information System (INIS)
Berman, P. R.; Ford, G. W.; Milonni, P. W.
2014-01-01
We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength. However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r −4 , a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called “remarkable formula” for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented
Wang, Peng-Fei; Ruan, Xiao-Dong; Xu, Zhong-Bin; Fu, Xin
2015-11-01
The Hong-Strogatz (HS) model of globally coupled phase oscillators with attractive and repulsive interactions reflects the fact that each individual (oscillator) has its own attitude (attractive or repulsive) to the same environment (mean field). Previous studies on HS model focused mainly on the stable states on Ott-Antonsen (OA) manifold. In this paper, the eigenvalues of the Jacobi matrix of each fixed point in HS model are explicitly derived, with the aim to understand the local dynamics around each fixed point. Phase transitions are described according to relative population and coupling strength. Besides, the dynamics off OA manifold is studied. Supported by the National Basic Research Program of China under Grant No. 2015CB057301, the Applied Research Project of Public Welfare Technology of Zhejiang Province under Grant No. 201SC31109 and China Postdoctoral Science Foundation under Grant No. 2014M560483
Nonstandard scaling law of fluctuations in finite-size systems of globally coupled oscillators.
Nishikawa, Isao; Tanaka, Gouhei; Aihara, Kazuyuki
2013-08-01
Universal scaling laws form one of the central issues in physics. A nonstandard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems. Recently, we found that a statistical quantity related to fluctuations follows a nonstandard scaling law with respect to the system size in a synchronized state of globally coupled nonidentical phase oscillators [I. Nishikawa et al., Chaos 22, 013133 (2012)]. However, it is still unclear how widely this nonstandard scaling law is observed. In the present paper, we discuss the conditions required for the unusual scaling law in globally coupled oscillator systems and validate the conditions by numerical simulations of several different models.
Explosive death of conjugate coupled Van der Pol oscillators on networks
Zhao, Nannan; Sun, Zhongkui; Yang, Xiaoli; Xu, Wei
2018-06-01
Explosive death phenomenon has been gradually gaining attention of researchers due to the research boom of explosive synchronization, and it has been observed recently for the identical or nonidentical coupled systems in all-to-all network. In this work, we investigate the emergence of explosive death in networked Van der Pol (VdP) oscillators with conjugate variables coupling. It is demonstrated that the network structures play a crucial role in identifying the types of explosive death behaviors. We also observe that the damping coefficient of the VdP system not only can determine whether the explosive death state is generated but also can adjust the forward transition point. We further show that the backward transition point is independent of the network topologies and the damping coefficient, which is well confirmed by theoretical analysis. Our results reveal the generality of explosive death phenomenon in different network topologies and are propitious to promote a better comprehension for the oscillation quenching behaviors.
A hybrid system of a membrane oscillator coupled to ultracold atoms
Kampschulte, Tobias
2015-05-01
The control over micro- and nanomechanical oscillators has recently made impressive progress. First experiments demonstrated ground-state cooling and single-phonon control of high-frequency oscillators using cryogenic cooling and techniques of cavity optomechanics. Coupling engineered mechanical structures to microscopic quantum system with good coherence properties offers new possibilities for quantum control of mechanical vibrations, precision sensing and quantum-level signal transduction. Ultracold atoms are an attractive choice for such hybrid systems: Mechanical can either be coupled to the motional state of trapped atoms, which can routinely be ground-state cooled, or to the internal states, for which a toolbox of coherent manipulation and detection exists. Furthermore, atomic collective states with non-classical properties can be exploited to infer the mechanical motion with reduced quantum noise. Here we use trapped ultracold atoms to sympathetically cool the fundamental vibrational mode of a Si3N4 membrane. The coupling of membrane and atomic motion is mediated by laser light over a macroscopic distance and enhanced by an optical cavity around the membrane. The observed cooling of the membrane from room temperature to 650 +/- 230 mK shows that our hybrid mechanical-atomic system operates at a large cooperativity. Our scheme could provide ground-state cooling and quantum control of low-frequency oscillators such as levitated nanoparticles, in a regime where purely optomechanical techniques cannot reach the ground state. Furthermore, we will present a scheme where an optomechanical system is coupled to internal states of ultracold atoms. The mechanical motion is translated into a polarization rotation which drives Raman transitions between atomic ground states. Compared to the motional-state coupling, the new scheme enables to couple atoms to high-frequency structures such as optomechanical crystals.
Kori, Hiroshi; Kiss, István Z.; Jain, Swati; Hudson, John L.
2018-04-01
Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters and desynchronized states, repulsive coupling results in synchronized oscillations. The experiments are interpreted with a phenomenological model that captures the waveform of the oscillations (exponential increase) followed by a refractory period. The globally coupled autocatalytic integrate-and-fire model predicts the development of partially synchronized states that occur through attracting heteroclinic cycles between out-of-phase two-cluster states. Similar behavior can be expected in many other systems where the oscillations occur close to a saddle-loop bifurcation, e.g., with Morris-Lecar neurons.
Ghoshal, Gourab; Muñuzuri, Alberto P.; Pérez-Mercader, Juan
2016-01-01
Oscillatory phenomena are ubiquitous in Nature. The ability of a large population of coupled oscillators to synchronize constitutes an important mechanism to express information and establish communication among members. To understand such phenomena, models and experimental realizations of globally coupled oscillators have proven to be invaluable in settings as varied as chemical, biological and physical systems. A variety of rich dynamical behavior has been uncovered, although usually in the context of a single state of synchronization or lack thereof. Through the experimental and numerical study of a large population of discrete chemical oscillators, here we report on the unexpected discovery of a new phenomenon revealing the existence of dynamically distinct synchronized states reflecting different degrees of communication. Specifically, we discover a novel large-amplitude super-synchronized state separated from the conventionally reported synchronized and quiescent states through an unusual sharp jump transition when sampling the strong coupling limit. Our results assume significance for further elucidating globally coherent phenomena, such as in neuropathologies, bacterial cell colonies, social systems and semiconductor lasers.
Coupled Oscillator Model of the Business Cycle withFluctuating Goods Markets
Ikeda, Y.; Aoyama, H.; Fujiwara, Y.; Iyetomi, H.; Ogimoto, K.; Souma, W.; Yoshikawa, H.
The sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand, is a matter of interest in physics and economics. We consider an economic system made up of industry sectors and goods markets in order to analyze the sectoral synchronization observed for the Japanese business cycle. A coupled oscillator model that exhibits synchronization is developed based on the Kuramoto model with inertia by adding goods markets, and analytic solutions of the stationary state and the coupling strength are obtained. We simulate the effects on synchronization of a sectoral shock for systems with different price elasticities and the coupling strengths. Synchronization is reproduced as an equilibrium solution in a nearest neighbor graph. Analysis of the order parameters shows that the synchronization is stable for a finite elasticity, whereas the synchronization is broken and the oscillators behave like a giant oscillator with a certain frequency additional to the common frequency for zero elasticity.
Coherent oscillation in a linear quantum system coupled to a thermal bath
International Nuclear Information System (INIS)
Bell, N.F.; Volkas, R.R.; Sawyer, R.F.
2000-01-01
We consider the time development of the density matrix for a system coupled to a thermal bath, in models that go beyond the standard two-level systems through addition of an energy excitation degree of freedom and through the possibility of the replacement of the spin algebra by a more complex algebra. We find conditions under which increasing the coupling to the bath above a certain level decreases the rate of entropy production, and in which the limiting behavior is a dissipationless sinusoidal oscillation that could be interpreted as the synchronization of many modes of the uncoupled system
Optimum output coupling for a mid-infrared KTiOAsO4 optical parametric oscillator
International Nuclear Information System (INIS)
Li, Guochao; Gao, Yesheng; Zheng, Guangjin; Zhao, Yao; Chen, Kunfeng; Wang, Qingpu; Bai, Fen
2013-01-01
Taking into account the turn off time of the Q-switch, the coupled equations for a mid-infrared KTiOAsO 4 optical parametric oscillator (OPO) are given. These rate equations are solved numerically and some key parameters for designing the laser system are determined. The key parameters include the optimal coupling and nonlinear crystal length which maximize the output power and OPO conversion efficiency. We found that a low-loss singly resonant OPO cavity not only enhances the mid-infrared output but also decreases the optimal OPO crystal length. (paper)
Synchronization effects in two coupled one-dimensional lattices of phase oscillators
International Nuclear Information System (INIS)
Pando L, Carlos L.
2001-03-01
We study synchronization effects in a model consisting of two identical unidirectionally coupled 1-D arrays of phase oscillators. The master array is in the spatio-temporal chaos regime and the coupling across the two arrays is not strong enough in order to reach complete synchronization. The time series of the distance between the arrays is the main object of our study and this shows on-off intermittency. We can approximate the dynamics of the aforementioned time series with that of a first-order Markov process with two symbols. This model can be implemented in arrays of phase-locked loops (PPL) and Josephson junctions. (author)
Automatic Correction of Betatron Coupling in the LHC Using Injection Oscillations
Persson, T; Jacquet, D; Kain, V; Levinsen, Y; McAteer, M-J; Maclean, E; Skowronski, P; Tomas, R; Vanbavinckhove, G; Miyamoto, R
2013-01-01
The control of the betatron coupling at injection and during the energy ramp is critical for the safe operation of the tune feedback and for the dynamic aperture. In the LHC every fill is preceded by the injection of a pilot bunch with low intensity. Using the injection oscillations from the pilot bunch we are able to measure the coupling at each individual BPM. The measurement is used to calculate a global coupling correction. The correction is based on the use of two orthogonal knobs which correct the real and imaginary part of the difference resonance term f1001, respectively. This method to correct the betatron coupling has been proven successful during the normal operation of the LHC. This paper presents the method used to calculate the corrections and its performance.
Energy Technology Data Exchange (ETDEWEB)
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: lminati@istituto-besta.it [Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy); Center for Mind/Brain Sciences, University of Trento, Trento (Italy); Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge [Center for Mind/Brain Sciences, University of Trento, Trento (Italy); D' Incerti, Ludovico [Neuroradiology Unit, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2015-03-15
In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D{sub 2}), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.
International Nuclear Information System (INIS)
Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge; D'Incerti, Ludovico
2015-01-01
In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D 2 ), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes
International Nuclear Information System (INIS)
Luo Jian; Lu Di; Du Chaoling; Liu Youwen; Shi Daning; Lai Wei; Guo Chunlei; Gong Shangqing
2012-01-01
We theoretically investigate how to control the Rabi oscillation of excitons of the coupling quantum dots by manipulating static electric fields. Our results show that, for a single-photon process, when direct excitons change into indirect excitons with a bias applied on the sample, the Rabi oscillation rarely alters. However, for the two-photon process, a pronounced enhancement of Rabi oscillation is observed, which can be utilized as the logic gate in quantum information. (paper)
International Nuclear Information System (INIS)
Chuan-Sheng, Shen; Han-Shuang, Chen; Ji-Qian, Zhang
2008-01-01
We study the dynamic behaviour of two intracellular calcium oscillators that are coupled through gap junctions both to Ca 2+ and inositol(1,4,5)-trisphosphate (IP 3 ). It is found that synchronized anti-phase and in-phase oscillations of cytoplasmic calcium coexist in parameters space. Especially, synchronized anti-phase oscillations only occur near the onset of a Hopf bifurcation point when the velocity of IP 3 synthesis is increased. In addition, two kinds of coupling effects, i.e., the diffusions of Ca 2+ and IP 3 among cells on synchronous behaviour, are considered. We find that small coupling of Ca 2+ and large coupling of IP 3 facilitate the emergence of synchronized anti-phase oscillations. However, the result is contrary for the synchronized in-phase case. Our findings may provide a qualitative understanding about the mechanism of synchronous behaviour of intercellular calcium signalling
The intercellular synchronization of Ca2+ oscillations evaluates Cx36-dependent coupling.
Directory of Open Access Journals (Sweden)
Sabine Bavamian
Full Text Available Connexin36 (Cx36 plays an important role in insulin secretion by controlling the intercellular synchronization of Ca(2+ transients induced during stimulation. The lack of drugs acting on Cx36 channels is a major limitation in further unraveling the molecular mechanism underlying this effect. To screen for such drugs, we have developed an assay allowing for a semi-automatic, fluorimetric quantification of Ca(2+ transients in large populations of MIN6 cells. Here, we show that (1 compared to control cells, MIN6 cells with reduced Cx36 expression or function showed decreased synchrony of glucose-induced Ca(2+ oscillations; (2 glibenclamide, a sulphonylurea which promotes Cx36 junctions and coupling, increased the number of synchronous MIN6 cells, whereas quinine, an antimalarial drug which inhibits Cx36-dependent coupling, decreased this proportion; (3 several drugs were identified that altered the intercellular Ca(2+ synchronization, cell coupling and distribution of Cx36; (4 some of them also affected insulin content. The data indicate that the intercellular synchronization of Ca(2+ oscillations provides a reliable and non-invasive measurement of Cx36-dependent coupling, which is useful to identify novel drugs affecting the function of β-cells, neurons, and neuron-related cells that express Cx36.
International Nuclear Information System (INIS)
Doron, E.; Smilanski, U.
1991-11-01
We discuss the spectra of quantized chaotic billiards from the point of view of scattering theory. We show that the spectral and resonance density functions both fluctuate about a common mean. A semiclassical treatment explains this in terms of classical scattering trajectories and periodic orbits of the poincare scattering map. This formalism is used to interpret recent experiments where the spectra of chaotic cavities where measured by microwave scattering. (author)
Mixing enhancement and transport reduction in chaotic advection
Benzekri , Tounsia; Chandre , Cristel; Leoncini , Xavier; Lima , Ricardo; Vittot , Michel
2005-01-01
We present a method for reducing chaotic transport in a model of chaotic advection due to time-periodic forcing of an oscillating vortex chain. We show that by a suitable modification of this forcing, the modified model combines two effects: enhancement of mixing within the rolls and suppression of chaotic transport along the channel.
Excitation transfer in two two-level systems coupled to an oscillator
International Nuclear Information System (INIS)
Hagelstein, P L; Chaudhary, I U
2008-01-01
We consider a generalization of the spin-boson model in which two different two-level systems are coupled to an oscillator, under conditions where the oscillator energy is much less than the two-level system energies, and where the oscillator is highly excited. We find that the two-level system transition energy is shifted, producing a Bloch-Siegert shift in each two-level system similar to what would be obtained if the other were absent. At resonances associated with energy exchange between a two-level system and the oscillator, the level splitting is about the same as would be obtained in the spin-boson model at a Bloch-Siegert resonance. However, there occur resonances associated with the transfer of excitation between one two-level system and the other, an effect not present in the spin-boson model. We use a unitary transformation leading to a rotated system in which terms responsible for the shift and splittings can be identified. The level splittings at the anticrossings associated with both energy exchange and excitation transfer resonances are accounted for with simple two-state models and degenerate perturbation theory using operators that appear in the rotated Hamiltonian
Directory of Open Access Journals (Sweden)
Po Hu
2016-06-01
Full Text Available The synchronous tuning of the self-oscillating wireless power transfer (WPT in a close-coupling condition is studied in this paper. The Hamel locus is applied to predict the self-oscillating points in the WPT system. In order to make the system operate stably at the most efficient point, which is the middle resonant point when there are middle resonant and split frequency points caused by frequency-splitting, the receiver (RX rather than the transmitter (TX current is chosen as the self-oscillating feedback variable. The automatic delay compensation is put forward to eliminate the influence of the intrinsic delay on frequency tuning for changeable parameters. In addition, the automatic circuit parameter tuning based on the phase difference is proposed to realize the synchronous tuning of frequency and circuit parameters. The experiments verified that the synchronous tuning proposed in this paper is effective, fully automatic, and more robust than the previous self-oscillating WPT system which use the TX current as the feedback variable.
Stability of phase locking in a ring of unidirectionally coupled oscillators
International Nuclear Information System (INIS)
Rogge, J A; Aeyels, D
2004-01-01
We discuss the dynamic behaviour of a finite group of phase oscillators unidirectionally coupled in a ring. The dynamics are based on the Kuramoto model. In the case of identical oscillators, all phase locking solutions and their stability properties are obtained. For nonidentical oscillators it is proven that there exist phase locking solutions for sufficiently strong coupling. An algorithm to obtain all phase locking solutions is proposed. These solutions can be classified into classes, each with its own stability properties. The stability properties are obtained by means of a novel extension of Gershgorin's theorem. One class of stable solutions has the property that all phase differences between neighbouring cells are contained in (-π/2, π/2). Contrary to intuition, a second class of stable solutions is established with exactly one of the phase differences contained in (π/2, 3π/2). The stability results are extended from sinusoidal interconnections to a class of odd functions. To conclude, a connection with the field of active antenna arrays is made, generalizing some results earlier obtained in this field
Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle.
Feillet, Céline; Krusche, Peter; Tamanini, Filippo; Janssens, Roel C; Downey, Mike J; Martin, Patrick; Teboul, Michèle; Saito, Shoko; Lévi, Francis A; Bretschneider, Till; van der Horst, Gijsbertus T J; Delaunay, Franck; Rand, David A
2014-07-08
Daily synchronous rhythms of cell division at the tissue or organism level are observed in many species and suggest that the circadian clock and cell cycle oscillators are coupled. For mammals, despite known mechanistic interactions, the effect of such coupling on clock and cell cycle progression, and hence its biological relevance, is not understood. In particular, we do not know how the temporal organization of cell division at the single-cell level produces this daily rhythm at the tissue level. Here we use multispectral imaging of single live cells, computational methods, and mathematical modeling to address this question in proliferating mouse fibroblasts. We show that in unsynchronized cells the cell cycle and circadian clock robustly phase lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronized way with a common frequency. Dexamethasone-induced synchronization reveals additional clock states. As well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock. Cells transition to these states after dexamethasone synchronization. The temporal coordination of cell division by phase locking to the clock at a single-cell level has significant implications because disordered circadian function is increasingly being linked to the pathogenesis of many diseases, including cancer.
Parihar, Abhinav; Shukla, Nikhil; Datta, Suman; Raychowdhury, Arijit
2015-02-01
Computing with networks of synchronous oscillators has attracted wide-spread attention as novel materials and device topologies have enabled realization of compact, scalable and low-power coupled oscillatory systems. Of particular interest are compact and low-power relaxation oscillators that have been recently demonstrated using MIT (metal-insulator-transition) devices using properties of correlated oxides. Further the computational capability of pairwise coupled relaxation oscillators has also been shown to outperform traditional Boolean digital logic circuits. This paper presents an analysis of the dynamics and synchronization of a system of two such identical coupled relaxation oscillators implemented with MIT devices. We focus on two implementations of the oscillator: (a) a D-D configuration where complementary MIT devices (D) are connected in series to provide oscillations and (b) a D-R configuration where it is composed of a resistor (R) in series with a voltage-triggered state changing MIT device (D). The MIT device acts like a hysteresis resistor with different resistances in the two different states. The synchronization dynamics of such a system has been analyzed with purely charge based coupling using a resistive (RC) and a capacitive (CC) element in parallel. It is shown that in a D-D configuration symmetric, identical and capacitively coupled relaxation oscillator system synchronizes to an anti-phase locking state, whereas when coupled resistively the system locks in phase. Further, we demonstrate that for certain range of values of RC and CC, a bistable system is possible which can have potential applications in associative computing. In D-R configuration, we demonstrate the existence of rich dynamics including non-monotonic flows and complex phase relationship governed by the ratios of the coupling impedance. Finally, the developed theoretical formulations have been shown to explain experimentally measured waveforms of such pairwise coupled
Directory of Open Access Journals (Sweden)
Diego Lozano-Soldevilla
2016-08-01
Full Text Available Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in animals and humans have found that the amplitude of fast oscillations (> 40 Hz occur non-uniformly within the phase of slower oscillations, forming the so-called cross-frequency coupling (CFC. However, the CFC patterns be influenced by features in the signal that do not relate to underlying physiological interactions. For example, CFC estimates may be sensitive to spectral correlations due to non-sinusoidal properties of the alpha band wave morphology. To investigate this issue, we performed CFC analysis using experimental and synthetic data. The former consisted in a double-blind magnetoencephalography pharmacological study in which participants received either placebo, 0.5 mg or 1.5 mg of lorazepam (LZP; GABAergic enhancer in different experimental sessions. By recording oscillatory brain activity with during rest and working memory (WM, we were able to demonstrate that posterior alpha (8 – 12 Hz phase was coupled to beta-low gamma band (20 – 45 Hz amplitude envelope during all sessions. Importantly, bicoherence values around the harmonics of the alpha frequency were similar both in magnitude and topographic distribution to the cross-frequency coherence (CFCoh values observed in the alpha-phase to beta-low gamma coupling. In addition, despite the large CFCoh we found no significant cross-frequency directionality (CFD. Critically, simulations demonstrated that a sizable part of our empirical CFCoh between alpha and beta-low gamma coupling and the lack of CFD could be explained by two-three harmonics aligned in zero phase-lag produced by the physiologically characteristic alpha asymmetry in the amplitude of the peaks relative to the troughs
Analysis of the time structure of synchronization in multidimensional chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Makarenko, A. V., E-mail: avm.science@mail.ru [Constructive Cybernetics Research Group (Russian Federation)
2015-05-15
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.
Analysis of the time structure of synchronization in multidimensional chaotic systems
International Nuclear Information System (INIS)
Makarenko, A. V.
2015-01-01
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete
Adiabatic approximation in the ultrastrong-coupling regime of an oscillator and two qubits
Energy Technology Data Exchange (ETDEWEB)
Yang, Ping; Zou, Ping [Laboratory of Nanophotonic Functional Materials and Devices, SIPSE and LQIT, South China Normal University, Guangzhou 510006 (China); Zhang, Zhi-Ming, E-mail: zmzhang@scnu.edu.cn [Laboratory of Nanophotonic Functional Materials and Devices, SIPSE and LQIT, South China Normal University, Guangzhou 510006 (China)
2012-10-01
We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyze the system by the adiabatic approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Relative energy-level spectrum of the system in the adiabatic displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution. -- Highlights: ► Our work shows that the adiabatic approximations may work also in the ultrastrong coupling limit. ► Both of the approximation methods are valid in a large range of coupling strength, including the ultrastrong coupling regime. ► The results of the approximate formula meet well the exact numerical solution.
Identical phase oscillators with global sinusoidal coupling evolve by Mobius group action.
Marvel, Seth A; Mirollo, Renato E; Strogatz, Steven H
2009-12-01
Systems of N identical phase oscillators with global sinusoidal coupling are known to display low-dimensional dynamics. Although this phenomenon was first observed about 20 years ago, its underlying cause has remained a puzzle. Here we expose the structure working behind the scenes of these systems by proving that the governing equations are generated by the action of the Mobius group, a three-parameter subgroup of fractional linear transformations that map the unit disk to itself. When there are no auxiliary state variables, the group action partitions the N-dimensional state space into three-dimensional invariant manifolds (the group orbits). The N-3 constants of motion associated with this foliation are the N-3 functionally independent cross ratios of the oscillator phases. No further reduction is possible, in general; numerical experiments on models of Josephson junction arrays suggest that the invariant manifolds often contain three-dimensional regions of neutrally stable chaos.
Control of entanglement dynamics in a system of three coupled quantum oscillators.
Gonzalez-Henao, J C; Pugliese, E; Euzzor, S; Meucci, R; Roversi, J A; Arecchi, F T
2017-08-30
Dynamical control of entanglement and its connection with the classical concept of instability is an intriguing matter which deserves accurate investigation for its important role in information processing, cryptography and quantum computing. Here we consider a tripartite quantum system made of three coupled quantum parametric oscillators in equilibrium with a common heat bath. The introduced parametrization consists of a pulse train with adjustable amplitude and duty cycle representing a more general case for the perturbation. From the experimental observation of the instability in the classical system we are able to predict the parameter values for which the entangled states exist. A different amount of entanglement and different onset times emerge when comparing two and three quantum oscillators. The system and the parametrization considered here open new perspectives for manipulating quantum features at high temperatures.
Inversion of Qubit Energy Levels in Qubit-Oscillator Circuits in the Deep-Strong-Coupling Regime
Yoshihara, F.; Fuse, T.; Ao, Z.; Ashhab, S.; Kakuyanagi, K.; Saito, S.; Aoki, T.; Koshino, K.; Semba, K.
2018-05-01
We report on experimentally measured light shifts of superconducting flux qubits deep-strongly coupled to L C oscillators, where the coupling constants are comparable to the qubit and oscillator resonance frequencies. By using two-tone spectroscopy, the energies of the six lowest levels of each circuit are determined. We find huge Lamb shifts that exceed 90% of the bare qubit frequencies and inversions of the qubits' ground and excited states when there are a finite number of photons in the oscillator. Our experimental results agree with theoretical predictions based on the quantum Rabi model.
Partial synchronization in a system of coupled logistic maps
DEFF Research Database (Denmark)
Taborov, A.V.; Maistrenko, Y.L; Mosekilde, Erik
1999-01-01
The phenomenon of clustering (or partial synchronization) in a system of globqally coupled chaotic oscillators is studied by means of a model of three coupled logistic maps. We determine the regions in parameter space where total and partial synchronization take place, examine the bifurcations...
The Southern Oscillation in a coupled GCM: Implications for climate sensitivity and climate change
International Nuclear Information System (INIS)
Meehl, G.A.
1990-01-01
Results are presented from a global coupled ocean-atmosphere general circulation climate model developed at the National Center for Atmospheric Research. The atmospheric part of the coupled model is a global spectral (R15, 4.5 degree latitude by 7.5 degree longitude, 9 layers in the vertical) general circulation model. The ocean is coarse-grid (5 degree latitude by 5 degree longitude, 4 layers in the vertical) global general circulation model. The coupled model includes a simple thermodynamic sea-ice model. Due mainly to inherent limitations in the ocean model, the coupled model simulates sea surface temperatures that are too low in the tropics and too high in the extratropics in the mean. In spite of these limitations, the coupled model simulates active interannual variability of the global climate system involving signals in the tropical Pacific that resemble, in some respects, the observed Southern Oscillation. These signals in the tropics are associated with teleconnections to the extratropics of both hemispheres. The implications of this model-simulated interannual variability of the coupled system relating to climate sensitivity and climate change due to an increase of atmospheric carbon dioxide are discussed
The Southern Oscillation in a coupled GCM: Implications for climate sensitivity and climate change
International Nuclear Information System (INIS)
Meehl, G.A.
1991-01-01
Results are presented from a global coupled ocean-atmosphere general circulation climate model developed at the National Center for Atmospheric Research. The atmospheric part of the coupled model is a global spectral (R15, 4.5 degree latitude by 7.5 degree longitude, 9 layers in the vertical) general circulation model. The ocean is coarse-grid (5 degree latitude by 5 degree longitude, 4 layers in the vertical) global general circulation model. The coupled model includes a simple thermodynamic sea-ice model. Due mainly to inherent limitations in the ocean model, the coupled model simulates sea surface temperatures that are too low in the tropics and too high in the extratropics in the mean. In spite of these limitations, the coupled model simulates active interannual variability of the global climate system involving signals in the tropical Pacific that resemble, in some respects, the observed Southern Oscillation. These signals in the tropics are associated with teleconnections to the extratropics of both hemispheres. The implications of this model-simulated interannual variability of the coupled system relating to climate sensitivity and climate change due to an increase of atmospheric carbon dioxide are discussed. 25 refs.; 9 figs
Rigatos, Gerasimos
2014-12-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
Dynamics of a model of two delay-coupled relaxation oscillators
Ruelas, R. E.; Rand, R. H.
2010-08-01
This paper investigates the dynamics of a new model of two coupled relaxation oscillators. The model replaces the usual DDE (differential-delay equation) formulation with a discrete-time approach with jumps. Existence, bifurcation and stability of in-phase periodic motions is studied. Simple periodic motions, which involve exactly two jumps per period, are found to have large plateaus in parameter space. These plateaus are separated by regions of complicated dynamics, reminiscent of the Devil's Staircase. Stability of motions in the in-phase manifold are contrasted with stability of motions in the full phase space.
Quantization of a free particle interacting linearly with a harmonic oscillator
International Nuclear Information System (INIS)
Mainiero, Thomas; Porter, Mason A.
2007-01-01
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system's two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic
Chaos crisis in coupled Duffing's systems with initial phase difference
International Nuclear Information System (INIS)
Bi Qinsheng
2007-01-01
The dynamics of coupled Duffing's oscillators with initial phase difference is investigated in this Letter. For the averaged equations, different equilibrium points can be observed, the number of which may vary with the parameters. The stable equilibrium points, corresponding to the periodic motion of the original coupled oscillators, may coexist with different patterns of dynamics, including chaos. Furthermore, two different chaotic attractors associated with different attracting basin coexist for certain parameter conditions, which may interact with each other to form an enlarged chaotic attractor. Several new dynamical phenomena such as boundary chaos crises have been predicted as the initial phase difference varies
International Nuclear Information System (INIS)
Schaefer, Mirko
2011-01-01
The main topic of this thesis is the investigation of dynamical properties of coupled Tchebycheff map networks. The results give insights into the chaotic string model and its network generalization from a dynamical point of view. As a first approach, discrete symmetry transformations of the model are studied. These transformations are formulated in a general way in order to be also applicable to similar dynamics on bipartite network structures. The dynamics is studied numerically via Lyapunov measures, spatial correlations, and ergodic properties. It is shown that the zeros of the interaction energy are distinguished only with respect to this specific observable, but not by a more general dynamical principle. The original chaotic string model is defined on a one-dimensional lattice (ring-network) as the underlying network topology. This thesis studies a modification of the model based on the introduction of tunable disorder. The effects of inhomogeneous coupling weights as well as small-world perturbations of the ring-network structure on the interaction energy are discussed. Synchronization properties of the chaotic string model and its network generalization are studied in later chapters of this thesis. The analysis is based on the master stability formalism, which relates the stability of the synchronized state to the spectral properties of the network. Apart from complete synchronization, where the dynamics at all nodes of the network coincide, also two-cluster synchronization on bipartite networks is studied. For both types of synchronization it is shown that depending on the type of coupling the synchronized dynamics can display chaotic as well as periodic or quasi-periodic behaviour. The semi-analytical calculations reveal that the respective synchronized states are often stable for a wide range of coupling values even for the ring-network, although the respective basins of attraction may inhabit only a small fraction of the phase space. To provide
Periodic Forcing of a 555-IC Based Electronic Oscillator in the Strong Coupling Limit
Santillán, Moisés
We designed and developed a master-slave electronic oscillatory system (based on the 555-timer IC working in the astable mode), and investigated its dynamic behavior regarding synchronization. For that purpose, we measured the rotation numbers corresponding to the phase-locking rhythms achieved in a large set of values of the normalized forcing frequency (NFF) and of the coupling strength between the master and the slave oscillators. In particular, we were interested in the system behavior in the strong-coupling limit, because such problem has not been extensively studied from an experimental perspective. Our results indicate that, in such a limit, a degenerate codimension-2 bifurcation point at NFF = 2 exists, in which all the phase-locking regions converge. These findings were corroborated by means of a mathematical model developed to that end, as well as by ad hoc further experiments.
Choe, Chol-Ung; Kim, Ryong-Son; Ri, Ji-Song
2017-09-01
We consider a ring of phase oscillators with nonlocal coupling strength and heterogeneous phase lags. We analyze the effects of heterogeneity in the phase lags on the existence and stability of a variety of steady states. A nonlocal coupling with heterogeneous phase lags that allows the system to be solved analytically is suggested and the stability of solutions along the Ott-Antonsen invariant manifold is explored. We present a complete bifurcation diagram for stationary patterns including the uniform drift and modulated drift states as well as chimera state, which reveals that the stable modulated drift state and a continuum of metastable drift states could occur due to the heterogeneity of the phase lags. We verify our theoretical results using the direct numerical simulations of the model system.
Park, DaeKil
2018-06-01
The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schrödinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily time dependent. We derive the spectral and Schmidt decompositions for vacuum solution. Using the decompositions, we derive the analytical expressions for von Neumann and Rényi entropies. Making use of Wigner distribution function defined in phase space, we derive the time dependence of position-momentum uncertainty relations. To show the dynamics of entanglement and uncertainty relation graphically, we introduce two toy models and one realistic quenched model. While the dynamics can be conjectured by simple consideration in the toy models, the dynamics in the realistic quenched model is somewhat different from that in the toy models. In particular, the dynamics of entanglement exhibits similar pattern to dynamics of uncertainty parameter in the realistic quenched model.
Learning-enhanced coupling between ripple oscillations in association cortices and hippocampus.
Khodagholy, Dion; Gelinas, Jennifer N; Buzsáki, György
2017-10-20
Consolidation of declarative memories requires hippocampal-neocortical communication. Although experimental evidence supports the role of sharp-wave ripples in transferring hippocampal information to the neocortex, the exact cortical destinations and the physiological mechanisms of such transfer are not known. We used a conducting polymer-based conformable microelectrode array (NeuroGrid) to record local field potentials and neural spiking across the dorsal cortical surface of the rat brain, combined with silicon probe recordings in the hippocampus, to identify candidate physiological patterns. Parietal, midline, and prefrontal, but not primary cortical areas, displayed localized ripple (100 to 150 hertz) oscillations during sleep, concurrent with hippocampal ripples. Coupling between hippocampal and neocortical ripples was strengthened during sleep following learning. These findings suggest that ripple-ripple coupling supports hippocampal-association cortical transfer of memory traces. Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.
Pintér, Balázs; Erdélyi, R.
2018-01-01
Solar fundamental (f) acoustic mode oscillations are investigated analytically in a magnetohydrodynamic (MHD) model. The model consists of three layers in planar geometry, representing the solar interior, the magnetic atmosphere, and a transitional layer sandwiched between them. Since we focus on the fundamental mode here, we assume the plasma is incompressible. A horizontal, canopy-like, magnetic field is introduced to the atmosphere, in which degenerated slow MHD waves can exist. The global (f-mode) oscillations can couple to local atmospheric Alfvén waves, resulting, e.g., in a frequency shift of the oscillations. The dispersion relation of the global oscillation mode is derived, and is solved analytically for the thin-transitional layer approximation and for the weak-field approximation. Analytical formulae are also provided for the frequency shifts due to the presence of a thin transitional layer and a weak atmospheric magnetic field. The analytical results generally indicate that, compared to the fundamental value (ω =√{ gk }), the mode frequency is reduced by the presence of an atmosphere by a few per cent. A thin transitional layer reduces the eigen-frequencies further by about an additional hundred microhertz. Finally, a weak atmospheric magnetic field can slightly, by a few percent, increase the frequency of the eigen-mode. Stronger magnetic fields, however, can increase the f-mode frequency by even up to ten per cent, which cannot be seen in observed data. The presence of a magnetic atmosphere in the three-layer model also introduces non-permitted propagation windows in the frequency spectrum; here, f-mode oscillations cannot exist with certain values of the harmonic degree. The eigen-frequencies can be sensitive to the background physical parameters, such as an atmospheric density scale-height or the rate of the plasma density drop at the photosphere. Such information, if ever observed with high-resolution instrumentation and inverted, could help to
El-Nashar, Hassan F.
2017-06-01
We consider a system of three nonidentical coupled phase oscillators in a ring topology. We explore the conditions that must be satisfied in order to obtain the phases at the transition to a synchrony state. These conditions lead to the correct mathematical expressions of phases that aid to find a simple analytic formula for critical coupling when the oscillators transit to a synchronization state having a common frequency value. The finding of a simple expression for the critical coupling allows us to perform a linear stability analysis at the transition to the synchronization stage. The obtained analytic forms of the eigenvalues show that the three coupled phase oscillators with periodic boundary conditions transit to a synchrony state when a saddle-node bifurcation occurs.
An analysis of heart rhythm dynamics using a three-coupled oscillator model
International Nuclear Information System (INIS)
Gois, Sandra R.F.S.M.; Savi, Marcelo A.
2009-01-01
Rhythmic phenomena represent one of the most striking manifestations of the dynamic behavior in biological systems. Understanding the mechanisms responsible for biological rhythms is crucial for the comprehension of the dynamics of life. Natural rhythms could be either regular or irregular over time and space. Each kind of dynamical behavior may be related to both normal and pathological physiological functioning. The cardiac conducting system can be treated as a network of self-excitatory elements and, since these elements exhibit oscillatory behavior, they can be modeled as nonlinear oscillators. This paper proposes a mathematical model to describe heart rhythms considering three modified Van der Pol oscillators connected with time delay couplings. Therefore, the heart dynamics is represented by a system of differential difference equations. Numerical simulations are carried out presenting qualitative agreement with the general heart rhythm behavior. Normal and pathological rhythms represented by the ECG signals are reproduced. Pathological rhythms are generated by either the coupling alterations that represents communications aspects in the heart electric system or forcing excitation representing external pacemaker excitation.
Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.
2018-01-01
In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.
Tunneling conductance oscillations in spin-orbit coupled metal-insulator-superconductor junctions
Kapri, Priyadarshini; Basu, Saurabh
2018-01-01
The tunneling conductance for a device consisting of a metal-insulator-superconductor (MIS) junction is studied in presence of Rashba spin-orbit coupling (RSOC) via an extended Blonder-Tinkham-Klapwijk formalism. We find that the tunneling conductance as a function of an effective barrier potential that defines the insulating layer and lies intermediate to the metallic and superconducting electrodes, displays an oscillatory behavior. The tunneling conductance shows high sensitivity to the RSOC for certain ranges of this potential, while it is insensitive to the RSOC for others. Additionally, when the period of oscillations is an odd multiple of a certain value of the effective potential, the conductance spectrum as a function of the biasing energy demonstrates a contrasting trend with RSOC, compared to when it is not an odd multiple. The explanations for the observation can be found in terms of a competition between the normal and Andreev reflections. Similar oscillatory behavior of the conductance spectrum is also seen for other superconducting pairing symmetries, thereby emphasizing that the insulating layer plays a decisive role in the conductance oscillations of a MIS junction. For a tunable Rashba coupling, the current flowing through the junction can be controlled with precision.
International Nuclear Information System (INIS)
Suarez Antola, R.
2008-11-01
The cores of nuclear reactors, including its structural parts and cooling fluids, are complex mechanical systems able to vibrate in a set of normal modes and frequencies, if suitable perturbed. The cyclic variations in the strain state of the core materials may produce changes in density. Changes in density modify the reactivity. Changes in reactivity modify thermal power. Modifications in thermal power produce variations in temperature fields. Variations in temperature produce variations in strain due to thermal-elastic effects. If the variation of the temperature field is fast enough and if the Doppler Effect and other stabilizing prompt effects in the fuel are weak enough, a fast oscillatory instability could be produced, coupled with mechanical vibrations of small amplitude. A recently constructed, simple mathematical model of nuclear reactor kinetics, that improves the one due to A.S. Thompson, is reviewed. It was constructed in order to study, in a first approximation, the stability of the reactor: a nonlinear nuclear-thermal oscillator (that corresponds to reactor point kinetics with thermal-elastic feedback and with frozen delayed neutron effects) is coupled nonlinearly with a linear mechanical-thermal oscillator (that corresponds to the first normal mode of mechanical vibrations excited by thermo-elastic effects). This mathematical model is studied here from the standpoint of mechanical vibrations. It is shown how, under certain conditions, a suitable mechanical perturbation could elicit fast and growing oscillatory instabilities in the reactor power. Applying the asymptotic method due to Krylov, Bogoliubov and Mitropolsky, analytical formulae that may be used in the calculation of the time varying amplitude and phase of the mechanical oscillations are given, as functions of the mechanical, thermal and nuclear parameters of the reactor. The consequences for the mechanical integrity of the reactor are assessed. Some conditions, mainly, but not exclusively
Research on out-phase oscillation in a nuclear-coupled parallel double-channel boiling system
International Nuclear Information System (INIS)
Zhou Linglan; Zhang Hong; Liu Yu; Zang Xi'nian
2011-01-01
In this paper, the RELAP5 thermal-hydraulic system code is coupled with the TDOT-T 3D neutron kinetic code by PVM (Parallel Virtual Machine). A parallel double-channel boiling system is built by the coupled code and the instability boundary of out-of-phase oscillation in the system is obtained. The effects of axis power distribution and neutron feedback on the out-of-phase oscillation are analyzed in details. It is found that there are type-Ⅰ and type-Ⅱ density wave oscillation regions when the axial power peak is located at upstream of the heating section. At relatively lower values of fuel time constant, the neutron feedback always delays both types of density wave oscillations. (authors)
Cluster synchronization in networks of identical oscillators with α-function pulse coupling.
Chen, Bolun; Engelbrecht, Jan R; Mirollo, Renato
2017-02-01
We study a network of N identical leaky integrate-and-fire model neurons coupled by α-function pulses, weighted by a coupling parameter K. Studies of the dynamics of this system have mostly focused on the stability of the fully synchronized and the fully asynchronous splay states, which naturally depends on the sign of K, i.e., excitation vs inhibition. We find that there is also a rich set of attractors consisting of clusters of fully synchronized oscillators, such as fixed (N-1,1) states, which have synchronized clusters of sizes N-1 and 1, as well as splay states of clusters with equal sizes greater than 1. Additionally, we find limit cycles that clarify the stability of previously observed quasiperiodic behavior. Our framework exploits the neutrality of the dynamics for K=0 which allows us to implement a dimensional reduction strategy that simplifies the dynamics to a continuous flow on a codimension 3 subspace with the sign of K determining the flow direction. This reduction framework naturally incorporates a hierarchy of partially synchronized subspaces in which the new attracting states lie. Using high-precision numerical simulations, we describe completely the sequence of bifurcations and the stability of all fixed points and limit cycles for N=2-4. The set of possible attracting states can be used to distinguish different classes of neuron models. For instance from our previous work [Chaos 24, 013114 (2014)CHAOEH1054-150010.1063/1.4858458] we know that of the types of partially synchronized states discussed here, only the (N-1,1) states can be stable in systems of identical coupled sinusoidal (i.e., Kuramoto type) oscillators, such as θ-neuron models. Upon introducing a small variation in individual neuron parameters, the attracting fixed points we discuss here generalize to equivalent fixed points in which neurons need not fire coincidently.
Role of multistability in the transition to chaotic phase synchronization
DEFF Research Database (Denmark)
Postnov, D.E.; Vadivasova, T.E.; Sosnovtseva, Olga
1999-01-01
In this paper we describe the transition to phase synchronization for systems of coupled nonlinear oscillators that individually follow the Feigenbaum route to chaos. A nested structure of phase synchronized regions of different attractor families is observed. With this structure, the transition...... to nonsynchronous behavior is determined by the loss of stability for the most stable synchronous mode. It is shown that the appearance of hyperchaos and the transition from lag synchronization to phase synchronization are related to the merging of chaotic attractors from different families. Numerical examples...
Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing
Kumar, Suhas; Strachan, John Paul; Williams, R. Stanley
2017-08-01
At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal-insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator and observe a tunable range of periodic and chaotic self-oscillations. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such
Nori, Franco; Ashhab, Sahel
2011-03-01
We consider a system composed of a two-level system (i.e. a qubit) and a harmonic oscillator in the ultrastrong-coupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. We explore the possibility of preparing nonclassical states in this system, especially in the ground state of the combined system. The nonclassical states that we consider include squeezed states, Schrodinger-cat states and entangled states. We also analyze the nature of the change in the ground state as the coupling strength is increased, going from a separable ground state in the absence of coupling to a highly entangled ground state in the case of very strong coupling. Reference: S. Ashhab and F. Nori, Phys. Rev. A 81, 042311 (2010). We thank support from DARPA, AFOSR, NSA, LPS, ARO, NSF, MEXT, JSPS, FIRST, and JST.
Rouse, Andrew A; Cook, Peter F; Large, Edward W; Reichmuth, Colleen
2016-01-01
Human capacity for entraining movement to external rhythms-i.e., beat keeping-is ubiquitous, but its evolutionary history and neural underpinnings remain a mystery. Recent findings of entrainment to simple and complex rhythms in non-human animals pave the way for a novel comparative approach to assess the origins and mechanisms of rhythmic behavior. The most reliable non-human beat keeper to date is a California sea lion, Ronan, who was trained to match head movements to isochronous repeating stimuli and showed spontaneous generalization of this ability to novel tempos and to the complex rhythms of music. Does Ronan's performance rely on the same neural mechanisms as human rhythmic behavior? In the current study, we presented Ronan with simple rhythmic stimuli at novel tempos. On some trials, we introduced "perturbations," altering either tempo or phase in the middle of a presentation. Ronan quickly adjusted her behavior following all perturbations, recovering her consistent phase and tempo relationships to the stimulus within a few beats. Ronan's performance was consistent with predictions of mathematical models describing coupled oscillation: a model relying solely on phase coupling strongly matched her behavior, and the model was further improved with the addition of period coupling. These findings are the clearest evidence yet for parity in human and non-human beat keeping and support the view that the human ability to perceive and move in time to rhythm may be rooted in broadly conserved neural mechanisms.
Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators
International Nuclear Information System (INIS)
Giacomin, Giambattista; Pakdaman, Khashayar; Pellegrin, Xavier
2012-01-01
We study the dynamics of the large N limit of the Kuramoto model of coupled phase oscillators, subject to white noise. We introduce the notion of shadow inertial manifold and we prove their existence for this model, supporting the fact that the long-term dynamics of this model is finite dimensional. Following this, we prove that the global attractor of this model takes one of two forms. When coupling strength is below a critical value, the global attractor is a single equilibrium point corresponding to an incoherent state. Otherwise, when coupling strength is beyond this critical value, the global attractor is a two-dimensional disc composed of radial trajectories connecting a saddle-point equilibrium (the incoherent state) to an invariant closed curve of locally stable equilibria (partially synchronized state). Our analysis hinges, on the one hand, upon sharp existence and uniqueness results and their consequence for the existence of a global attractor, and, on the other hand, on the study of the dynamics in the vicinity of the incoherent and coherent (or synchronized) equilibria. We prove in particular nonlinear stability of each synchronized equilibrium, and normal hyperbolicity of the set of such equilibria. We explore mathematically and numerically several properties of the global attractor, in particular we discuss the limit of this attractor as noise intensity decreases to zero
Coupling switches and oscillators as a means to shape cellular signals in biomolecular systems
International Nuclear Information System (INIS)
Zhou, Peipei; Cai, Shuiming; Liu, Zengrong; Chen, Luonan; Wang, Ruiqi
2013-01-01
To understand how a complex biomolecular network functions, a decomposition or a reconstruction process of the network is often needed so as to provide new insights into the regulatory mechanisms underlying various dynamical behaviors and also to gain qualitative knowledge of the network. Unfortunately, it seems that there are still no general rules on how to decompose a complex network into simple modules. An alternative resolution is to decompose a complex network into small modules or subsystems with specified functions such as switches and oscillators and then integrate them by analyzing the interactions between them. The main idea of this approach can be illustrated by considering a bidirectionally coupled network in this paper, i.e., coupled Toggle switch and Repressilator, and analyzing the occurrence of various dynamics, although the theoretical principle may hold for a general class of networks. We show that various biomolecular signals can be shaped by regulating the coupling between the subsystems. The approach presented here can be expected to simplify and analyze even more complex biological networks
Coupling switches and oscillators as a means to shape cellular signals in biomolecular systems
Energy Technology Data Exchange (ETDEWEB)
Zhou, Peipei [Institute of Systems Biology, Shanghai University, Shanghai 200444 (China); Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013 (China); Cai, Shuiming [Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013 (China); Liu, Zengrong [Institute of Systems Biology, Shanghai University, Shanghai 200444 (China); Chen, Luonan [Key Laboratory of Systems Biology, SIBS-Novo Nordisk Translational Research Center for PreDiabetes, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai 200031 (China); Collaborative Research Center for Innovative Mathematical Modeling, Institute of Industrial Science, University of Tokyo, Tokyo 153-8505 (Japan); Wang, Ruiqi [Institute of Systems Biology, Shanghai University, Shanghai 200444 (China)
2013-05-15
To understand how a complex biomolecular network functions, a decomposition or a reconstruction process of the network is often needed so as to provide new insights into the regulatory mechanisms underlying various dynamical behaviors and also to gain qualitative knowledge of the network. Unfortunately, it seems that there are still no general rules on how to decompose a complex network into simple modules. An alternative resolution is to decompose a complex network into small modules or subsystems with specified functions such as switches and oscillators and then integrate them by analyzing the interactions between them. The main idea of this approach can be illustrated by considering a bidirectionally coupled network in this paper, i.e., coupled Toggle switch and Repressilator, and analyzing the occurrence of various dynamics, although the theoretical principle may hold for a general class of networks. We show that various biomolecular signals can be shaped by regulating the coupling between the subsystems. The approach presented here can be expected to simplify and analyze even more complex biological networks.
Directory of Open Access Journals (Sweden)
Andrew A Rouse
2016-06-01
Full Text Available Human capacity for entraining movement to external rhythms—i.e., beat keeping—is ubiquitous, but its evolutionary history and neural underpinnings remain a mystery. Recent findings of entrainment to simple and complex rhythms in non-human animals pave the way for a novel comparative approach to assess the origins and mechanisms of rhythmic behavior. The most reliable non-human beat keeper to date is a California sea lion, Ronan, who was trained to match head movements to isochronous repeating stimuli and showed spontaneous generalization of this ability to novel tempos and to the complex rhythms of music. Does Ronan’s performance rely on the same neural mechanisms as human rhythmic behavior? In the current study, we presented Ronan with simple rhythmic stimuli at novel tempos. On some trials, we introduced perturbations, altering either tempo or phase in the middle of a presentation. Ronan quickly adjusted her behavior following all perturbations, recovering her consistent phase and tempo relationships to the stimulus within a few beats. Ronan’s performance was consistent with predictions of mathematical models describing coupled oscillation: a model relying solely on phase coupling strongly matched her behavior, and the model was further improved with the addition of period coupling. These findings are the clearest evidence yet for parity in human and non-human beat keeping and support the view that the human ability to perceive and move in time to rhythm may be rooted in broadly conserved neural mechanisms.
Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity.
Heitmann, Stewart; Ermentrout, G Bard
2015-06-01
Spatiotemporal waves of synchronized activity are known to arise in oscillatory neural networks with lateral inhibitory coupling. How such patterns respond to dynamic changes in coupling strength is largely unexplored. The present study uses analysis and simulation to investigate the evolution of wave patterns when the strength of lateral inhibition is varied dynamically. Neural synchronization was modeled by a spatial ring of Kuramoto oscillators with Mexican hat lateral coupling. Broad bands of coexisting stable wave solutions were observed at all levels of inhibition. The stability of these waves was formally analyzed in both the infinite ring and the finite ring. The broad range of multi-stability predicted hysteresis in transitions between neighboring wave solutions when inhibition is slowly varied. Numerical simulation confirmed the predicted transitions when inhibition was ramped down from a high initial value. However, non-wave solutions emerged from the uniform solution when inhibition was ramped upward from zero. These solutions correspond to spatially periodic deviations of phase that we call ripple states. Numerical continuation showed that stable ripple states emerge from synchrony via a supercritical pitchfork bifurcation. The normal form of this bifurcation was derived analytically, and its predictions compared against the numerical results. Ripple states were also found to bifurcate from wave solutions, but these were locally unstable. Simulation also confirmed the existence of hysteresis and ripple states in two spatial dimensions. Our findings show that spatial synchronization patterns can remain structurally stable despite substantial changes in network connectivity.
True-slime-mould-inspired hydrostatically coupled oscillator system exhibiting versatile behaviours
International Nuclear Information System (INIS)
Umedachi, Takuya; Ito, Kentaro; Idei, Ryo; Ishiguro, Akio
2013-01-01
Behavioural diversity is an indispensable attribute of living systems, which makes them intrinsically adaptive and responsive to the demands of a dynamically changing environment. In contrast, conventional engineering approaches struggle to suppress behavioural diversity in artificial systems to reach optimal performance in given environments for desired tasks. The goals of this research include understanding the essential mechanism that endows living systems with behavioural diversity and implementing the mechanism in robots to exhibit adaptive behaviours. For this purpose, we have focused on an amoeba-like unicellular organism: the plasmodium of true slime mould. Despite the absence of a central nervous system, the plasmodium exhibits versatile spatiotemporal oscillatory patterns and switches spontaneously among these patterns. By exploiting this behavioural diversity, it is able to exhibit adaptive behaviour according to the situation encountered. Inspired by this organism, we built a real physical robot using hydrostatically coupled oscillators that produce versatile oscillatory patterns and spontaneous transitions among the patterns. The experimental results show that exploiting physical hydrostatic interplay—the physical dynamics of the robot—allows simple phase oscillators to promote versatile behaviours. The results can contribute to an understanding of how a living system generates versatile and adaptive behaviours with physical interplays among body parts. (paper)
Atsumi, Yu; Nakao, Hiroya
2012-05-01
A system of phase oscillators with repulsive global coupling and periodic external forcing undergoing asynchronous rotation is considered. The synchronization rate of the system can exhibit persistent fluctuations depending on parameters and initial phase distributions, and the amplitude of the fluctuations scales with the system size for uniformly random initial phase distributions. Using the Watanabe-Strogatz transformation that reduces the original system to low-dimensional macroscopic equations, we show that the fluctuations are collective dynamics of the system corresponding to low-dimensional trajectories of the reduced equations. It is argued that the amplitude of the fluctuations is determined by the inhomogeneity of the initial phase distribution, resulting in system-size scaling for the random case.
Coupling of Thalamocortical Sleep Oscillations Are Important for Memory Consolidation in Humans.
Directory of Open Access Journals (Sweden)
Mohammad Niknazar
Full Text Available Sleep, specifically non-rapid eye movement (NREM sleep, is thought to play a critical role in the consolidation of recent memories. Two main oscillatory activities observed during NREM, cortical slow oscillations (SO, 0.5-1.0 Hz and thalamic spindles (12-15 Hz, have been shown to independently correlate with memory improvement. Yet, it is not known how these thalamocortical events interact, or the significance of this interaction, during the consolidation process. Here, we found that systemic administration of the GABAergic drug (zolpidem increased both the phase-amplitude coupling between SO and spindles, and verbal memory improvement in humans. These results suggest that thalamic spindles that occur during transitions to the cortical SO Up state are optimal for memory consolidation. Our study predicts that the timely interactions between cortical and thalamic events during consolidation, contribute to memory improvement and is mediated by the level of inhibitory neurotransmission.
Learning of spatio-temporal codes in a coupled oscillator system.
Orosz, Gábor; Ashwin, Peter; Townley, Stuart
2009-07-01
In this paper, we consider a learning strategy that allows one to transmit information between two coupled phase oscillator systems (called teaching and learning systems) via frequency adaptation. The dynamics of these systems can be modeled with reference to a number of partially synchronized cluster states and transitions between them. Forcing the teaching system by steady but spatially nonhomogeneous inputs produces cyclic sequences of transitions between the cluster states, that is, information about inputs is encoded via a "winnerless competition" process into spatio-temporal codes. The large variety of codes can be learned by the learning system that adapts its frequencies to those of the teaching system. We visualize the dynamics using "weighted order parameters (WOPs)" that are analogous to "local field potentials" in neural systems. Since spatio-temporal coding is a mechanism that appears in olfactory systems, the developed learning rules may help to extract information from these neural ensembles.
Suppression of mode-beating in a saturated hole-coupled FEL oscillator
International Nuclear Information System (INIS)
Krishnagopal, S.; Xie, M.; Kim, K.J.
1992-08-01
In a hole-coupled resonator, either empty or loaded with a linear FEL gain medium, the phenomenon of mode-degeneracy and mode-beating have been studied. When the magnitudes of the eigenvalues, derived from a linear analysis, are equal for two or more dominant eigenmodes, the system cannot achieve a stable beam-profile. We investigate this phenomenon when a saturated FEL is present within the cavity, thus introducing non-linearity. We use a three-dimensional FEL oscillator code, based on the amplifier code TDA, and show that mode-beating is completely suppressed in the nonlinear saturated regime. We suggest a simple, qualitative model for the mechanism responsible for this suppression
Radwan, Basma; Dvorak, Dino; Fenton, André
2016-01-01
Fragile X syndrome (FXS) patients do not make the fragile X mental retardation protein (FMRP). Absence of FMRP causes dysregulated translation, abnormal synaptic plasticity and the most common form of inherited intellectual disability. But FMRP loss has minimal effects on memory itself, making it difficult to understand why absence of FMRP impairs memory discrimination and increases risk of autistic symptoms in patients, such as exaggerated responses to environmental changes. While Fmr1 knockout (KO) and wild-type (WT) mice perform cognitive discrimination tasks, we find abnormal patterns of coupling between theta and gamma oscillations in perisomatic and dendritic hippocampal CA1 local field potentials of the KO. Perisomatic CA1 theta-gamma phase-amplitude coupling (PAC) decreases with familiarity in both the WT and KO, but activating an invisible shock zone, subsequently changing its location, or turning it off, changes the pattern of oscillatory events in the LFPs recorded along the somato-dendritic axis of CA1. The cognition-dependent changes of this pattern of neural activity are relatively constrained in WT mice compared to KO mice, which exhibit abnormally weak changes during the cognitive challenge caused by changing the location of the shock zone and exaggerated patterns of change when the shock zone is turned off. Such pathophysiology might explain how dysregulated translation leads to intellectual disability in FXS. These findings demonstrate major functional abnormalities after the loss of FMRP in the dynamics of neural oscillations and that these impairments would be difficult to detect by steady-state measurements with the subject at rest or in steady conditions. PMID:26792400
Bukh, Andrei; Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim
2017-11-01
We study numerically the dynamics of a network made of two coupled one-dimensional ensembles of discrete-time systems. The first ensemble is represented by a ring of nonlocally coupled Henon maps and the second one by a ring of nonlocally coupled Lozi maps. We find that the network of coupled ensembles can realize all the spatio-temporal structures which are observed both in the Henon map ensemble and in the Lozi map ensemble while uncoupled. Moreover, we reveal a new type of spatiotemporal structure, a solitary state chimera, in the considered network. We also establish and describe the effect of mutual synchronization of various complex spatiotemporal patterns in the system of two coupled ensembles of Henon and Lozi maps.
Directory of Open Access Journals (Sweden)
Bo Sun
2014-09-01
Full Text Available Consider the Klein-Gordon equation with variable coefficients, a van der Pol cubic nonlinearity in one of the boundary conditions and a spatially distributed antidamping term, we use a variable-substitution technique together with the analogy with the 1-dimensional wave equation to prove that for the Klein-Gordon equation chaos occurs for a class of equations and boundary conditions when system parameters enter a certain regime. Chaotic and nonchaotic profiles of solutions are illustrated by computer graphics.
Energy Technology Data Exchange (ETDEWEB)
Ajayamohan, R.S. [University of Victoria, Canadian Centre for Climate Modelling and Analysis, P.O. Box 3065, Victoria, BC (Canada); Annamalai, H.; Hafner, Jan [University of Hawaii, International Pacific Research Center, Honolulu (United States); Luo, Jing-Jia [Japan Agency for Marine-Earth Science and Technology, Frontier Research Centre for Global Change, Yokohama (Japan); Yamagata, Toshio [Japan Agency for Marine-Earth Science and Technology, Frontier Research Centre for Global Change, Yokohama (Japan); The University of Tokyo, Department of Earth and Planetary Science, Tokyo (Japan)
2011-09-15
The study compares the simulated poleward migration characteristics of boreal summer intraseasonal oscillations (BSISO) in a suite of coupled ocean-atmospheric model sensitivity integrations. The sensitivity experiments are designed in such a manner to allow full coupling in specific ocean basins but forced by temporally varying monthly climatological sea surface temperature (SST) adopted from the fully coupled model control runs (ES10). While the local air-sea interaction is suppressed in the tropical Indian Ocean and allowed in the other oceans in the ESdI run, it is suppressed in the tropical Pacific and allowed in the other oceans in the ESdP run. Our diagnostics show that the basic mean state in precipitation and easterly vertical shear as well as the BSISO properties remain unchanged due to either inclusion or exclusion of local air-sea interaction. In the presence of realistic easterly vertical shear, the continuous emanation of Rossby waves from the equatorial convection is trapped over the monsoon region that enables the poleward propagation of BSISO anomalies in all the model sensitivity experiments. To explore the internal processes that maintain the tropospheric moisture anomalies ahead of BSISO precipitation anomalies, moisture and moist static energy budgets are performed. In all model experiments, advection of anomalous moisture by climatological winds anchors the moisture anomalies that in turn promote the northward migration of BSISO precipitation. While the results indicate the need for realistic simulation of all aspects of the basic state, our model results need to be taken with caution because in the ECHAM family of coupled models the internal variance at intraseasonal timescales is indeed very high, and therefore local air-sea interactions may not play a pivotal role. (orig.)
Encryption in Chaotic Systems with Sinusoidal Excitations
Directory of Open Access Journals (Sweden)
G. Obregón-Pulido
2014-01-01
Full Text Available In this contribution an encryption method using a chaotic oscillator, excited by “n” sinusoidal signals, is presented. The chaotic oscillator is excited by a sum of “n” sinusoidal signals and a message. The objective is to encrypt such a message using the chaotic behavior and transmit it, and, as the chaotic system is perturbed by the sinusoidal signal, the transmission security could be increased due to the effect of such a perturbation. The procedure is based on the regulation theory and consider that the receiver knows the frequencies of the perturbing signal, with this considerations the algorithm estimates the excitation in such a way that the receiver can cancel out the perturbation and all the undesirable dynamics in order to produce only the message. In this way we consider that the security level is increased.
Directory of Open Access Journals (Sweden)
Muhammad Iqbal
2018-02-01
Full Text Available This paper exploits the dynamical modeling, behavior analysis, and synchronization of a network of four different FitzHugh–Nagumo (FHN neurons with unknown parameters linked in a ring configuration under direction-dependent coupling. The main purpose is to investigate a robust adaptive control law for the synchronization of uncertain and perturbed neurons, communicating in a medium of bidirectional coupling. The neurons are assumed to be different and interconnected in a ring structure. The strength of the gap junctions is taken to be different for each link in the network, owing to the inter-neuronal coupling medium properties. Robust adaptive control mechanism based on Lyapunov stability analysis is employed and theoretical criteria are derived to realize the synchronization of the network of four FHN neurons in a ring form with unknown parameters under direction-dependent coupling and disturbances. The proposed scheme for synchronization of dissimilar neurons, under external electrical stimuli, coupled in a ring communication topology, having all parameters unknown, and subject to directional coupling medium and perturbations, is addressed for the first time as per our knowledge. To demonstrate the efficacy of the proposed strategy, simulation results are provided.
Iqbal, Muhammad; Rehan, Muhammad; Hong, Keum-Shik
2018-01-01
This paper exploits the dynamical modeling, behavior analysis, and synchronization of a network of four different FitzHugh–Nagumo (FHN) neurons with unknown parameters linked in a ring configuration under direction-dependent coupling. The main purpose is to investigate a robust adaptive control law for the synchronization of uncertain and perturbed neurons, communicating in a medium of bidirectional coupling. The neurons are assumed to be different and interconnected in a ring structure. The strength of the gap junctions is taken to be different for each link in the network, owing to the inter-neuronal coupling medium properties. Robust adaptive control mechanism based on Lyapunov stability analysis is employed and theoretical criteria are derived to realize the synchronization of the network of four FHN neurons in a ring form with unknown parameters under direction-dependent coupling and disturbances. The proposed scheme for synchronization of dissimilar neurons, under external electrical stimuli, coupled in a ring communication topology, having all parameters unknown, and subject to directional coupling medium and perturbations, is addressed for the first time as per our knowledge. To demonstrate the efficacy of the proposed strategy, simulation results are provided. PMID:29535622
Wang, Yongqiang; Nunez, Felipe; Doyle III, Francis J.
2012-01-01
This paper addresses the synchronization rate of weakly connected pulse-coupled oscillators (PCOs). We prove that besides coupling strength, the phase response function is also a determinant of synchronization rate. Inspired by the result, we propose to increase the synchronization rate of PCOs by designing the phase response function. This has important significance in PCO-based clock synchronization of wireless networks. By designing the phase response function, synchronization rate is incr...
Entanglement entropy in the quantum networks of a coupled quantum harmonic oscillator
International Nuclear Information System (INIS)
Jafarizadeh, M A; Nami, S; Eghbalifam, F
2015-01-01
We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a network are calculated.In partitioning an arbitrary graph into two parts there are some nodes in each part which are not connected to the nodes of the other part. So, these nodes of each part can be in distinct subsets. Therefore, the graph is separated into four subsets. The nodes of the first and last subsets are those which are not connected to the nodes of the other part. In theorem 1, by using the generalized Schur complement method in these four subsets, we prove that all the graphs whose connections between the two alternative subsets are complete, have the same entropy. A large number of graphs satisfy this theorem. Then the entanglement entropy in the limit of the large coupling and large size of the system is investigated in these graphs. Also, the asymptotic behaviors of the Schmidt numbers and entanglement entropy in the limit of infinite coupling are shown.One important quantity about partitioning is the conductance of the graph. The conductance of the graph is considered in various graphs. In these graphs we compare the conductance of the graph and the entanglement entropy. (paper)
Design of Threshold Controller Based Chaotic Circuits
DEFF Research Database (Denmark)
Mohamed, I. Raja; Murali, K.; Sinha, Sudeshna
2010-01-01
We propose a very simple implementation of a second-order nonautonomous chaotic oscillator, using a threshold controller as the only source of nonlinearity. We demonstrate the efficacy and simplicity of our design through numerical and experimental results. Further, we show that this approach...... of using a threshold controller as a nonlinear element, can be extended to obtain autonomous and multiscroll chaotic attractor circuits as well....
International Nuclear Information System (INIS)
Macias-Diaz, J.E.; Puri, A.
2007-01-01
In the present Letter, we simulate the propagation of binary signals in semi-infinite, mechanical chains of coupled oscillators harmonically driven at the end, by making use of the recently discovered process of nonlinear supratransmission. Our numerical results-which are based on a brand-new computational technique with energy-invariant properties-show an efficient and reliable transmission of information
Michiels, W.; Nijmeijer, H.
2009-01-01
We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the
Energy Technology Data Exchange (ETDEWEB)
Lafranceschina, Jacopo, E-mail: jlafranceschina@alaska.edu; Wackerbauer, Renate, E-mail: rawackerbauer@alaska.edu [Department of Physics, University of Alaska, Fairbanks, Alaska 99775-5920 (United States)
2015-01-15
Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Weak excitatory synapses can increase the Lyapunov exponent, expedite the collapse, and promote the collapse to the rest state rather than the pulse state. A single traveling pulse solution may no longer be asymptotic for certain combinations of network topology and (weak) coupling strengths, and initiate spatiotemporal chaos. Multiple pulses can cause chaos initiation due to diffusive and synaptic pulse-pulse interaction. In the presence of chaos initiation, intermittent spatiotemporal chaos exists until typically a collapse to the rest state.
International Nuclear Information System (INIS)
Lafranceschina, Jacopo; Wackerbauer, Renate
2015-01-01
Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Weak excitatory synapses can increase the Lyapunov exponent, expedite the collapse, and promote the collapse to the rest state rather than the pulse state. A single traveling pulse solution may no longer be asymptotic for certain combinations of network topology and (weak) coupling strengths, and initiate spatiotemporal chaos. Multiple pulses can cause chaos initiation due to diffusive and synaptic pulse-pulse interaction. In the presence of chaos initiation, intermittent spatiotemporal chaos exists until typically a collapse to the rest state
The Madden-Julian oscillation in ECHAM4 coupled and uncoupled general circulation models
Energy Technology Data Exchange (ETDEWEB)
Sperber, Kenneth R. [Lawrence Livermore National Laboratory, Program for Climate Model Diagnosis and Intercomparison, Livermore, CA (United States); Gualdi, Silvio [National Institute of Geophysics and Volcanology, Bologna (Italy); Legutke, Stephanie; Gayler, Veronika [Max Planck Institute of Meteorology, Models and Data Group, Hamburg (Germany)
2005-08-01
The Madden-Julian oscillation (MJO) dominates tropical variability on timescales of 30-70 days. During the boreal winter/spring, it is manifested as an eastward propagating disturbance, with a strong convective signature over the eastern hemisphere. The space-time structure of the MJO is analyzed using simulations with the ECHAM4 atmospheric general circulation model run with observed monthly mean sea-surface temperatures (SSTs), and coupled to three different ocean models. The coherence of the eastward propagation of MJO convection is sensitive to the ocean model to which ECHAM4 is coupled. For ECHAM4/OPYC and ECHO-G, models for which 100 years of daily data is available, Monte Carlo sampling indicates that their metrics of eastward propagation are different at the 1% significance level. The flux-adjusted coupled simulations, ECHAM4/OPYC and ECHO-G, maintain a more realistic mean-state, and have a more realistic MJO simulation than the nonadjusted scale interaction experiment (SINTEX) coupled runs. The SINTEX model exhibits a cold bias in Indian Ocean and tropical West Pacific Ocean sea-surface temperature of 0.5 C. This cold bias affects the distribution of time-mean convection over the tropical eastern hemisphere. Furthermore, the eastward propagation of MJO convection in this model is not as coherent as in the two models that used flux adjustment or when compared to an integration of ECHAM4 with prescribed observed SST. This result suggests that simulating a realistic basic state is at least as important as air-sea interaction for organizing the MJO. While all of the coupled models simulate the warm (cold) SST anomalies that precede (succeed) the MJO convection, the interaction of the components of the net surface heat flux that lead to these anomalies are different over the Indian Ocean. The ECHAM4/OPYC model in which the atmospheric model is run at a horizontal resolution of T42, has eastward propagating zonal wind anomalies and latent heat flux anomalies
Chaotic bursting in semiconductor lasers
Ruschel, Stefan; Yanchuk, Serhiy
2017-11-01
We investigate the dynamic mechanisms for low frequency fluctuations in semiconductor lasers subjected to delayed optical feedback, using the Lang-Kobayashi model. This system of delay differential equations displays pronounced envelope dynamics, ranging from erratic, so called low frequency fluctuations to regular pulse packages, if the time scales of fast oscillations and envelope dynamics are well separated. We investigate the parameter regions where low frequency fluctuations occur and compute their Lyapunov spectra. Using the geometric singular perturbation theory, we study this intermittent chaotic behavior and characterize these solutions as bursting slow-fast oscillations.
Chaos of the Relativistic Forced van der Pol Oscillator
International Nuclear Information System (INIS)
Ashkenazya, Y.; Gorma, C; Horwitz, L. P.
1998-01-01
A manifestly relativistically covariant form of the van der Pol oscillator in 1 + 1 dimensions is studied. We show that the driven relativistic equations, for which z and t are coupled, relax very quickly to a pair of identical decoupled equations, due to a rapid vanishing of the angular momentum (the boost in 1 + 1 dimensions). A similar effect occurs in the damped driven covariant Duffing oscillator previously treated. This effect is an example of entrainment, or synchronization (phase locking) , of coupled chaotic systems. The Lyapunov exponents are calculated using the very efficient method of Habib and Ryne. We show a Poincare map that demonstrates this effect and maintains remarkable stability in spite of the inevitable accumulation of computer error in the chaotic region. For our choice of parameters, the positive Lyapunov exponent is about 0.242 almost independently of the integration method
On analytical justification of phase synchronization in different chaotic systems
International Nuclear Information System (INIS)
Erjaee, G.H.
2009-01-01
In analytical or numerical synchronizations studies of coupled chaotic systems the phase synchronizations have less considered in the leading literatures. This article is an attempt to find a sufficient analytical condition for stability of phase synchronization in some coupled chaotic systems. The method of nonlinear feedback function and the scheme of matrix measure have been used to justify this analytical stability, and tested numerically for the existence of the phase synchronization in some coupled chaotic systems.
International Nuclear Information System (INIS)
Zhu Yun; Zheng Zhi-Gang; Yang Jun-Zhong
2013-01-01
Dynamics of a one-dimensional array of non-locally coupled Kuramoto phase oscillators with an external potential is studied. A four-cluster chimera state is observed for the moderate strength of the external potential. Different from the clustered chimera states studied before, the instantaneous frequencies of the oscillators in a synchronized cluster are different in the presence of the external potential. As the strength of the external potential increases, a bifurcation from the two-cluster chimera state to the four-cluster chimera states can be found. These phenomena are well predicted analytically with the help of the Ott—Antonsen ansatz. (general)
Simulations of the Madden-Julian oscillation in four pairs of coupled and uncoupled global models
Energy Technology Data Exchange (ETDEWEB)
Zhang, Chidong; Dong, Min [RSMAS, University of Miami, Miami, FL (United States); Gualdi, Silvio [National Institute of Geophysics and Volcanology, Bologna (Italy); Hendon, Harry H. [BMRC, Melbourne, VIC (Australia); Maloney, Eric D. [Oregon State University, Corvallis, OR (United States); Marshall, Andrew [Monash University, Melbourne, VIC (Australia); Sperber, Kenneth R. [PCMDI, Lawrence Livermore National Laboratory, Livermore, CA (United States); Wang, Wanqiu [CPC/NCEP/NOAA, Camp Springs, MD (United States)
2006-11-15
The status of the numerical reproduction of the Madden-Julian Oscillation (MJO) by current global models was assessed through diagnoses of four pairs of coupled and uncoupled simulations. Slow eastward propagation of the MJO, especially in low-level zonal wind, is realistic in all these simulations. However, the simulated MJO suffers from several common problems. The MJO signal in precipitation is generally too weak and often eroded by an unrealistic split of an equatorial maximum of precipitation into a double ITCZ structure over the western Pacific. The MJO signal in low-level zonal wind, on the other hand, is sometimes too strong over the eastern Pacific but too weak over the Indian Ocean. The observed phase relationship between precipitation and low-level zonal wind associated with the MJO in the western Pacific and their coherence in general are not reproduced by the models. The seasonal migration in latitude of MJO activity is missing in most simulations. Air-sea coupling generally strengthens the simulated eastward propagating signal, but its effects on the phase relationship and coherence between precipitation and low-level zonal wind, and on their geographic distributions, seasonal cycles, and interannual variability are inconsistent among the simulations. Such inconsistency cautions generalization of results from MJO simulations using a single model. In comparison to observations, biases in the simulated MJO appear to be related to biases in the background state of mean precipitation, low-level zonal wind, and boundary-layer moisture convergence. This study concludes that, while the realistic simulations of the eastward propagation of the MJO are encouraging, reproducing other fundamental features of the MJO by current global models remains an unmet challenge. (orig.)
Influence of topology in the mobility enhancement of pulse-coupled oscillator synchronization
Beardo, A.; Prignano, L.; Sagarra, O.; Díaz-Guilera, A.
2017-12-01
In this work we revisit the nonmonotonic behavior (NMB) of synchronization time with velocity reported for systems of mobile pulse-coupled oscillators (PCOs). We devise a control parameter that allows us to predict in which range of velocities NMB may occur, also uncovering the conditions allowing us to establish the emergence of NMB based on specific features of the connectivity rule. Specifically, our results show that if the connectivity rule is such that the interaction patterns are sparse and, more importantly, include a large fraction of nonreciprocal interactions, then the system will display NMB. We furthermore provide a microscopic explanation relating the presence of such features of the connectivity patterns to the existence of local clusters unable to synchronize, termed frustrated clusters, for which we also give a precise definition in terms of simple graph concepts. We conclude that, if the probability of finding a frustrated cluster in a system of moving PCOs is high enough, NMB occurs in a predictable range of velocities.
Stability and oscillation of two coupled Duffing equations with time delay state feedback
International Nuclear Information System (INIS)
El-Bassiouny, A F
2006-01-01
This paper presents an analytical study of the simultaneous principal parametric resonances of two coupled Duffing equations with time delay state feedback. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. The method of multiple scales is used to determine a set of ordinary differential equations governing the modulation of the amplitudes and phases of the two modes. The first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the frequency-response curves. We analyse the effect of time delay and the other different parameters on these oscillations. The stability of the fixed points is examined by using the variational method. Numerical solutions are carried out and graphical representations of the results are presented and discussed. Increasing in the time delay τ given decreasing and increasing in the regions of definition and stability respectively and the first mode has decreased magnitudes. The multivalued solutions disappear when decreasing the coefficients of cubic nonlinearities of the second mode α 3 and the detuning parameter σ 2 respectively. Both modes shift to the left for increasing linear feedback gain v 1 and the coefficient of parametric excitation f 1 respectively
Tunable Coupling to a Mechanical Oscillator Circuit Using a Coherent Feedback Network
Directory of Open Access Journals (Sweden)
Joseph Kerckhoff
2013-06-01
Full Text Available We demonstrate a fully cryogenic microwave feedback network composed of modular superconducting devices connected by transmission lines and designed to control a mechanical oscillator that is coupled to one of the devices. The network features an electromechanical device and a tunable controller that coherently receives, processes, and feeds back continuous microwave signals that modify the dynamics and readout of the mechanical state. While previous electromechanical systems represent some compromise between efficient control and efficient readout of the mechanical state, as set by the electromagnetic decay rate, the tunable controller produces a closed-loop network that can be dynamically and continuously tuned between both extremes much faster than the mechanical response time. We demonstrate that the microwave decay rate may be modulated by at least a factor of 10 at a rate greater than 10^{4} times the mechanical response rate. The system is easy to build and suggests that some useful functions may arise most naturally at the network level of modular, quantum electromagnetic devices.
Power harvesting by electromagnetic coupling from wind-induced limit cycle oscillations
Boccalero, G.; Olivieri, S.; Mazzino, A.; Boragno, C.
2017-09-01
Recent developments of low-power microprocessors open to new applications such as wireless sensor networks (WSN) with the consequent problem of autonomous powering. For this purpose, a possible strategy is represented by energy harvesting from wind or other flows exploiting fluid-structure interactions. In this work, we present an updated picture of a flutter-based device characterized by fully passive dynamics and a simple constructive layout, where limit cycle oscillations are undergone by an elastically bounded wing. In this case, the conversion from mechanical to electrical energy is performed by means of an electromagnetic coupling between a pair of coils and magnets. A centimetric-size prototype is shown to harvest energy from low wind velocities (between 2 and 4 m s-1), reaching a power peak of 14 mW, representing a valuable amount for applications related to WSN. A mathematical description of the nonlinear dynamics is then provided by a quasi-steady phenomenological model, revealing satisfactory agreement with the experimental framework within a certain parametric range and representing a useful tool for future optimizations.
Chaotic neoclassical separatrix dissipation in parametric drift-wave decay.
Kabantsev, A A; Tsidulko, Yu A; Driscoll, C F
2014-02-07
Experiments and theory characterize a parametric decay instability between plasma drift waves when the nonlinear coupling is modified by an electrostatic barrier. Novel mode coupling terms representing enhanced dissipation and mode phase shifts are caused by chaotic separatrix crossings on the wave-ruffled separatrix. Experimental determination of these coupling terms is in broad agreement with new chaotic neoclassical transport analyses.