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.
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
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
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....
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.
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...
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
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....
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
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.
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 ...
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 ...
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...
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...
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.
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.
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)
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.
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.
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
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).
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.
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.
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.
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
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
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.
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.
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)
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 ...
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
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)
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.
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.
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)
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
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)
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.
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
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.
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
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)
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.
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 .
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
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.
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.
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.
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.)
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.
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.
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)
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.
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
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)
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.
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.
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
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.
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.
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.
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.
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
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.}
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)
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
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
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.
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.
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.
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%.
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...
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
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.
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.
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....
Eigenfunctions in chaotic quantum systems
Energy Technology Data Exchange (ETDEWEB)
Baecker, Arnd
2007-07-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Eigenfunctions in chaotic quantum systems
International Nuclear Information System (INIS)
Baecker, Arnd
2007-01-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
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.
Mallory, Kristina; van Gorder, Robert A.
We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky-Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky-Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.
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.
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.
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....
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.
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.
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 ...
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.
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 ...
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.
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)
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
Chaotic wave trains in an oscillatory/excitable medium
International Nuclear Information System (INIS)
Rabinovitch, A.; Gutman, M.; Biton, Y.; Aviram, I.
2006-01-01
We study the chaotic dynamics of a heterogeneous reaction-diffusion medium composed of two uniform regions: one oscillatory, and the other excitable. It is shown that, by altering the diffusion coefficient, local chaotic oscillations can be induced at the interface between regions, which in turn, generate different chaotic sequences of pulses traveling in the excitable region. We analyze the properties of the local chaotic driver, as well as the diffusion-induced transitions. A procedure based on the abnormal frequency-locking phenomenon is proposed for controlling such sequences. Relevance of the obtained results to cardiac dynamics is briefly discussed
Adaptive Synchronization of Memristor-based Chaotic Neural Systems
Directory of Open Access Journals (Sweden)
Xiaofang Hu
2014-11-01
Full Text Available Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.
International Nuclear Information System (INIS)
Wei Jun; Liao Xiaofeng; Wong, Kwok-wo; Xiang Tao
2006-01-01
Based on the study of some previously proposed chaotic encryption algorithms, we found that it is dangerous to mix chaotic state or iteration number of the chaotic system with ciphertext. In this paper, a new chaotic cryptosystem is proposed. Instead of simply mixing the chaotic signal of the proposed chaotic cryptosystem with the ciphertext, a noise-like variable is utilized to govern the encryption and decryption processes. This adds statistical sense to the new cryptosystem. Numerical simulations show that the new cryptosystem is practical whenever efficiency, ciphertext length or security is concerned
International Nuclear Information System (INIS)
Cook, A.
1990-09-01
An elementary account of the origin of chaotic behaviour in classical dynamics is given with examples from geophysics, and in conclusion some thoughts about what can be predicted of chaotic behaviour and what sorts of arguments can be used to guide human behaviour in chaotic conditions are presented. 4 refs
The transition to chaotic phase synchronization
DEFF Research Database (Denmark)
Mosekilde, E.; Laugesen, J. L.; Zhusubaliyev, Zh. T.
2012-01-01
The transition to chaotic phase synchronization for a periodically driven spiral-type chaotic oscillator is known to involve a dense set of saddle-node bifurcations. By following the synchronization transition through the cascade of period-doubling bifurcations in a forced Ro¨ssler system...... to the torus doubling bifurcations that take place outside this domain. By examining a physiology-based model of the blood flow regulation to the individual functional unit (nephron) of the kidney we demonstrate how a similar bifurcation structure may arise in this system as a response to a periodically...
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.
Complex economic dynamics: Chaotic saddle, crisis and intermittency
International Nuclear Information System (INIS)
Chian, Abraham C.-L.; Rempel, Erico L.; Rogers, Colin
2006-01-01
Complex economic dynamics is studied by a forced oscillator model of business cycles. The technique of numerical modeling is applied to characterize the fundamental properties of complex economic systems which exhibit multiscale and multistability behaviors, as well as coexistence of order and chaos. In particular, we focus on the dynamics and structure of unstable periodic orbits and chaotic saddles within a periodic window of the bifurcation diagram, at the onset of a saddle-node bifurcation and of an attractor merging crisis, and in the chaotic regions associated with type-I intermittency and crisis-induced intermittency, in non-linear economic cycles. Inside a periodic window, chaotic saddles are responsible for the transient motion preceding convergence to a periodic or a chaotic attractor. The links between chaotic saddles, crisis and intermittency in complex economic dynamics are discussed. We show that a chaotic attractor is composed of chaotic saddles and unstable periodic orbits located in the gap regions of chaotic saddles. Non-linear modeling of economic chaotic saddle, crisis and intermittency can improve our understanding of the dynamics of financial intermittency observed in stock market and foreign exchange market. Characterization of the complex dynamics of economic systems is a powerful tool for pattern recognition and forecasting of business and financial cycles, as well as for optimization of management strategy and decision technology
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...
On nonlinear control design for autonomous chaotic systems of integer and fractional orders
International Nuclear Information System (INIS)
Ahmad, Wajdi M.; Harb, Ahmad M.
2003-01-01
In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations
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.
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragó n, J. L.; Barrio, R. A.; Woolley, T. E.; Baker, R. E.; Maini, P. K.
2012-01-01
consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos
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...
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
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...
Generation and control of multi-scroll chaotic attractors in fractional order systems
International Nuclear Information System (INIS)
Ahmad, Wajdi M.
2005-01-01
The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations
International Nuclear Information System (INIS)
Jung, Jinwoo; Lee, Jewon; Song, Hanjung
2011-01-01
This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performed simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-μm single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with ±2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.
Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki
2013-01-01
The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented. PMID:23558425
International Nuclear Information System (INIS)
Munmuangsaen, Buncha; Srisuchinwong, Banlue
2011-01-01
Highlights: → Five new elementary chaotic snap flows and a generalization of an existing chaotic snap flow have been presented. → Three of all are conservative systems whilst three others are dissipative systems. → Four cases need only a single control parameter and a single nonlinearity. → A cubic case in a jerk representation requires only two terms and a single nonlinearity. - Abstract: Hyperjerk systems with 4th-order derivative of the form x .... =f(x ... ,x .. ,x . ,x) have been referred to as snap systems. Five new elementary chaotic snap flows and a generalization of an existing flow are presented through an extensive numerical search. Four of these flows demonstrate elegant simplicity of a single control parameter based on a single nonlinearity of a quadratic, a piecewise-linear or an exponential type. Two others demonstrate elegant simplicity of all unity-in-magnitude parameters based on either a single cubic nonlinearity or three cubic nonlinearities. The chaotic snap flow with a single cubic nonlinearity requires only two terms and can be transformed to its equivalent dynamical form of only five terms which have a single nonlinearity. An advantage is that such a chaotic flow offers only five terms even though the (four) dimension is high. Three of the chaotic snap flows are characterized as conservative systems whilst three others are dissipative systems. Basic dynamical properties are described.
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.
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)
Cascade Chaotic System With Applications.
Zhou, Yicong; Hua, Zhongyun; Pun, Chi-Man; Chen, C L Philip
2015-09-01
Chaotic maps are widely used in different applications. Motivated by the cascade structure in electronic circuits, this paper introduces a general chaotic framework called the cascade chaotic system (CCS). Using two 1-D chaotic maps as seed maps, CCS is able to generate a huge number of new chaotic maps. Examples and evaluations show the CCS's robustness. Compared with corresponding seed maps, newly generated chaotic maps are more unpredictable and have better chaotic performance, more parameters, and complex chaotic properties. To investigate applications of CCS, we introduce a pseudo-random number generator (PRNG) and a data encryption system using a chaotic map generated by CCS. Simulation and analysis demonstrate that the proposed PRNG has high quality of randomness and that the data encryption system is able to protect different types of data with a high-security level.
Quantifying chaotic dynamics from integrate-and-fire processes
Energy Technology Data Exchange (ETDEWEB)
Pavlov, A. N. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Saratov State Technical University, Politehnicheskaya Str. 77, 410054 Saratov (Russian Federation); Pavlova, O. N. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Mohammad, Y. K. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Tikrit University Salahudin, Tikrit Qadisiyah, University Str. P.O. Box 42, Tikrit (Iraq); Kurths, J. [Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam (Germany); Institute of Physics, Humboldt University Berlin, 12489 Berlin (Germany)
2015-01-15
Characterizing chaotic dynamics from integrate-and-fire (IF) interspike intervals (ISIs) is relatively easy performed at high firing rates. When the firing rate is low, a correct estimation of Lyapunov exponents (LEs) describing dynamical features of complex oscillations reflected in the IF ISI sequences becomes more complicated. In this work we discuss peculiarities and limitations of quantifying chaotic dynamics from IF point processes. We consider main factors leading to underestimated LEs and demonstrate a way of improving numerical determining of LEs from IF ISI sequences. We show that estimations of the two largest LEs can be performed using around 400 mean periods of chaotic oscillations in the regime of phase-coherent chaos. Application to real data is discussed.
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
FPGA implementation of fractional-order discrete memristor chaotic ...
Indian Academy of Sciences (India)
Anitha Karthikeyan
Corresponding author. E-mail: rkarthiekeyan@gmail.com. MS received 10 August 2017; revised 4 September 2017; accepted 5 September 2017; published online 30 December 2017. Abstract. A new fourth-order memristor chaotic oscillator is taken to investigate its fractional-order discrete synchronisation.
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...
Applications of chaotic neurodynamics in pattern recognition
Baird, Bill; Freeman, Walter J.; Eeckman, Frank H.; Yao, Yong
1991-08-01
Network algorithms and architectures for pattern recognition derived from neural models of the olfactory system are reviewed. These span a range from highly abstract to physiologically detailed, and employ the kind of dynamical complexity observed in olfactory cortex, ranging from oscillation to chaos. A simple architecture and algorithm for analytically guaranteed associative memory storage of analog patterns, continuous sequences, and chaotic attractors in the same network is described. A matrix inversion determines network weights, given prototype patterns to be stored. There are N units of capacity in an N node network with 3N2 weights. It costs one unit per static attractor, two per Fourier component of each sequence, and three to four per chaotic attractor. There are no spurious attractors, and for sequences there is a Liapunov function in a special coordinate system which governs the approach of transient states to stored trajectories. Unsupervised or supervised incremental learning algorithms for pattern classification, such as competitive learning or bootstrap Widrow-Hoff can easily be implemented. The architecture can be ''folded'' into a recurrent network with higher order weights that can be used as a model of cortex that stores oscillatory and chaotic attractors by a Hebb rule. Network performance is demonstrated by application to the problem of real-time handwritten digit recognition. An effective system with on-line learning has been written by Eeckman and Baird for the Macintosh. It utilizes static, oscillatory, and/or chaotic attractors of two kinds--Lorenze attractors, or attractors resulting from chaotically interacting oscillatory modes. The successful application to an industrial pattern recognition problem of a network architecture of considerable physiological and dynamical complexity, developed by Freeman and Yao, is described. The data sets of the problem come in three classes of difficulty, and performance of the biological network is
International Nuclear Information System (INIS)
Kawai, Y.
1991-08-01
It has recently been recognized that the research on various aspects of chaotic dynamics grows rapidly as one of some areas in nonlinear science. On the other hands, the plasma has long been called a treasure-house of nonlinear phenomena, so it is easy to imagine that the plasma is abundant in chaotic phenomena. In fact, the research on plasma chaos is going on, such as the research on the stochastic magnetic field and the chaotic orbit in the toroidal helical system, as well as the research in other experiments. To review the present status of the research on plasma chaos and to make clear the basic common physics, a working group was organized in 1990 as a collaboration research of National Institute for Fusion Science. This is the report on its activity in 1990, with a stress on experimental data obtained in basic plasma experiments and RFP, and on the relaxed theories and computer simulations. (author)
Cryptography with chaotic mixing
International Nuclear Information System (INIS)
Oliveira, Luiz P.L. de; Sobottka, Marcelo
2008-01-01
We propose a cryptosystem based on one-dimensional chaotic maps of the form H p (x)=r p -1 0G0r p (x) defined in the interval [0, 10 p ) for a positive integer parameter p, where G(x)=10x(mod10) and r p (x)= p √(x), which is a topological conjugacy between G and the shift map σ on the space Σ of the sequences with 10 symbols. There are three advantages in comparison with the recently proposed cryptosystem based on chaotic logistic maps F μ (x)=μx(1-x) with 3 p is always chaotic for all parameters p, (b) the knowledge of an ergodic measure allows assignments of the alphabetic symbols to equiprobable sites of H p 's domain and (c) for each p, the security of the cryptosystem is manageable against brute force attacks
Hypogenetic chaotic jerk flows
International Nuclear Information System (INIS)
Li, Chunbiao; Sprott, Julien Clinton; Xing, Hongyan
2016-01-01
Removing the amplitude or polarity information in the feedback loop of a jerk structure shows that special nonlinearities with partial information in the variable can also lead to chaos. Some striking properties are found for this kind of hypogenetic chaotic jerk flow, including multistability of symmetric coexisting attractors from an asymmetric structure, hidden attractors with respect to equilibria but with global attraction, easy amplitude control, and phase reversal which is convenient for chaos applications. - Highlights: • Hypogenetic chaotic jerk flows with incomplete feedback of amplitude or polarity are obtained. • Multistability of symmetric coexisting attractors from an asymmetric structure is found. • Some jerk systems have hidden attractors with respect to equilibria but have global attraction. • These chaotic jerk flows have the properties of amplitude control and phase reversal.
Initial conditions for chaotic inflation
International Nuclear Information System (INIS)
Brandenberger, R.; Kung, J.; Feldman, H.
1991-01-01
In contrast to many other inflationary Universe models, chaotic inflation does not depend on fine tuning initial conditions. Within the context of linear perturbation theory, it is shown that chaotic inflation is stable towards both metric and matter perturbations. Neglecting gravitational perturbations, it is shown that chaotic inflation is an attractor in initial condition space. (orig.)
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 ...
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.
Stability of operation versus temperature of a three-phase clock-driven chaotic circuit
International Nuclear Information System (INIS)
Zhou Ji-Chao; Son Hyunsik; Song Han Jung; Kim Namtae
2013-01-01
We evaluate the influence of temperature on the behavior of a three-phase clock-driven metal—oxide—semiconductor (MOS) chaotic circuit. The chaotic circuit consists of two nonlinear functions, a level shifter, and three sample and hold blocks. It is necessary to analyze a CMOS-based chaotic circuit with respect to variation in temperature for stability because the circuit is sensitive to the behavior of the circuit design parameters. The temperature dependence of the proposed chaotic circuit is investigated via the simulation program with integrated circuit emphasis (SPICE) using 0.6-μm CMOS process technology with a 5-V power supply and a 20-kHz clock frequency. The simulation results demonstrate the effects of temperature on the chaotic dynamics of the proposed chaotic circuit. The time series, frequency spectra, bifurcation phenomena, and Lyapunov exponent results are provided. (general)
International Nuclear Information System (INIS)
Linde, A.D.
1986-05-01
It is shown that the universe evolution in the chaotic inflation scenario has no end and may have no beginning. According to this scenario, the universe consists of exponentially large number of different mini-universes inside which all possible metastable vacuum states and all possible types of compactification are realized. (author)
Chimera states in a population of identical oscillators under planar ...
Indian Academy of Sciences (India)
finding, observed in both a collection of van der Pol oscillators and chaotic Rössler oscillators, fur- ther simplifies the existence criterion for chimeras, thereby broadens the range of their applicability to real-world situations. Keywords. Synchronization; chimera; Rössler system; van der Pol oscillator. PACS Nos 05.45.
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
Regular and chaotic dynamics in time-dependent relativistic mean-field theory
International Nuclear Information System (INIS)
Vretenar, D.; Ring, P.; Lalazissis, G.A.; Poeschl, W.
1997-01-01
Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that reproduce experimental data on monopole resonances in 208 Pb show that the motion of the collective coordinate is regular for isoscalar oscillations, and that it becomes chaotic when initial conditions correspond to the isovector mode. Regular collective dynamics coexists with chaotic oscillations on the microscopic level. Time histories, Fourier spectra, state-space plots, Poincare sections, autocorrelation functions, and Lyapunov exponents are used to characterize the nonlinear system and to identify chaotic oscillations. Analogous considerations apply to higher multipolarities. copyright 1997 The American Physical Society
Replicate periodic windows in the parameter space of driven oscillators
Energy Technology Data Exchange (ETDEWEB)
Medeiros, E.S., E-mail: esm@if.usp.br [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil); Souza, S.L.T. de [Universidade Federal de Sao Joao del-Rei, Campus Alto Paraopeba, Minas Gerais (Brazil); Medrano-T, R.O. [Departamento de Ciencias Exatas e da Terra, Universidade Federal de Sao Paulo, Diadema, Sao Paulo (Brazil); Caldas, I.L. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)
2011-11-15
Highlights: > We apply a weak harmonic perturbation to control chaos in two driven oscillators. > We find replicate periodic windows in the driven oscillator parameter space. > We find that the periodic window replication is associated with the chaos control. - Abstract: In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation replicates these periodic windows giving rise to parameter regions correspondent to periodic orbits. The new windows are composed of parameters whose periodic orbits have the same periodicity and pattern of stable and unstable periodic orbits already existent for the unperturbed oscillator. Moreover, these unstable periodic orbits are embedded in chaotic attractors in phase space regions where the new stable orbits are identified. Thus, the observed periodic window replication is an effective oscillator control process, once chaotic orbits are replaced by regular ones.
The chaotic dynamical aperture
International Nuclear Information System (INIS)
Lee, S.Y.; Tepikian, S.
1985-01-01
Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipoles should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles
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)
Gourville, John T
2005-06-01
CEO Peter Walsh faces a classic innovator's dilemma. His company, Crescordia, produces high-quality metal plates, pins, and screws that orthopedic surgeons use to repair broken bones. In fact, because the company has for decades refused to compromise on quality, there are orthopedic surgeons who use nothing but Crescordia hardware. And now these customers have begun to clamor for the next generation technology: resorbable hardware. Resorbables offer clear advantages over the traditional hardware. Like dissolving sutures, resorbable plates and screws are made of biodegradable polymers. They hold up long enough to support a healing bone, then gradually and harmlessly disintegrate in the patient's body. Surgeons are especially looking forward to using resorbables on children, so kids won't have to undergo a second operation to remove the old hardware after their bones heal, a common procedure in pediatrics. The new products, however, are not yet reliable; they fail about 8% of the time, sometimes disintegrating before the bone completely heals and sometimes not ever fully disintegrating. That's why Crescordia, mindful of its hard-earned reputation, has delayed launching a line using the new technology. But time is running out. A few competitors have begun to sell resorbables despite their imperfections, and these companies are picking up market share. Should Crescordia join the fray and risk tarnishing its brand? Or should the company sit tight until it can offer a perfect product? Commenting on this fictional case study are Robert A. Lutz, vice chairman of product development at General Motors; Clayton M. Christensen, the Robert and Jane Cizik Professor of Business Administration at Harvard Business School; Jason Wittes, a senior equity analyst covering medical supplies and devices at Leerink Swann; and Nick Galakatos, a general partner of MPM Capital.
Nonlinear mode conversion with chaotic soliton generation at plasma resonance
International Nuclear Information System (INIS)
Pietsch, H.; Laedke, E.W.; Spatschek, K.H.
1993-01-01
The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schroedinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations
Dynamic control of chaotic resonators
Di Falco, A.; Bruck, R.; Liu, C.; Muskens, O.; Fratalocchi, Andrea
2016-01-01
We report on the all-optical control of chaotic optical resonators based on silicon on insulator (SOI) platform. We show that simple non-chaotic cavities can be tuned to exhibit chaotic behavior via intense optical pump- ing, inducing a local change of refractive index. To this extent we have fabricated a number of devices and demonstrated experimentally and theoretically that chaos can be triggered on demand on an optical chip. © 2016 SPIE.
Dynamic control of chaotic resonators
Di Falco, A.
2016-02-16
We report on the all-optical control of chaotic optical resonators based on silicon on insulator (SOI) platform. We show that simple non-chaotic cavities can be tuned to exhibit chaotic behavior via intense optical pump- ing, inducing a local change of refractive index. To this extent we have fabricated a number of devices and demonstrated experimentally and theoretically that chaos can be triggered on demand on an optical chip. © 2016 SPIE.
New Chaotic Dynamical System with a Conic-Shaped Equilibrium Located on the Plane Structure
Directory of Open Access Journals (Sweden)
Jiri Petrzela
2017-09-01
Full Text Available This paper presents a new autonomous deterministic dynamical system with equilibrium degenerated into a plane-oriented hyperbolic geometrical structure. It is demonstrated via numerical analysis and laboratory experiments that the discovered system has both a structurally stable strange attractor and experimentally measurable chaotic behavior. It is shown that the evolution of complex dynamics can be associated with a single parameter of a mathematical model and, due to one-to-one correspondence, to a single circuit parameter. Two-dimensional high resolution plots of the largest Lyapunov exponent and basins of attraction expressed in terms of final state energy are calculated and put into the context of the discovered third-order mathematical model and real chaotic oscillator. Both voltage- and current-mode analog chaotic oscillators are presented and verified by visualization of the typical chaotic attractor in a different fashion.
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
Using Chaotic System in Encryption
Findik, Oğuz; Kahramanli, Şirzat
In this paper chaotic systems and RSA encryption algorithm are combined in order to develop an encryption algorithm which accomplishes the modern standards. E.Lorenz's weather forecast' equations which are used to simulate non-linear systems are utilized to create chaotic map. This equation can be used to generate random numbers. In order to achieve up-to-date standards and use online and offline status, a new encryption technique that combines chaotic systems and RSA encryption algorithm has been developed. The combination of RSA algorithm and chaotic systems makes encryption system.
A simple chaotic delay differential equation
International Nuclear Information System (INIS)
Sprott, J.C.
2007-01-01
The simplest chaotic delay differential equation with a sinusoidal nonlinearity is described, including the route to chaos, Lyapunov exponent spectrum, and chaotic diffusion. It is prototypical of many other high-dimensional chaotic systems
OnWien Bridge Oscillators as Modified Multi-vibrators
DEFF Research Database (Denmark)
Lindberg, Erik
2014-01-01
A tutorial introduction to electrical oscilla- tors. Investigating Wien bridge oscillators as modified multi-vibrators. Introducing chaotic behavior into a Wien bridge oscillator by means of adding a simple nonlinear cir- cuit as a load of one of the amplifier input terminals......A tutorial introduction to electrical oscilla- tors. Investigating Wien bridge oscillators as modified multi-vibrators. Introducing chaotic behavior into a Wien bridge oscillator by means of adding a simple nonlinear cir- cuit as a load of one of the amplifier input terminals...
Inhibition of chaotic escape from a potential well using small parametric modulations
International Nuclear Information System (INIS)
Chacon, R.; Balibrea, F.; Lopez, M.A.
1996-01-01
It is shown theoretically for the first time that, depending on its period, amplitude, and initial phase, a periodic parametric modulation can suppress a chaotic escape from a potential well. The instance of the Helmholtz oscillator is used to demonstrate, by means of Melnikov close-quote s method, that parametric modulations of the linear or quadratic potential terms inhibit chaotic escape when certain resonance conditions are met. copyright 1996 American Institute of Physics
Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincare map
International Nuclear Information System (INIS)
Bonakdar, Mohammad; Samadi, Mostafa; Salarieh, Hassan; Alasty, Aria
2008-01-01
In this paper a fuzzy control algorithm is used to stabilize the fixed points of a chaotic system. No knowledge of the dynamic equations of the system is needed in this approach and the whole system is considered as a black box. Two main approaches have been investigated: fuzzy clustering and table look up methods. As illustrative examples these methods have been applied to Bonhoeffer van der Pol oscillator and the Henon chaotic system and the convergence toward fixed points is observed
Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincare map
Energy Technology Data Exchange (ETDEWEB)
Bonakdar, Mohammad; Samadi, Mostafa [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of); Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of)
2008-05-15
In this paper a fuzzy control algorithm is used to stabilize the fixed points of a chaotic system. No knowledge of the dynamic equations of the system is needed in this approach and the whole system is considered as a black box. Two main approaches have been investigated: fuzzy clustering and table look up methods. As illustrative examples these methods have been applied to Bonhoeffer van der Pol oscillator and the Henon chaotic system and the convergence toward fixed points is observed.
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.
Mixed-mode chaotic circuit with Wien-bridge configuration: The results of experimental verification
Energy Technology Data Exchange (ETDEWEB)
Kilic, Recai [Erciyes University, Department of Electronic Engineering, 38039 Kayseri (Turkey)]. E-mail: kilic@erciyes.edu.tr
2007-05-15
In this paper, we deal with the experimentally implementation of inductorless Wien bridge-based mixed-mode chaotic circuit (MMCC) which is capable to exhibit both linear and nonlinear oscillations. The results of experimental implementation agree with the results of theoretical and computer simulation presented in literature. Since the proposed implementation of MMCC circuit uses different design blocks such as Wien bridge-based autonomous circuit part, CFOA (current feedback operational amplifier)-based floating inductance simulator, CFOA-based Chua's diode and switching mechanism, it offers very versatile chaotic circuit model for studying autonomous and nonautonomous chaotic dynamics.
Mixed-mode chaotic circuit with Wien-bridge configuration: The results of experimental verification
International Nuclear Information System (INIS)
Kilic, Recai
2007-01-01
In this paper, we deal with the experimentally implementation of inductorless Wien bridge-based mixed-mode chaotic circuit (MMCC) which is capable to exhibit both linear and nonlinear oscillations. The results of experimental implementation agree with the results of theoretical and computer simulation presented in literature. Since the proposed implementation of MMCC circuit uses different design blocks such as Wien bridge-based autonomous circuit part, CFOA (current feedback operational amplifier)-based floating inductance simulator, CFOA-based Chua's diode and switching mechanism, it offers very versatile chaotic circuit model for studying autonomous and nonautonomous chaotic dynamics
Predicting chaotic time series
International Nuclear Information System (INIS)
Farmer, J.D.; Sidorowich, J.J.
1987-01-01
We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we ''learn'' the induced nonlinear mapping using local approximation. This allows us to make short-term predictions of the future behavior of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its effectiveness by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow
Experimentally determined chaotic phase synchronization in a neuronal system
Makarenko, Vladimir; Llinás, Rodolfo
1998-01-01
Mathematical analysis of the subthreshold oscillatory properties of inferior olivary neurons in vitro indicates that the oscillation is nonlinear and supports low dimensional chaotic dynamics. This property leads to the generation of complex functional states that can be attained rapidly via phase coherence that conform to the category of “generalized synchronization.” Functionally, this translates into neuronal ensemble properties that can support maximum functional permissiveness and that r...
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
International Nuclear Information System (INIS)
Wang, C.; Wang, F.; Cao, J. C.
2014-01-01
Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation
Wang, C; Wang, F; Cao, J C
2014-09-01
Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.
Energy Technology Data Exchange (ETDEWEB)
Wang, C., E-mail: cwang@mail.sim.ac.cn; Wang, F.; Cao, J. C., E-mail: jccao@mail.sim.ac.cn [Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050 (China)
2014-09-01
Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.
Directory of Open Access Journals (Sweden)
Sergio Ruíz-Hernández
2015-01-01
Full Text Available This paper addresses an adaptive control approach for synchronizing two chaotic oscillators with saturated nonlinear function series as nonlinear functions. Mathematical models to characterize the behavior of the transmitter and receiver circuit were derived, including in the latter the adaptive control and taking into account, for both chaotic oscillators, the most influential performance parameters associated with operational amplifiers. Asymptotic stability of the full synchronization system is studied by using Lyapunov direct method. Theoretical derivations and related results are experimentally validated through implementations from commercially available devices. Finally, the full synchronization system can easily be reproducible at a low cost.
An aperiodic phenomenon of the unscented Kalman filter in filtering noisy chaotic signals
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A non-periodic oscillatory behavior of the unscented Kalman filter (UKF) when used to filter noisy contaminated chaotic signals is reported. We show both theoretically and experimentally that the gain of the UKF may not converge or diverge but oscillate aperiodically. More precisely, when a nonlinear system is periodic, the Kalman gain and error covariance of the UKF converge to zero. However, when the system being considered is chaotic, the Kalman gain either converges to a fixed point with a magnitude larger than zero or oscillates aperiodically.
Qualitative identification of chaotic systems behaviours
International Nuclear Information System (INIS)
Vicha, T.; Dohnal, M.
2008-01-01
There are only three qualitative values positive, negative and zero. This means that there is a maximal number of qualitatively distinguishable scenarios, prescribed by the number of variables and the highest qualitative derivative taken into consideration. There are several chaos related tasks, which can be solved with great difficulties on the numerical level if multidimensional problems are studied. One of them is the identification of all qualitatively different behaviours. To make sure that all distinctive qualitative scenarios are identified a qualitative interpretation of a classical quantitative phase portrait is used. The highest derivatives are usually the second derivatives as it is not possible to safely identify higher derivatives if tasks related to ecology or economics are studied. Two classical models are discussed - Damped oscillation (non chaotic) and Lorenz model (chaotic). There are 191 scenarios of the Lorenz model if only the second derivatives are considered. If the third derivatives are taken into consideration then the number of scenarios is 2619. Complete qualitative results are given in details
Correlation control theory of chaotic laser systems
International Nuclear Information System (INIS)
Li Fuli.
1986-04-01
A novel control theory of chaotic systems is studied. The correlation functions are calculated and used as feedback signals of the chaotic lasers. Computer experiments have shown that in this way the chaotic systems can be controlled to have time-independent output when the external control parameters are in chaotic domain. (author)
International Nuclear Information System (INIS)
Mitchel, G.; Shriner, J.
2005-01-01
Although the predictions of Random Matrix Theory (RMT) were available by the early 1960s, data of sufficiently high quality to adequately test the theory were only obtained a decade later by Rainwater. It was another decade later that Bohigas, Haq and Pandey combined the best available nuclear resonance data - the Columbia neutron resonances in heavy nuclei and the TUNL proton resonances in lighter nuclei - to form the Nuclear Data Ensemble. They obtained excellent agreement for the level statistics with the RMT predictions. The expected Porter-Thomas (PT) distribution was considered very early. However, since the widths (amplitudes squared) are measured, the predicted Gaussian distribution for the amplitudes was only qualitatively confirmed. A much more sensitive test was performed by measuring two widths and the relative phase between the two amplitudes. By comparison of the width and amplitude correlations, the Gaussian distribution was confirmed at the 1% level. Following the Bohigas conjecture - that quantum analogs of classically chaotic systems obey RMT - there was an explosion of activity utilizing level statistics in many different quantum systems. In nuclei the focus was verifying the range of applicability of RMT. Of particular interest was the effect of collectivity and of excitation energy on statistical properties. The effect of symmetry breaking on level statistics was examined and early predictions by Dyson were confirmed. The effect of symmetry breaking on the width distribution was also measured for the first time. Although heuristic arguments predicted no change from the PT distribution, experimentally there was a large deviation from the PT prediction. Later theoretical efforts were consistent with this result. The stringent conditions placed on the experiments - for eigenvalue tests the data need to be essentially perfect (few or no missing levels or mis assigned quantum numbers) - has limited the amount of suitable experimental data. The
Chaotic advection in the ocean
Energy Technology Data Exchange (ETDEWEB)
Koshel' , Konstantin V; Prants, Sergei V [V.I. Il' ichev Pacific Oceanological Institute, Far-Eastern Division of the Russian Academy of Sciences, Vladivostok (Russian Federation)
2006-11-30
The problem of chaotic advection of passive scalars in the ocean and its topological, dynamical, and fractal properties are considered from the standpoint of the theory of dynamical systems. Analytic and numerical results on Lagrangian transport and mixing in kinematic and dynamic chaotic advection models are described for meandering jet currents, topographical eddies in a barotropic ocean, and a two-layer baroclinic ocean. Laboratory experiments on hydrodynamic flows in rotating tanks as an imitation of geophysical chaotic advection are described. Perspectives of a dynamical system approach in physical oceanography are discussed. (reviews of topical problems)
Reconfigurable chaotic logic gates based on novel chaotic circuit
International Nuclear Information System (INIS)
Behnia, S.; Pazhotan, Z.; Ezzati, N.; Akhshani, A.
2014-01-01
Highlights: • A novel method for implementing logic gates based on chaotic maps is introduced. • The logic gates can be implemented without any changes in the threshold voltage. • The chaos-based logic gates may serve as basic components of future computing devices. - Abstract: The logical operations are one of the key issues in today’s computer architecture. Nowadays, there is a great interest in developing alternative ways to get the logic operations by chaos computing. In this paper, a novel implementation method of reconfigurable logic gates based on one-parameter families of chaotic maps is introduced. The special behavior of these chaotic maps can be utilized to provide same threshold voltage for all logic gates. However, there is a wide interval for choosing a control parameter for all reconfigurable logic gates. Furthermore, an experimental implementation of this nonlinear system is presented to demonstrate the robustness of computing capability of chaotic circuits
Electric Holding Company Areas
Department of Homeland Security — Holding companies are electric power utilities that have a holding company structure. This vector polygon layer represents the area served by electric power holding...
Synchronization of Tubular Pressure Oscillations in Interacting Nephrons
DEFF Research Database (Denmark)
Sosnovtseva, Olga; Postnov, D.E.; Mosekilde, Erik
2003-01-01
The pressure and flow regulation in the individual functional unit of the kidney (the nephron) tends to operate in an unstable regime. For normal rats, the regulation displays regular self-sustained oscillations, but for rats with high blood pressure the oscillations become chaotic. We explain...
Nuclear friction and chaotic motion
International Nuclear Information System (INIS)
Srokowski, T.; Szczurek, A.; Drozdz, S.
1990-01-01
The concept of nuclear friction is considered from the point of view of regular versus chaotic motion in an atomic nucleus. Using a realistic nuclear Hamiltonian it is explicitly shown that the frictional description of the gross features of nuclear collisions is adequate if the system behaves chaotically. Because of the core in the Hamiltonian, the three-body nuclear system already reveals a structure of the phase space rich enough for this concept to be applicable
Chaotic diagonal recurrent neural network
International Nuclear Information System (INIS)
Wang Xing-Yuan; Zhang Yi
2012-01-01
We propose a novel neural network based on a diagonal recurrent neural network and chaos, and its structure and learning algorithm are designed. The multilayer feedforward neural network, diagonal recurrent neural network, and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map. The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks. (interdisciplinary physics and related areas of science and technology)
Oscillation and chaos in physiological control systems.
Mackey, M C; Glass, L
1977-07-15
First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions. These results are discussed in relation to dynamical respiratory and hematopoietic diseases.
Experimental chaotic quantification in bistable vortex induced vibration systems
Huynh, B. H.; Tjahjowidodo, T.
2017-02-01
The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear
Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems
International Nuclear Information System (INIS)
Yau, H.-T.; Chen, C.-L.
2006-01-01
This paper proposes a chattering-free fuzzy sliding-mode control (FSMC) strategy for uncertain chaotic systems. A fuzzy logic control is used to replace the discontinuous sign function of the reaching law in traditional sliding-mode control (SMC), and hence a control input without chattering is obtained in the chaotic systems with uncertainties. Base on the Lyapunov stability theory, we address the design schemes of integration fuzzy sliding-mode control, where the reaching law is proposed by a set of linguistic rules and the control input is chattering free. The Genesio chaotic system is used to test the proposed control strategy and the simulation results show the FSMC not only can control the uncertain chaotic behaviors to a desired state without oscillator very fast, but also the switching function is smooth without chattering. This result implies that this strategy is feasible and effective for chaos control
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale
International Nuclear Information System (INIS)
Maslennikov, Oleg V.; Nekorkin, Vladimir I.
2016-01-01
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.
Dimension of chaotic attractors
Energy Technology Data Exchange (ETDEWEB)
Farmer, J.D.; Ott, E.; Yorke, J.A.
1982-09-01
Dimension is perhaps the most basic property of an attractor. In this paper we discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors. The relevant definitions of dimension are of two general types, those that depend only on metric properties, and those that depend on probabilistic properties (that is, they depend on the frequency with which a typical trajectory visits different regions of the attractor). Both our example and the previous work that we review support the conclusion that all of the probabilistic dimensions take on the same value, which we call the dimension of the natural measure, and all of the metric dimensions take on a common value, which we call the fractal dimension. Furthermore, the dimension of the natural measure is typically equal to the Lyapunov dimension, which is defined in terms of Lyapunov numbers, and thus is usually far easier to calculate than any other definition. Because it is computable and more physically relevant, we feel that the dimension of the natural measure is more important than the fractal dimension.
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.
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.
Studies in Chaotic adiabatic dynamics
International Nuclear Information System (INIS)
Jarzynski, C.
1994-01-01
Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the open-quotes goodnessclose quotes of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees)
Chaotic synchronization of symbolic information in the discrete nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Pando L, C.L.
2003-08-01
We have studied the discrete nonlinear Schrodinger equation (DNLSE) with on-site defects and periodic boundary conditions. When the array dynamics becomes chaotic, the otherwise quasiperiodic amplitude correlations between the oscillators are destroyed. However, we show that synchronization of symbolic information of suitable amplitude signals is possible in this hamiltonian system. (author)
The effects of extra-low-frequency atmospheric pressure oscillations on human mental activity
Delyukov, A. A.; Didyk, L.
Slight atmospheric pressure oscillations (APO) in the extra-low-frequency range below 0.1 Hz, which frequently occur naturally, can influence human mental activity. This phenomenon has been observed in experiments with a group of 12 healthy volunteers exposed to experimentally created APO with amplitudes 30-50 Pa in the frequency band 0.011-0.17 Hz. Exposure of the subjects to APO for 15-30 min caused significant changes in attention and short-term memory functions, performance rate, and mental processing flexibility. The character of the response depended on the APO frequency and coherence. Periodic APO promoted purposeful mental activity, accompanied by an increase in breath-holding duration and a slower heart rate. On the other hand, quasi-chaotic APO, similar to the natural perturbations of atmospheric pressure, disrupted mental activity. These observations suggest that APO could be partly responsible for meteorosensitivity in humans.
Sakai, Kenshi; Managi, Shunsuke; Vitanov, Nikolay K; Demura, Katsuhiko
2007-04-01
This paper investigates the transition of dynamics observed in an actual real agricultural economic dataset. Lyapunov spectrum analysis is conducted on the data to distinguish deterministic chaos and the limit cycle. Chaotic and periodic oscillation were identified before and after the second oil crisis, respectively. The statitonarity of the time series is investigated using recurrence plots. This shows that government intervention might reduce market instability by removing a chaotic market's long-term unpredictability.
Chaotic scattering and quantum dynamics
International Nuclear Information System (INIS)
Doron, Eyal.
1992-11-01
The main concern of this thesis is the application of the semiclassical approximation to quantum chaotic scattering systems. We deal with two separate, although interconnected, subjects. The first subject dealt with is the semiclassical characterization of the fluctuations of the S matrix. A particular important parameter is the magnetic field B, and we show how the correlation length and line shape of S matrix elements under a change of B may be derived. An effect which is present in many physical wave systems is absorption of energy flux. We show how absorption affects both the reflectivity and the scattering phase and time delay of a scattering system. In the second part of the thesis, we show how the formalism and results obtained from chaotic scattering can be applied to the investigation of closed chaotic systems, and in particular to chaotic billiards. The semiclassical expansion for billiards is presented. In the last part of the thesis we deal with the statistics of S matrices of chaotic scattering systems. The main message of this work is that scattering matrix, and its classical counterpart the Poincare Scattering Map can be used to yield a powerful formulation of the quantum mechanical dynamics of bounded systems. (author)
On synchronization of three chaotic systems
International Nuclear Information System (INIS)
Yan Jianping; Li Changpin
2005-01-01
In this paper, a simple but efficient method is applied to the synchronization of three chaotic systems, i.e., the chaotic Lorenz, Chua, and Chen systems. Numerical simulations show this method works very well
A new chaotic secure communication scheme
International Nuclear Information System (INIS)
Hua Changchun; Yang Bo; Ouyang Gaoxiang; Guan Xinping
2005-01-01
A new chaotic secure communication scheme is constructed. Unified chaotic system is used to encrypt the emitted signal. Different from the existing chaotic secure communication methods, the useful information is embodied in the parameter of chaotic systems in this Letter. The receiver is designed which can succeed in recovering the former signal. Finally computer simulations are done to verify the proposed methods, and the results show that the obtained theoretic results are feasible and efficient
Chaotic structure of oil prices
Bildirici, Melike; Sonustun, Fulya Ozaksoy
2018-01-01
The fluctuations in oil prices are very complicated and therefore, it is unable to predict its effects on economies. For modelling complex system of oil prices, linear economic models are not sufficient and efficient tools. Thus, in recent years, economists attached great attention to non-linear structure of oil prices. For analyzing this relationship, GARCH types of models were used in some papers. Distinctively from the other papers, in this study, we aimed to analyze chaotic pattern of oil prices. Thus, it was used the Lyapunov Exponents and Hennon Map to determine chaotic behavior of oil prices for the selected time period.
Chaotic signals in digital communications
Eisencraft, Marcio; Suyama, Ricardo
2013-01-01
Chaotic Signals in Digital Communications combines fundamental background knowledge with state-of-the-art methods for using chaotic signals and systems in digital communications. The book builds a bridge between theoretical works and practical implementation to help researchers attain consistent performance in realistic environments. It shows the possible shortcomings of the chaos-based communication systems proposed in the literature, particularly when they are subjected to non-ideal conditions. It also presents a toolbox of techniques for researchers working to actually implement such system
Lectures on chaotic dynamical systems
Afraimovich, Valentin
2002-01-01
This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics. The book will help readers who are not familiar with nonlinear dynamics to understand and appreciate sophisticated modern dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis.
Nonstationary oscillations in gyrotrons revisited
International Nuclear Information System (INIS)
Dumbrajs, O.; Kalis, H.
2015-01-01
Development of gyrotrons requires careful understanding of different regimes of gyrotron oscillations. It is known that in the planes of the generalized gyrotron variables: cyclotron resonance mismatch and dimensionless current or cyclotron resonance mismatch and dimensionless interaction length complicated alternating sequences of regions of stationary, periodic, automodulation, and chaotic oscillations exist. In the past, these regions were investigated on the supposition that the transit time of electrons through the interaction space is much shorter than the cavity decay time. This assumption is valid for short and/or high diffraction quality resonators. However, in the case of long and/or low diffraction quality resonators, which are often utilized, this assumption is no longer valid. In such a case, a different mathematical formalism has to be used for studying nonstationary oscillations. One example of such a formalism is described in the present paper
Chaotic expression dynamics implies pluripotency: when theory and experiment meet
Directory of Open Access Journals (Sweden)
Furusawa Chikara
2009-05-01
Full Text Available Abstract Background During normal development, cells undergo a unidirectional course of differentiation that progressively decreases the number of cell types they can potentially become. Pluripotent stem cells can differentiate into several types of cells, but terminally differentiated cells cannot differentiate any further. A fundamental problem in stem cell biology is the characterization of the difference in cellular states, e.g., gene expression profiles, between pluripotent stem cells and terminally differentiated cells. Presentation of the hypothesis To address the problem, we developed a dynamical systems model of cells with intracellular protein expression dynamics and interactions with each other. According to extensive simulations, cells with irregular (chaotic oscillations in gene expression dynamics have the potential to differentiate into other cell types. During development, such complex oscillations are lost successively, leading to a loss of pluripotency. These simulation results, together with recent single-cell-level measurements in stem cells, led us to the following hypothesis regarding pluripotency: Chaotic oscillation in the expression of some genes leads to cell pluripotency and affords cellular state heterogeneity, which is supported by itinerancy over quasi-stable states. Differentiation stabilizes these states, leading to a loss of pluripotency. Testing the hypothesis To test the hypothesis, it is crucial to measure the time course of gene expression levels at the single-cell level by fluorescence microscopy and fluorescence-activated cell sorting (FACS analysis. By analyzing the time series of single-cell-level expression data, one can distinguish whether the variation in protein expression level over time is due only to stochasticity in expression dynamics or originates from the chaotic dynamics inherent to cells, as our hypothesis predicts. By further analyzing the expression in differentiated cell types, one can
Chaotic mechanics in systems with impacts and friction
Blazejczyk-Okolewska, Barbara; Kapitaniak, Tomasz; Wojewoda, Jerzy
1999-01-01
This book is devoted to the theory of chaotic oscillations in mechanical systems. Detailed descriptions of the basic types of nonlinearity - impacts and dry friction - are presented. The properties of such behavior are discussed, and the numerical and experimental results obtained by the authors are presented.The dynamic properties of systems described here can be useful in the proper design and use of mechanics where such behavior still creates problems.This book will be very useful for anyone with a fundamental knowledge of nonlinear mechanics who is beginning research in the field.
Chaotic inflation and baryogenesis by right-handed sneutrinos
International Nuclear Information System (INIS)
Murayama, H.; Suzuki, H.; Yanagida, T.; Yokoyama, J.i.
1993-01-01
We present a model of chaotic inflation driven by the superpartner of the right-handed neutrino (N R ). This model gives the correct magnitude of the density perturbation observed by the Cosmic Background Explorer satellite with a right-handed neutrino mass congruent 10 13 GeV, which is also preferred by the Mikheyev-Smirnov-Wolfenstein solution to the solar neutrino problem. The reheating process is the dacay of the coherently oscillating N R . This decay process also generates lepton asymmetry via CP violation, which will be converted to baryon asymmetry thanks to the electroweak anomaly. This model can incorporate the τ-neutrino mass congruent 10 eV
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...
Barkai, E.
2002-01-01
We demonstrate aging behavior in a simple non-linear system. Our model is a chaotic map which generates deterministically sub-diffusion. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks, introduced previously to model diffusion in glasses.
Chaotic dynamics from interspike intervals
DEFF Research Database (Denmark)
Pavlov, A N; Sosnovtseva, Olga; Mosekilde, Erik
2001-01-01
Considering two different mathematical models describing chaotic spiking phenomena, namely, an integrate-and-fire and a threshold-crossing model, we discuss the problem of extracting dynamics from interspike intervals (ISIs) and show that the possibilities of computing the largest Lyapunov expone...
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
Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system
Mobayen, Saleh; Kingni, Sifeu Takougang; Pham, Viet-Thanh; Nazarimehr, Fahimeh; Jafari, Sajad
2018-02-01
This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master-slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.
Applications of Chaotic Dynamics in Robotics
Directory of Open Access Journals (Sweden)
Xizhe Zang
2016-03-01
Full Text Available This article presents a summary of applications of chaos and fractals in robotics. Firstly, basic concepts of deterministic chaos and fractals are discussed. Then, fundamental tools of chaos theory used for identifying and quantifying chaotic dynamics will be shared. Principal applications of chaos and fractal structures in robotics research, such as chaotic mobile robots, chaotic behaviour exhibited by mobile robots interacting with the environment, chaotic optimization algorithms, chaotic dynamics in bipedal locomotion and fractal mechanisms in modular robots will be presented. A brief survey is reported and an analysis of the reviewed publications is also presented.
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 ...
Does the classically chaotic Henon–Heiles oscillator exhibit ...
Indian Academy of Sciences (India)
The threshold intensity of the laser field for an electron moving in the HH potential to reach its continuum is identified and in this region quantum chaos has been diagnosed through a combination of various dynamical signatures such as the autocorrelation function, quantum `phase-space' volume, `phase-space' trajectory, ...
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.
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)
Dynamic Parameter-Control Chaotic System.
Hua, Zhongyun; Zhou, Yicong
2016-12-01
This paper proposes a general framework of 1-D chaotic maps called the dynamic parameter-control chaotic system (DPCCS). It has a simple but effective structure that uses the outputs of a chaotic map (control map) to dynamically control the parameter of another chaotic map (seed map). Using any existing 1-D chaotic map as the control/seed map (or both), DPCCS is able to produce a huge number of new chaotic maps. Evaluations and comparisons show that chaotic maps generated by DPCCS are very sensitive to their initial states, and have wider chaotic ranges, better unpredictability and more complex chaotic behaviors than their seed maps. Using a chaotic map of DPCCS as an example, we provide a field-programmable gate array design of this chaotic map to show the simplicity of DPCCS in hardware implementation, and introduce a new pseudo-random number generator (PRNG) to investigate the applications of DPCCS. Analysis and testing results demonstrate the excellent randomness of the proposed PRNG.
Visibility graphlet approach to chaotic time series
Energy Technology Data Exchange (ETDEWEB)
Mutua, Stephen [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega (Kenya); Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn; Yang, Huijie, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2016-05-15
Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems. Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.
Advances and applications in chaotic systems
Volos, Christos
2016-01-01
This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.
Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Perez-Pinacho, Claudia A.
2014-06-01
The main issue of this work is related with the design of a class of nonlinear observer in order to synchronize chaotic dynamical systems in a master-slave scheme, considering different initial conditions. The oscillator of Chen is proposed as a benchmark model and a bounded-type observer is proposed to reach synchronicity between both two chaotic systems. The proposed observer contains a proportional and sigmoid form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Some numerical simulations were carrying out in order to show the operation of the proposed methodology, with possible applications to secure data communications issues.
Control uncertain Genesio-Tesi chaotic system: Adaptive sliding mode approach
International Nuclear Information System (INIS)
Dadras, Sara; Momeni, Hamid Reza
2009-01-01
An adaptive sliding mode control (ASMC) technique is introduced in this paper for a chaotic dynamical system (Genesio-Tesi system). Using the sliding mode control technique, a sliding surface is determined and the control law is established. An adaptive sliding mode control law is derived to make the states of the Genesio-Tesi system asymptotically track and regulate the desired state. The designed control scheme can control the uncertain chaotic behaviors to a desired state without oscillating very fast and guarantee the property of asymptotical stability. An illustrative simulation result is given to demonstrate the effectiveness of the proposed adaptive sliding mode control design.
A new type of chaotic synchronization with application to communication systems
International Nuclear Information System (INIS)
Kharel, Rupak; Busawon, Krishna
2011-01-01
In this paper, we propose a new methodology to synchronize a class of chaotic systems starting from different initial conditions under some given conditions. The method we propose is not based on the unidirectional synchronization method like the one proposed by Pecora-Caroll. The proposed method is unique in the sense that the chaotic oscillators to be synchronized have no direct connection between them; that is, there is no signal being sent from one to the other. Simulation result is presented to show the synchronization performance.
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
Chaotic orbits of a pendulum with variable length
Directory of Open Access Journals (Sweden)
Massimo Furi
2004-03-01
Full Text Available The main purpose of this investigation is to show that a pendulum, whose pivot oscillates vertically in a periodic fashion, has uncountably many chaotic orbits. The attribute chaotic is given according to the criterion we now describe. First, we associate to any orbit a finite or infinite sequence as follows. We write 1 or $-1$ every time the pendulum crosses the position of unstable equilibrium with positive (counterclockwise or negative (clockwise velocity, respectively. We write 0 whenever we find a pair of consecutive zero's of the velocity separated only by a crossing of the stable equilibrium, and with the understanding that different pairs cannot share a common time of zero velocity. Finally, the symbol $omega$, that is used only as the ending symbol of a finite sequence, indicates that the orbit tends asymptotically to the position of unstable equilibrium. Every infinite sequence of the three symbols ${1,-1,0}$ represents a real number of the interval $[0,1]$ written in base 3 when $-1$ is replaced with 2. An orbit is considered chaotic whenever the associated sequence of the three symbols ${1,2,0}$ is an irrational number of $[0,1]$. Our main goal is to show that there are uncountably many orbits of this type.
Predicting chaos in memristive oscillator via harmonic balance method.
Wang, Xin; Li, Chuandong; Huang, Tingwen; Duan, Shukai
2012-12-01
This paper studies the possible chaotic behaviors in a memristive oscillator with cubic nonlinearities via harmonic balance method which is also called the method of describing function. This method was proposed to detect chaos in classical Chua's circuit. We first transform the considered memristive oscillator system into Lur'e model and present the prediction of the existence of chaotic behaviors. To ensure the prediction result is correct, the distortion index is also measured. Numerical simulations are presented to show the effectiveness of theoretical results.
International Nuclear Information System (INIS)
Hu Manfeng; Xu Zhenyuan; Zhang Rong; Hu Aihua
2007-01-01
Based on the active control idea and the invariance principle of differential equations, a general scheme of adaptive full state hybrid projective synchronization (FSHPS) and parameters identification of a class of chaotic (hyper-chaotic) systems with linearly dependent uncertain parameters is proposed in this Letter. With this effective scheme parameters identification and FSHPS of chaotic and hyper-chaotic systems can be realized simultaneously. Numerical simulations on the chaotic Chen system and the hyper-chaotic Chen system are presented to verify the effectiveness of the proposed scheme
Wave Physics Oscillations - Solitons - Chaos
Nettel, Stephen
2009-01-01
This textbook is intended for those second year undergraduates in science and engineering who will later need an understanding of electromagnetic theory and quantum mechanics. The classical physics of oscillations and waves is developed at a more advanced level than has been customary for the second year, providing a basis for the quantum mechanics that follows. In this new edition the Green's function is explained, reinforcing the integration of quantum mechanics with classical physics. The text may also form the basis of an "introduction to theoretical physics" for physics majors. The concluding chapters give special attention to topics in current wave physics: nonlinear waves, solitons, and chaotic behavior.
Controlling a Chaotic System through Control Parameter Self-Modulation
International Nuclear Information System (INIS)
Pastor, I.
1994-01-01
A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously existing unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and it is compared with them. One of its most attractive features is that it should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations modelling the coupling of two self-oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters
Controlling a Chaotic System through Control Parameter Self-Modulation
International Nuclear Information System (INIS)
Pastor, I.
1994-01-01
A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously oxi sting unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and i t is compared with them. One of its most attractive features is that is should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations model ling the coupling of two se If - oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the no possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters. (Author) 28 refs
A chaotic model for advertising diffusion problem with competition
Ip, W. H.; Yung, K. L.; Wang, Dingwei
2012-08-01
In this article, the author extends Dawid and Feichtinger's chaotic advertising diffusion model into the duopoly case. A computer simulation system is used to test this enhanced model. Based on the analysis of simulation results, it is found that the best advertising strategy in duopoly is to increase the advertising investment to reach the best Win-Win situation where the oscillation of market portion will not occur. In order to effectively arrive at the best situation, we define a synthetic index and two thresholds. An estimation method for the parameters of the index and thresholds is proposed in this research. We can reach the Win-Win situation by simply selecting the control parameters to make the synthetic index close to the threshold of min-oscillation state. The numerical example and computational results indicated that the proposed chaotic model is useful to describe and analyse advertising diffusion process in duopoly, it is an efficient tool for the selection and optimisation of advertising strategy.
Controlling a Chaotic System through Control Parameter Self-Modulation
Energy Technology Data Exchange (ETDEWEB)
Pastor, I
1994-07-01
A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously oxi sting unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and i t is compared with them. One of its most attractive features is that is should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations model ling the coupling of two se If - oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the no possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters. (Author) 28 refs.
Illusion optics in chaotic light
International Nuclear Information System (INIS)
Zhang Suheng; Gan Shu; Xiong Jun; Zhang Xiangdong; Wang Kaige
2010-01-01
The time-reversal process provides the possibility to counteract the time evolution of a physical system. Recent research has shown that such a process can occur in the first-order field correlation of chaotic light and result in the spatial interference and phase-reversal diffraction in an unbalanced interferometer. Here we report experimental investigations on the invisibility cloak and illusion phenomena in chaotic light. In an unbalanced interferometer illuminated by thermal light, we have observed the cloak effect and the optical transformation of one object into another object. The experimental results can be understood by the phase-reversal diffraction, and they demonstrate the theoretical proposal of similar effects in complementary media.
Chaotic attractors with separated scrolls
International Nuclear Information System (INIS)
Bouallegue, Kais
2015-01-01
This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This new approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results
Chaotic evolution of arms races
Tomochi, Masaki; Kono, Mitsuo
1998-12-01
A new set of model equations is proposed to describe the evolution of the arms race, by extending Richardson's model with special emphases that (1) power dependent defensive reaction or historical enmity could be a motive force to promote armaments, (2) a deterrent would suppress the growth of armaments, and (3) the defense reaction of one nation against the other nation depends nonlinearly on the difference in armaments between two. The set of equations is numerically solved to exhibit stationary, periodic, and chaotic behavior depending on the combinations of parameters involved. The chaotic evolution is realized when the economic situation of each country involved in the arms race is quite different, which is often observed in the real world.
Anomalous diffusion in chaotic scattering
International Nuclear Information System (INIS)
Srokowski, T.; Ploszajczak, M.
1994-01-01
The anomalous diffusion is found for peripheral collision of atomic nuclei described in the framework of the molecular dynamics. Similarly as for chaotic billiards, the long free paths are the source of the long-time correlations and the anomalous diffusion. Consequences of this finding for the energy dissipation in deep-inelastic collisions and the dynamics of fission in hot nuclei are discussed (authors). 30 refs., 2 figs
CHAOTIC CAPTURE OF NEPTUNE TROJANS
International Nuclear Information System (INIS)
Nesvorny, David; Vokrouhlicky, David
2009-01-01
Neptune Trojans (NTs) are swarms of outer solar system objects that lead/trail planet Neptune during its revolutions around the Sun. Observations indicate that NTs form a thick cloud of objects with a population perhaps ∼10 times more numerous than that of Jupiter Trojans and orbital inclinations reaching ∼25 deg. The high inclinations of NTs are indicative of capture instead of in situ formation. Here we study a model in which NTs were captured by Neptune during planetary migration when secondary resonances associated with the mean-motion commensurabilities between Uranus and Neptune swept over Neptune's Lagrangian points. This process, known as chaotic capture, is similar to that previously proposed to explain the origin of Jupiter's Trojans. We show that chaotic capture of planetesimals from an ∼35 Earth-mass planetesimal disk can produce a population of NTs that is at least comparable in number to that inferred from current observations. The large orbital inclinations of NTs are a natural outcome of chaotic capture. To obtain the ∼4:1 ratio between high- and low-inclination populations suggested by observations, planetary migration into a dynamically excited planetesimal disk may be required. The required stirring could have been induced by Pluto-sized and larger objects that have formed in the disk.
Chaotic dynamics of respiratory sounds
International Nuclear Information System (INIS)
Ahlstrom, C.; Johansson, A.; Hult, P.; Ask, P.
2006-01-01
There is a growing interest in nonlinear analysis of respiratory sounds (RS), but little has been done to justify the use of nonlinear tools on such data. The aim of this paper is to investigate the stationarity, linearity and chaotic dynamics of recorded RS. Two independent data sets from 8 + 8 healthy subjects were recorded and investigated. The first set consisted of lung sounds (LS) recorded with an electronic stethoscope and the other of tracheal sounds (TS) recorded with a contact accelerometer. Recurrence plot analysis revealed that both LS and TS are quasistationary, with the parts corresponding to inspiratory and expiratory flow plateaus being stationary. Surrogate data tests could not provide statistically sufficient evidence regarding the nonlinearity of the data. The null hypothesis could not be rejected in 4 out of 32 LS cases and in 15 out of 32 TS cases. However, the Lyapunov spectra, the correlation dimension (D 2 ) and the Kaplan-Yorke dimension (D KY ) all indicate chaotic behavior. The Lyapunov analysis showed that the sum of the exponents was negative in all cases and that the largest exponent was found to be positive. The results are partly ambiguous, but provide some evidence of chaotic dynamics of RS, both concerning LS and TS. The results motivate continuous use of nonlinear tools for analysing RS data
Chaotic dynamics of respiratory sounds
Energy Technology Data Exchange (ETDEWEB)
Ahlstrom, C. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden) and Biomedical Engineering, Orebro University Hospital, S-70185 Orebro (Sweden)]. E-mail: christer@imt.liu.se; Johansson, A. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden); Hult, P. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden); Biomedical Engineering, Orebro University Hospital, S-70185 Orebro (Sweden); Ask, P. [Department of Biomedical Engineering, Linkoepings Universitet, IMT/LIU, Universitetssjukhuset, S-58185 Linkoeping (Sweden); Biomedical Engineering, Orebro University Hospital, S-70185 Orebro (Sweden)
2006-09-15
There is a growing interest in nonlinear analysis of respiratory sounds (RS), but little has been done to justify the use of nonlinear tools on such data. The aim of this paper is to investigate the stationarity, linearity and chaotic dynamics of recorded RS. Two independent data sets from 8 + 8 healthy subjects were recorded and investigated. The first set consisted of lung sounds (LS) recorded with an electronic stethoscope and the other of tracheal sounds (TS) recorded with a contact accelerometer. Recurrence plot analysis revealed that both LS and TS are quasistationary, with the parts corresponding to inspiratory and expiratory flow plateaus being stationary. Surrogate data tests could not provide statistically sufficient evidence regarding the nonlinearity of the data. The null hypothesis could not be rejected in 4 out of 32 LS cases and in 15 out of 32 TS cases. However, the Lyapunov spectra, the correlation dimension (D {sub 2}) and the Kaplan-Yorke dimension (D {sub KY}) all indicate chaotic behavior. The Lyapunov analysis showed that the sum of the exponents was negative in all cases and that the largest exponent was found to be positive. The results are partly ambiguous, but provide some evidence of chaotic dynamics of RS, both concerning LS and TS. The results motivate continuous use of nonlinear tools for analysing RS data.
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
Robust state feedback controller design of STATCOM using chaotic optimization algorithm
Directory of Open Access Journals (Sweden)
Safari Amin
2010-01-01
Full Text Available In this paper, a new design technique for the design of robust state feedback controller for static synchronous compensator (STATCOM using Chaotic Optimization Algorithm (COA is presented. The design is formulated as an optimization problem which is solved by the COA. Since chaotic planning enjoys reliability, ergodicity and stochastic feature, the proposed technique presents chaos mapping using Lozi map chaotic sequences which increases its convergence rate. To ensure the robustness of the proposed damping controller, the design process takes into account a wide range of operating conditions and system configurations. The simulation results reveal that the proposed controller has an excellent capability in damping power system low frequency oscillations and enhances greatly the dynamic stability of the power systems. Moreover, the system performance analysis under different operating conditions shows that the phase based controller is superior compare to the magnitude based controller.
Rajagopal, Karthikeyan; Jafari, Sajad; Akgul, Akif; Karthikeyan, Anitha; Çiçek, Serdar; Shekofteh, Yasser
2018-05-01
In this paper, we report a novel chaotic snap oscillator with one nonlinear function. Dynamic analysis of the system shows the existence of bistability. To study the time delay effects on the proposed snap oscillator, we introduce multiple time delay in the fourth state equation. Investigation of dynamical properties of the time-delayed system shows that the snap oscillator exhibits the same multistable properties as the nondelayed system. The new multistable hyperjerk chaotic system has been tested in chaos shift keying and symmetric choc shift keying modulated communication designs for engineering applications. It has been determined that the symmetric chaos shift keying modulated communication system implemented with the new chaotic system is more successful than the chaos shift keying modulation for secure communication. Also, circuit implementation of the chaotic snap oscillator with tangent function is carried out showing its feasibility.
Characterizing chaotic melodies in automatic music composition
Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang
2010-09-01
In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.
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)
Robust synchronization of chaotic systems via feedback
Energy Technology Data Exchange (ETDEWEB)
Femat, Ricardo [IPICYT, San Luis Potosi (Mexico). Dept. de Matematicas Aplicadas; Solis-Perales, Gualberto [Universidad de Guadalajara, Centro Univ. de Ciencias Exactas e Ingenierias (Mexico). Div. de Electronica y Computacion
2008-07-01
This volume includes the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, the concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behaviour and what synchronization phenomena can be found under feedback interconnection. A compilation of these findings is described in this book. This book shows a perspective on synchronization of chaotic systems. (orig.)
International Nuclear Information System (INIS)
McNeill, G.A.
1981-01-01
Present high-speed data acquisition systems in nuclear diagnostics use high-frequency oscillators to provide timing references for signals recorded on fast, traveling-wave oscilloscopes. An oscillator's sinusoidal wave shape is superimposed on the recorded signal with each cycle representing a fixed time increment. During data analysis the sinusoid is stripped from the signal, leaving a clean signal shape with known timing. Since all signal/time relationships are totally dependant upon working oscillators, these critical devices must have remote verification of proper operation. This manual presents the newly-developed oscillator monitor which will provide the required verification
Chaotic Modes in Scale Free Opinion Networks
Kusmartsev, Feo V.; Kürten, Karl E.
2010-12-01
In this paper, we investigate processes associated with formation of public opinion in varies directed random, scale free and small-world social networks. The important factor of the opinion formation is the existence of contrarians which were discovered by Granovetter in various social psychology experiments1,2,3 long ago and later introduced in sociophysics by Galam.4 When the density of contrarians increases the system behavior drastically changes at some critical value. At high density of contrarians the system can never arrive to a consensus state and periodically oscillates with different periods depending on specific structure of the network. At small density of the contrarians the behavior is manifold. It depends primary on the initial state of the system. If initially the majority of the population agrees with each other a state of stable majority may be easily reached. However when originally the population is divided in nearly equal parts consensus can never be reached. We model the emergence of collective decision making by considering N interacting agents, whose opinions are described by two state Ising spin variable associated with YES and NO. We show that the dynamical behaviors are very sensitive not only to the density of the contrarians but also to the network topology. We find that a phase of social chaos may arise in various dynamical processes of opinion formation in many realistic models. We compare the prediction of the theory with data describing the dynamics of the average opinion of the USA population collected on a day-by-day basis by varies media sources during the last six month before the final Obama-McCain election. The qualitative ouctome is in reasonable agreement with the prediction of our theory. In fact, the analyses of these data made within the paradigm of our theory indicates that even in this campaign there were chaotic elements where the public opinion migrated in an unpredictable chaotic way. The existence of such a phase
Unstable periodic orbits and chaotic economic growth
International Nuclear Information System (INIS)
Ishiyama, K.; Saiki, Y.
2005-01-01
We numerically find many unstable periodic solutions embedded in a chaotic attractor in a macroeconomic growth cycle model of two countries with different fiscal policies, and we focus on a special type of the unstable periodic solutions. It is confirmed that chaotic behavior represented by the model is qualitatively and quantitatively related to the unstable periodic solutions. We point out that the structure of a chaotic solution is dissolved into a class of finite unstable periodic solutions picked out among a large number of periodic solutions. In this context it is essential for the unstable periodic solutions to be embedded in the chaotic attractor
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...
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.
Yu, Yue; Zhang, Zhengdi; Han, Xiujing
2018-03-01
In this work, we aim to demonstrate the novel routes to periodic and chaotic bursting, i.e., the different bursting dynamics via delayed pitchfork bifurcations around stable attractors, in the classical controlled Lü system. First, by computing the corresponding characteristic polynomial, we determine where some critical values about bifurcation behaviors appear in the Lü system. Moreover, the transition mechanism among different stable attractors has been introduced including homoclinic-type connections or chaotic attractors. Secondly, taking advantage of the above analytical results, we carry out a study of the mechanism for bursting dynamics in the Lü system with slowly periodic variation of certain control parameter. A distinct delayed supercritical pitchfork bifurcation behavior can be discussed when the control item passes through bifurcation points periodically. This delayed dynamical behavior may terminate at different parameter areas, which leads to different spiking modes around different stable attractors (equilibriums, limit cycles, or chaotic attractors). In particular, the chaotic attractor may appear by Shilnikov connections or chaos boundary crisis, which leads to the occurrence of impressive chaotic bursting oscillations. Our findings enrich the study of bursting dynamics and deepen the understanding of some similar sorts of delayed bursting phenomena. Finally, some numerical simulations are included to illustrate the validity of our study.
The EPA is providing notice of an Administrative Penalty Assessment in the form of an Expedited Storm Water Settlement Agreement against Rock Equity Holdings, LLC, for alleged violations at The Cove at Kettlestone/98th Street Reconstruction located at 3015
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Lites, B.W.; Rutten, R.J.; Thomas, J.H.
1995-01-01
We show results from SO/Sacramento Peak data to discuss three issues: (i)--the spatial occurrence of chromospheric 3--min oscillations; (ii)--the validity of Ca II H&K line-center Doppler Shift measurements; (iii)--the signi ?cance of oscillation power and phase at frequencies above 10 mHz.
Energy Technology Data Exchange (ETDEWEB)
Yuce, C [Physics Department, Anadolu University, Eskisehir (Turkey); Kilic, A [Physics Department, Anadolu University, Eskisehir (Turkey); Coruh, A [Physics Department, Sakarya University, Sakarya (Turkey)
2006-07-15
The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wavefunction for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete, and the energy is given as a linear function of the quantum number n.
Bubanja, I. N.; Ivanović-Šašić, A.; Čupić, Ž.; Anić, S.; Kolar-Anić, Lj.
2017-12-01
Chaotic dynamic states with intermittent oscillations were generated in a Bray-Liebhafsky (BL) oscillatory reaction in an isothermal open reactor i.e., in the continuously-fed well-stirred tank reactor (CSTR) when the inflow concentration of potassium iodate was the control parameter. They are found between periodic oscillations obtained when [KIO3]0 4.10 × 10-2 M. It was shown that the most chaotic states obtained experimentally somewhere in the middle of this region are in high correlation with results obtained by means of largest Lyapunov exponents and phenomenological analysis based on the quantitative characteristics of intermittent oscillations.
Current oscillations in avalanche particle detectors with PNIPN-structure
International Nuclear Information System (INIS)
Lukin, K.A.
1995-08-01
The model of an avalanche high energy particle detector consisting of two pn-junctions, connected through an intrinsic semiconductor with a reverse biased voltage applied. This detector is able to generate the oscillatory response on the single particle passage through the structure. The possibility of oscillations leading to chaotic behaviour is pointed out
Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics
Changaival, Boonyarit; Rosalie, Martin; Danoy, Grégoire; Lavangnananda, Kittichai; Bouvry, Pascal
2017-12-01
Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs via the Lozi map and the Rössler system. To compare various dynamics effects on our algorithm, we present an original way to perform the exploration of a parameter space using a bifurcation diagram with respect to the topological structure of attractors. The resulting algorithm is an efficient and nonresource demanding algorithm, and is therefore very suitable for partial traversal of very large and/or unknown environment graphs. CHAT performance using Lozi map is proven superior than the, commonly known, Random Walk, in terms of number of nodes visited (coverage percentage) and computation time where the environment is unknown and memory usage is restricted.
Application of the Lyapunov exponent to detect noise-induced chaos in oscillating microbial cultures
International Nuclear Information System (INIS)
Patnaik, P.R.
2005-01-01
Oscillating microbial processes can, under certain conditions, gravitate into chaotic behavior induced by external noise. Detection and control of chaos are important for the survival of the microorganisms and to operate a process usefully. In this study the largest Lyapunov exponent is recommended as a convenient and reliable index of chaos in continuous oscillating cultures. For the growth of Saccharomyces cerevisiae as a model system, the exponents increase with the oxygen mass transfer coefficient and decrease as the dilution rate increases. By comparing with the corresponding time-domain oscillations determined earlier, it is inferred that weakly oscillating cultures are less likely to be driven to chaotic behavior. The main carbon source, glucose, is quite robust to chaotic destabilization, thus enhancing its suitability as a manipulated variable for bioreactor control
Chaotic fluctuations in mathematical economics
Energy Technology Data Exchange (ETDEWEB)
Yoshida, Hiroyuki, E-mail: yoshida.hiroyuki@nihon-u.ac.jp [College of Economics, Nihon University, Chiyoda-ku, Tokyo 101-8360 (Japan)
2011-03-01
In this paper we examine a Cournot duopoly model, which expresses the strategic interaction between two firms. We formulate the dynamic adjustment process and investigate the dynamic properties of the stationary point. By introducing a memory mechanism characterized by distributed lag functions, we presuppose that each firm makes production decisions in a cautious manner. This implies that we have to deal with the system of integro-differential equations. By means of numerical simulations we show the occurrence of chaotic fluctuations in the case of fixed delays.
International Nuclear Information System (INIS)
Chien, T.-I.; Liao, T.-L.
2005-01-01
This paper presents a secure digital communication system based on chaotic modulation, cryptography, and chaotic synchronization techniques. The proposed system consists of a Chaotic Modulator (CM), a Chaotic Secure Transmitter (CST), a Chaotic Secure Receiver (CSR) and a Chaotic Demodulator (CDM). The CM module incorporates a chaotic system and a novel Chaotic Differential Peaks Keying (CDPK) modulation scheme to generate analog patterns corresponding to the input digital bits. The CST and CSR modules are designed such that a single scalar signal is transmitted in the public channel. Furthermore, by giving certain structural conditions of a particular class of chaotic system, the CST and the nonlinear observer-based CSR with an appropriate observer gain are constructed to synchronize with each other. These two slave systems are driven simultaneously by the transmitted signal and are designed to synchronize and generate appropriate cryptography keys for encryption and decryption purposes. In the CDM module, a nonlinear observer is designed to estimate the chaotic modulating system in the CM. A demodulation mechanism is then applied to decode the transmitted input digital bits. The effectiveness of the proposed scheme is demonstrated through the numerical simulation of an illustrative communication system. Synchronization between the chaotic circuits of the transmitter and receiver modules is guaranteed through the Lyapunov stability theorem. Finally, the security features of the proposed system in the event of attack by an intruder in either the time domain or the frequency domain are discussed
Theory and practice of chaotic cryptography
International Nuclear Information System (INIS)
Amigo, J.M.; Kocarev, L.; Szczepanski, J.
2007-01-01
In this Letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems. We propose a conceptual framework and illustrate it with different examples from private and public key cryptography. We elaborate also on possible limits of chaotic cryptography
Synthesizing chaotic maps with prescribed invariant densities
International Nuclear Information System (INIS)
Rogers, Alan; Shorten, Robert; Heffernan, Daniel M.
2004-01-01
The Inverse Frobenius-Perron Problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this Letter, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized
Repetitive learning control of continuous chaotic systems
International Nuclear Information System (INIS)
Chen Maoyin; Shang Yun; Zhou Donghua
2004-01-01
Combining a shift method and the repetitive learning strategy, a repetitive learning controller is proposed to stabilize unstable periodic orbits (UPOs) within chaotic attractors in the sense of least mean square. If nonlinear parts in chaotic systems satisfy Lipschitz condition, the proposed controller can be simplified into a simple proportional repetitive learning controller
A Hybrid Chaotic Quantum Evolutionary Algorithm
DEFF Research Database (Denmark)
Cai, Y.; Zhang, M.; Cai, H.
2010-01-01
A hybrid chaotic quantum evolutionary algorithm is proposed to reduce amount of computation, speed up convergence and restrain premature phenomena of quantum evolutionary algorithm. The proposed algorithm adopts the chaotic initialization method to generate initial population which will form a pe...... tests. The presented algorithm is applied to urban traffic signal timing optimization and the effect is satisfied....
Approximating chaotic saddles for delay differential equations.
Taylor, S Richard; Campbell, Sue Ann
2007-04-01
Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a "logistic" delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.
Approximating chaotic saddles for delay differential equations
Taylor, S. Richard; Campbell, Sue Ann
2007-04-01
Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a “logistic” delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.
Chaotic behaviour of an electrical analogue to the mechanical double pendulum
Directory of Open Access Journals (Sweden)
M. P. Hanias
2008-02-01
Full Text Available In this paper the analogy between a mechanical double pendulum and an oscillating electrical system is presented. Instead of using analytic equations, we used the MultiSim circuit simulation environment in order to reproduce and interpret the response of the electrical oscillator. The electrical double pendulum presents a chaotic regime which is studied quantita-tively by means of state space reconstruction. For this purpose the optimal delay time is calculated and the minimum em-bedding dimension is found with the method of False Nearest Neighbors.
Electrochemical Noise Chaotic Analysis of NiCoAg Alloy in Hank Solution
Directory of Open Access Journals (Sweden)
D. Bahena
2011-01-01
Full Text Available The potential and current oscillations during corrosion of NiCoAg alloy in Hank solution were studied. Detailed nonlinear fractal analyses were used to characterize complex time series clearly showing that the irregularity in these time series corresponds to deterministic chaos rather than to random noise. The chaotic oscillations were characterized by power spectral densities, phase space, and Lyapunov exponents. Electrochemical impedance was also applied the fractal dimensions for the corroded surface was obtained, and a corrosion mechanism was proposed.
Investigation of a chaotic thermostat
Morales, G. J.
2018-03-01
A numerical study is presented of a free particle interacting with a deterministic thermostat in which the usual friction force is supplemented with a fluctuating force that depends on the self-consistent damping coefficient associated with coupling to the heat bath. It is found that this addition results in a chaotic environment in which a particle self-heats from rest and moves in positive and negative directions, exhibiting a characteristic diffusive behavior. The frequency power spectrum of the dynamical quantities displays the exponential frequency dependence ubiquitous to chaotic dynamics. The velocity distribution function approximates a Maxwellian distribution, but it does show departures from perfect thermal equilibrium, while the distribution function for the damping coefficient shows a closer fit. The behavior for the classic Nosé-Hoover (NH) thermostat is compared to that of the enlarged Martyna-Klein-Tuckerman (MKT) model. Over a narrow amplitude range, the application of a constant external force results quantitatively in the Einstein relation for the NH thermostat, and for the MKT model it differs by a factor of 2.
Hybrid chaotic ant swarm optimization
International Nuclear Information System (INIS)
Li Yuying; Wen Qiaoyan; Li Lixiang; Peng Haipeng
2009-01-01
Chaotic ant swarm optimization (CASO) is a powerful chaos search algorithm that is used to find the global optimum solution in search space. However, the CASO algorithm has some disadvantages, such as lower solution precision and longer computational time, when solving complex optimization problems. To resolve these problems, an improved CASO, called hybrid chaotic swarm optimization (HCASO), is proposed in this paper. The new algorithm introduces preselection operator and discrete recombination operator into the CASO; meanwhile it replaces the best position found by own and its neighbors' ants with the best position found by preselection operator and discrete recombination operator in evolution equation. Through testing five benchmark functions with large dimensionality, the experimental results show the new method enhances the solution accuracy and stability greatly, as well as reduces the computational time and computer memory significantly when compared to the CASO. In addition, we observe the results can become better with swarm size increasing from the sensitivity study to swarm size. And we gain some relations between problem dimensions and swam size according to scalability study.
Chaotic Transport in Circumterrestrial Orbits
Rosengren, Aaron Jay
2018-04-01
The slow deformation of circumterrestrial orbits in the medium region, subject to lunisolar secular resonances, is well approximated by a Hamiltonian system with 2.5 degrees of freedom. This dynamical model is referred to in the astrophysical and celestial dynamics communities as the quadrupolar, secular, hierarchical three-body problem, and, in the non-autonomous case, gives rise to the classical Kozai-Lidov mechanism. In the time-dependent model, brought about in our case by the Moon's perturbed motion, the action variables of the system may experience chaotic variations and large drifts due to the possible overlap of nearby resonances. Using variational chaos indicators, we compute high-resolution portraits of the action space, revealing the existence of tori and structures filling chaotic regions. Our refined and elaborate calculations allow us to isolate precise initial conditions near specific areas of interest and to study their asymptotic behavior in time. We highlight in particular how the drift in phase space is mediated by the complement of the numerically detected KAM tori. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors, and, like the small body remnants of Solar system formation, they have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.
Indian Academy of Sciences (India)
IMTECH),. Chandigarh. Praveen Kumar is pursuing his PhD in chemical dynamics at. Panjab University,. Chandigarh. Keywords. Chemical oscillations, autoca-. talYSis, Lotka-Volterra model, bistability, hysteresis, Briggs-. Rauscher reaction.
Indian Academy of Sciences (India)
the law of mass-action that every simple reaction approaches ... from thermodynamic equilibrium. Such oscillating systems cor- respond to thermodynamically open systems. .... experimentally observable, and the third is always unstable.
International Nuclear Information System (INIS)
Cunningham, R.C.
1978-01-01
A tube holding rig is described for the lateral support of tubes arranged in tight parcels in a heat exchanger. This tube holding rig includes not less than two tube supporting assemblies, with a space between them, located crosswise with respect to the tubes, each supporting assembly comprising a first set of parallel components in contact with the tubes, whilst a second set of components is also in contact with the tubes. These two sets of parts together define apertures through which the tubes pass [fr
Optimal parameters uncoupling vibration modes of oscillators
Le, K. C.; Pieper, A.
2017-07-01
This paper proposes a novel optimization concept for an oscillator with two degrees of freedom. By using specially defined motion ratios, we control the action of springs to each degree of freedom of the oscillator. We aim at showing that, if the potential action of the springs in one period of vibration, used as the payoff function for the conservative oscillator, is maximized among all admissible parameters and motions satisfying Lagrange's equations, then the optimal motion ratios uncouple vibration modes. A similar result holds true for the dissipative oscillator having dampers. The application to optimal design of vehicle suspension is discussed.
Nonstationary behavior in a delayed feedback traveling wave tube folded waveguide oscillator
International Nuclear Information System (INIS)
Ryskin, N.M.; Titov, V.N.; Han, S.T.; So, J.K.; Jang, K.H.; Kang, Y.B.; Park, G.S.
2004-01-01
Folded waveguide traveling-wave tubes (FW TWT) are among the most promising candidates for powerful compact amplifiers and oscillators in millimeter and submillimeter wave bands. In this paper, the nonstationary behavior of a FW TWT oscillator with delayed feedback is investigated. Starting conditions of the oscillations are derived analytically. Results of numerical simulation of single-frequency, self-modulation (multifrequency) and chaotic generation regimes are presented. Mode competition phenomena, multistability and hysteresis are discussed
Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation
Directory of Open Access Journals (Sweden)
Ying Zhang
2016-01-01
Full Text Available The generation and evolution of chaotic motion in double-well Duffing oscillator under harmonic parametrical excitation are investigated. Firstly, the complex dynamical behaviors are studied by applying multibifurcation diagram and Poincaré sections. Secondly, by means of Melnikov’s approach, the threshold value of parameter μ for generation of chaotic behavior in Smale horseshoe sense is calculated. By the numerical simulation, it is obvious that as μ exceeds this threshold value, the behavior of Duffing oscillator is still steady-state periodic but the transient motion is chaotic; until the top Lyapunov exponent turns to positive, the motion of system turns to permanent chaos. Therefore, in order to gain an insight into the evolution of chaotic behavior after μ passing the threshold value, the transient motion, basin of attraction, and basin boundary are also investigated.
Yang, Ningning; Xu, Cheng; Wu, Chaojun; Jia, Rong; Liu, Chongxin
2017-12-01
Memristor is a nonlinear “missing circuit element”, that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua’s diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation.
Introduction To Control Of Oscillations And Chaos
International Nuclear Information System (INIS)
Fradkov, A. L.; Pogromsky, A. Yu.
1998-01-01
This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc. A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van dar Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diodes, stabilization of swings in power systems, increasing predictability of business-cycles are also presented. The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West. Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it
On dynamics analysis of a new chaotic attractor
International Nuclear Information System (INIS)
Zhou Wuneng; Xu Yuhua; Lu Hongqian; Pan Lin
2008-01-01
In this Letter, a new chaotic system is discussed. Some basic dynamical properties, such as Lyapunov exponents, Poincare mapping, fractal dimension, bifurcation diagram, continuous spectrum and chaotic dynamical behaviors of the new chaotic system are studied, either numerically or analytically. The obtained results show clearly that the system discussed in this Letter is a new chaotic system and deserves a further detailed investigation
Chaotic bubbling and nonstagnant foams.
Tufaile, Alberto; Sartorelli, José Carlos; Jeandet, Philippe; Liger-Belair, Gerard
2007-06-01
We present an experimental investigation of the agglomeration of bubbles obtained from a nozzle working in different bubbling regimes. This experiment consists of a continuous production of bubbles from a nozzle at the bottom of a liquid column, and these bubbles create a two-dimensional (2D) foam (or a bubble raft) at the top of this column. The bubbles can assemble in various dynamically stable arrangement, forming different kinds of foams in a liquid mixture of water and glycerol, with the effect that the bubble formation regimes influence the foam obtained from this agglomeration of bubbles. The average number of bubbles in the foam is related to the bubble formation frequency and the bubble mean lifetime. The periodic bubbling can generate regular or irregular foam, while a chaotic bubbling only generates irregular foam.
Chaotic hydrodynamics of fluidized beds
Energy Technology Data Exchange (ETDEWEB)
Van der Stappen, M.L.M. [Unit Process and Systems Engineering, Advanced Manufacturing Technology Group, Unilever Research Laboratorium, Vlaardingen (Netherlands)
1996-12-31
The major goals of this thesis are: (1) to develop and evaluate an analysis method based on techniques from non-linear chaos theory to characterize the nonlinear hydrodynamics of gas-solids fluidized beds quantitatively; and (2) to determine the dependence of the chaotic invariants on the operating conditions and investigate how the chaos analysis method can be profitably applied to improve scale-up and design of gas-solids fluidized bed reactors. Chaos theory is introduced in chapter 2 with emphasis on analysis techniques for (experimental) time series, known from literature at the start of this work (1990-1991). In chapter 3, the testing of existing and newly developed techniques on both model and fluidized bed data is described. This leads to the development of the chaos analysis method to analyze measured pressure fluctuations time series of a fluidized bed. Following, in chapter 4, this method is tested and all choices for the parameters are evaluated. The influence of the experimental parameters and external disturbances on the measurements and analysis results is discussed and quantified. The result is a chaos measurement and analysis protocol, which is further used in this work. In chapter 5, the applications to fluidized beds are discussed. It is shown that the entropy is a good measure for the characterization of the dynamical behavior of gas-solids bubbling/slugging fluidized beds. Entropy is applied to characterize the influence of the operating conditions, to assess regime transitions and to analyze dimensionless similar beds of different scale. Quantitative design correlations that relate entropy to the operating parameters (including the bed diameter) are described. Finally, it is discussed how the results of this work might be used in scaling up the chaotic dynamics of fluidized beds. The overall conclusions and outlook from this work are presented in chapter 6. 182 refs.
Regular transport dynamics produce chaotic travel times.
Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F; Toledo, Benjamín; Valdivia, Juan Alejandro
2014-06-01
In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.
Chaotic inflation in models with flat directions
International Nuclear Information System (INIS)
Graziani, F.; Olive, K.
1989-01-01
We consider the chaotic inflationary scenario in models with flat directions. We find that unless the scalars along the flat directions have vacuum expectation values p or 10 14 M p 15 M p depending on the expectation values of the chaotic inflator, Ψ, one or two or more periods of inflation occur but with a resulting energy density perturbation δρ/ρ ≅ 10 -16 , far too small to be of any consequence for galaxy formation. Even with p only limited initial values of ≅ (3-200) M p result in inflation with reasonable density perturbations. Thus chaotic inflation in models with flat directions require rather special initial conditions. (orig.)
International Nuclear Information System (INIS)
Ahmadi, Mohamadreza; Mojallali, Hamed
2012-01-01
Highlights: ► A new meta-heuristic optimization algorithm. ► Integration of invasive weed optimization and chaotic search methods. ► A novel parameter identification scheme for chaotic systems. - Abstract: This paper introduces a novel hybrid optimization algorithm by taking advantage of the stochastic properties of chaotic search and the invasive weed optimization (IWO) method. In order to deal with the weaknesses associated with the conventional method, the proposed chaotic invasive weed optimization (CIWO) algorithm is presented which incorporates the capabilities of chaotic search methods. The functionality of the proposed optimization algorithm is investigated through several benchmark multi-dimensional functions. Furthermore, an identification technique for chaotic systems based on the CIWO algorithm is outlined and validated by several examples. The results established upon the proposed scheme are also supplemented which demonstrate superior performance with respect to other conventional methods.
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
Fitz-Clarke, John R
2018-03-25
Breath-hold diving is practiced by recreational divers, seafood divers, military divers, and competitive athletes. It involves highly integrated physiology and extreme responses. This article reviews human breath-hold diving physiology beginning with an historical overview followed by a summary of foundational research and a survey of some contemporary issues. Immersion and cardiovascular adjustments promote a blood shift into the heart and chest vasculature. Autonomic responses include diving bradycardia, peripheral vasoconstriction, and splenic contraction, which help conserve oxygen. Competitive divers use a technique of lung hyperinflation that raises initial volume and airway pressure to facilitate longer apnea times and greater depths. Gas compression at depth leads to sequential alveolar collapse. Airway pressure decreases with depth and becomes negative relative to ambient due to limited chest compliance at low lung volumes, raising the risk of pulmonary injury called "squeeze," characterized by postdive coughing, wheezing, and hemoptysis. Hypoxia and hypercapnia influence the terminal breakpoint beyond which voluntary apnea cannot be sustained. Ascent blackout due to hypoxia is a danger during long breath-holds, and has become common amongst high-level competitors who can suppress their urge to breathe. Decompression sickness due to nitrogen accumulation causing bubble formation can occur after multiple repetitive dives, or after single deep dives during depth record attempts. Humans experience responses similar to those seen in diving mammals, but to a lesser degree. The deepest sled-assisted breath-hold dive was to 214 m. Factors that might determine ultimate human depth capabilities are discussed. © 2018 American Physiological Society. Compr Physiol 8:585-630, 2018. Copyright © 2018 American Physiological Society. All rights reserved.
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 ...
Bifurcation Control of Chaotic Dynamical Systems
National Research Council Canada - National Science Library
Wang, Hua O; Abed, Eyad H
1992-01-01
A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems...
Prediction and Geometry of Chaotic Time Series
National Research Council Canada - National Science Library
Leonardi, Mary
1997-01-01
This thesis examines the topic of chaotic time series. An overview of chaos, dynamical systems, and traditional approaches to time series analysis is provided, followed by an examination of state space reconstruction...
Chaotic Zones around Rotating Small Bodies
Energy Technology Data Exchange (ETDEWEB)
Lages, José; Shevchenko, Ivan I. [Institut UTINAM, Observatoire des Sciences de l’Univers THETA, CNRS, Université de Franche-Comté, Besançon F-25030 (France); Shepelyansky, Dima L., E-mail: jose.lages@utinam.cnrs.fr [Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, Toulouse F-31062 (France)
2017-06-01
Small bodies of the solar system, like asteroids, trans-Neptunian objects, cometary nuclei, and planetary satellites, with diameters smaller than 1000 km usually have irregular shapes, often resembling dumb-bells or contact binaries. The spinning of such a gravitating dumb-bell creates around it a zone of chaotic orbits. We determine its extent analytically and numerically. We find that the chaotic zone swells significantly if the rotation rate is decreased; in particular, the zone swells more than twice if the rotation rate is decreased 10 times with respect to the “centrifugal breakup” threshold. We illustrate the properties of the chaotic orbital zones in examples of the global orbital dynamics about asteroid 243 Ida (which has a moon, Dactyl, orbiting near the edge of the chaotic zone) and asteroid 25143 Itokawa.
Nonlinear chaotic model for predicting storm surges
Directory of Open Access Journals (Sweden)
M. Siek
2010-09-01
Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.
Indirect adaptive control of discrete chaotic systems
International Nuclear Information System (INIS)
Salarieh, Hassan; Shahrokhi, Mohammad
2007-01-01
In this paper an indirect adaptive control algorithm is proposed to stabilize the fixed points of discrete chaotic systems. It is assumed that the functionality of the chaotic dynamics is known but the system parameters are unknown. This assumption is usually applicable to many chaotic systems, such as the Henon map, logistic and many other nonlinear maps. Using the recursive-least squares technique, the system parameters are identified and based on the feedback linearization method an adaptive controller is designed for stabilizing the fixed points, or unstable periodic orbits of the chaotic maps. The stability of the proposed scheme has been shown and the effectiveness of the control algorithm has been demonstrated through computer simulations
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.
Multiswitching compound antisynchronization of four chaotic systems
Indian Academy of Sciences (India)
Ayub Khan
2017-11-28
Nov 28, 2017 ... systems, electrical engineering, information process- ... model. The synchronization problem among three or more chaotic ...... we perform numerical simulations in MATLAB using ... In the simulation process we assume α1 =.
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Synchronizing a class of uncertain chaotic systems
International Nuclear Information System (INIS)
Chen Maoyin; Zhou Donghua; Shang Yun
2005-01-01
This Letter deals with the synchronization of a class of uncertain chaotic systems in the drive-response framework. A robust adaptive observer based response system is designed to synchronize a given chaotic system with unknown parameters and external disturbances. Lyapunov stability ensures the global synchronization between the drive and response systems even if Lipschitz constants on function matrices and bounds on uncertainties are unknown. Numerical simulation of Genesio-Tesi system verifies the effectiveness of this scheme
Improvement on generalised synchronisation of chaotic systems
International Nuclear Information System (INIS)
Hui-Bin, Zhu; Fang, Qiu; Bao-Tong, Cui
2010-01-01
In this paper, the problem of generalised synchronisation of two different chaotic systems is investigated. Some less conservative conditions are derived using linear matrix inequality other than existing results. Furthermore, a simple adaptive control scheme is proposed to achieve the generalised synchronisation of chaotic systems. The proposed method is simple and easy to implement in practice and can be applied to secure communications. Numerical simulations are also given to demonstrate the effectiveness and feasibility of the theoretical analysis
Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series
Directory of Open Access Journals (Sweden)
Qing Li
2016-01-01
Full Text Available According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and the optimal embedding dimension and saturated correlation dimension are calculated via the Grassberger–Procaccia (G-P method, respectively, so that the chaotic characteristics of vibration intensity time series can be jointly determined by the largest Lyapunov exponent and phase plane trajectory of vibration intensity time series, meanwhile, the largest Lyapunov exponent is calculated by the Wolf method and phase plane trajectory is illustrated using Duffing-Holmes Oscillator (DHO. The Hurst exponent and long range dependence prediction method are proposed to verify the typical fractional order features and improve the prediction accuracy of bearing vibration intensity time series, respectively. Experience shows that the vibration intensity time series have chaotic properties and the LRD prediction method is better than the other prediction methods (largest Lyapunov, auto regressive moving average (ARMA and BP neural network (BPNN model in prediction accuracy and prediction performance, which provides a new approach for running tendency predictions for rotating machinery and provide some guidance value to the engineering practice.
Chaotic behavior in a hydrodynamic model of a fluidized bed reactor
International Nuclear Information System (INIS)
Schouten, J.C.; van den Bleek, C.M.
1991-01-01
Recent preliminary experimental studies using time-series analysis have demonstrated that the multi-phase flow in fluidized bed reactors can be characterized as chaotic. In the present paper, it is therefore argued that the chaotic time-dependence of fluidization is a characteristic feature which should be included in scaling rules for fluidized bed reactors. For example, the similarity groups applied in dimensionless fluidized bed scaling should be improved by extending them with functions of the relevant numbers from chaos theory, such as the correlation and embedding dimension or the maximum Lyapunov exponent. This requires that the dependence of these numbers on fluidization parameters must be theoretically and experimentally investigated. The concept of chaos in fluidization also requires that the classical, empirically developed, hydrodynamic models that are applied in fluidized bed scaling are amended to include time-dependence, non-linearity as well as a sufficient level of complexity before they can predict any chaotic behavior. An example is given of chaotic behavior generated in the classical counter-current flow model according to Van Deemter by writing the upwards solids velocity as a harmonic oscillating function of time. A low-dimensional strange attractor is found, embedded in two-dimensional phase space, of which the correlation dimension depends on the solids exchange coefficient
Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Valtierra-Rodríguez, M.
2017-12-01
In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master-slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua's systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0 , 1 ] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.
THE ASTEROID BELT AS A RELIC FROM A CHAOTIC EARLY SOLAR SYSTEM
Energy Technology Data Exchange (ETDEWEB)
Izidoro, André; Raymond, Sean N.; Pierens, Arnaud [Laboratoire d’astrophysique de Bordeaux, Université de Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, F-33615 Pessac (France); Morbidelli, Alessandro [University of Nice-Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, Laboratoire Lagrange, BP 4229, F-06304 Nice Cedex 4 (France); Winter, Othon C. [UNESP, Univ. Estadual Paulista—Grupo de Dinâmica Orbital and Planetologia, Guaratinguetá, CEP 12.516-410, São Paulo (Brazil); Nesvorny' , David, E-mail: izidoro.costa@gmail.com [Department of Space Studies, Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder, CO 80302 (United States)
2016-12-10
The orbital structure of the asteroid belt holds a record of the solar system’s dynamical history. The current belt only contains ∼10{sup −3} Earth masses yet the asteroids’ orbits are dynamically excited, with a large spread in eccentricity and inclination. In the context of models of terrestrial planet formation, the belt may have been excited by Jupiter’s orbital migration. The terrestrial planets can also be reproduced without invoking a migrating Jupiter; however, as it requires a severe mass deficit beyond Earth’s orbit, this model systematically under-excites the asteroid belt. Here we show that the orbits of the asteroids may have been excited to their current state if Jupiter’s and Saturn’s early orbits were chaotic. Stochastic variations in the gas giants’ orbits cause resonances to continually jump across the main belt and excite the asteroids’ orbits on a timescale of tens of millions of years. While hydrodynamical simulations show that the gas giants were likely in mean motion resonance at the end of the gaseous disk phase, small perturbations could have driven them into a chaotic but stable state. The gas giants’ current orbits were achieved later, during an instability in the outer solar system. Although it is well known that the present-day solar system exhibits chaotic behavior, our results suggest that the early solar system may also have been chaotic.
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
A vast amount of various invariant tori in the Nosé-Hoover oscillator.
Wang, Lei; Yang, Xiao-Song
2015-12-01
This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of "chaotic region" and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a "chaotic sea" for the Nosé-Hoover oscillator.
A vast amount of various invariant tori in the Nosé-Hoover oscillator
Energy Technology Data Exchange (ETDEWEB)
Wang, Lei [School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 (China); Department of Mathematics and Physics, Hefei University, Hefei 230601 (China); Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn [School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 (China)
2015-12-15
This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of “chaotic region” and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a “chaotic sea” for the Nosé-Hoover oscillator.
A vast amount of various invariant tori in the Nosé-Hoover oscillator
Wang, Lei; Yang, Xiao-Song
2015-12-01
This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of "chaotic region" and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a "chaotic sea" for the Nosé-Hoover oscillator.
International Nuclear Information System (INIS)
Wang Xing-Yuan; Bao Xue-Mei
2013-01-01
In this paper, we propose a novel block cryptographic scheme based on a spatiotemporal chaotic system and a chaotic neural network (CNN). The employed CNN comprises a 4-neuron layer called a chaotic neuron layer (CNL), where the spatiotemporal chaotic system participates in generating its weight matrix and other parameters. The spatiotemporal chaotic system used in our scheme is the typical coupled map lattice (CML), which can be easily implemented in parallel by hardware. A 160-bit-long binary sequence is used to generate the initial conditions of the CML. The decryption process is symmetric relative to the encryption process. Theoretical analysis and experimental results prove that the block cryptosystem is secure and practical, and suitable for image encryption. (general)
Composing chaotic music from the letter m
Sotiropoulos, Anastasios D.
Chaotic music is composed from a proposed iterative map depicting the letter m, relating the pitch, duration and loudness of successive steps. Each of the two curves of the letter m is based on the classical logistic map. Thus, the generating map is xn+1 = r xn(1/2 - xn) for xn between 0 and 1/2 defining the first curve, and xn+1 = r (xn - 1/2)(1 - xn) for xn between 1/2 and 1 representing the second curve. The parameter r which determines the height(s) of the letter m varies from 2 to 16, the latter value ensuring fully developed chaotic solutions for the whole letter m; r = 8 yielding full chaotic solutions only for its first curve. The m-model yields fixed points, bifurcation points and chaotic regions for each separate curve, as well as values of the parameter r greater than 8 which produce inter-fixed points, inter-bifurcation points and inter-chaotic regions from the interplay of the two curves. Based on this, music is composed from mapping the m- recurrence model solutions onto actual notes. The resulting musical score strongly depends on the sequence of notes chosen by the composer to define the musical range corresponding to the range of the chaotic mathematical solutions x from 0 to 1. Here, two musical ranges are used; one is the middle chromatic scale and the other is the seven- octaves range. At the composer's will and, for aesthetics, within the same composition, notes can be the outcome of different values of r and/or shifted in any octave. Compositions with endings of non-repeating note patterns result from values of r in the m-model that do not produce bifurcations. Scores of chaotic music composed from the m-model and the classical logistic model are presented.
Estimating model parameters in nonautonomous chaotic systems using synchronization
International Nuclear Information System (INIS)
Yang, Xiaoli; Xu, Wei; Sun, Zhongkui
2007-01-01
In this Letter, a technique is addressed for estimating unknown model parameters of multivariate, in particular, nonautonomous chaotic systems from time series of state variables. This technique uses an adaptive strategy for tracking unknown parameters in addition to a linear feedback coupling for synchronizing systems, and then some general conditions, by means of the periodic version of the LaSalle invariance principle for differential equations, are analytically derived to ensure precise evaluation of unknown parameters and identical synchronization between the concerned experimental system and its corresponding receiver one. Exemplifies are presented by employing a parametrically excited 4D new oscillator and an additionally excited Ueda oscillator. The results of computer simulations reveal that the technique not only can quickly track the desired parameter values but also can rapidly respond to changes in operating parameters. In addition, the technique can be favorably robust against the effect of noise when the experimental system is corrupted by bounded disturbance and the normalized absolute error of parameter estimation grows almost linearly with the cutoff value of noise strength in simulation
Distributed MIMO chaotic radar based on wavelength-division multiplexing technology.
Yao, Tingfeng; Zhu, Dan; Ben, De; Pan, Shilong
2015-04-15
A distributed multiple-input multiple-output chaotic radar based on wavelength-division multiplexing technology (WDM) is proposed and demonstrated. The wideband quasi-orthogonal chaotic signals generated by different optoelectronic oscillators (OEOs) are emitted by separated antennas to gain spatial diversity against the fluctuation of a target's radar cross section and enhance the detection capability. The received signals collected by the receive antennas and the reference signals from the OEOs are delivered to the central station for joint processing by exploiting WDM technology. The centralized signal processing avoids precise time synchronization of the distributed system and greatly simplifies the remote units, which improves the localization accuracy of the entire system. A proof-of-concept experiment for two-dimensional localization of a metal target is demonstrated. The maximum position error is less than 6.5 cm.
Tlelo-Cuautle, Esteban; de la Fraga, Luis Gerardo
2016-01-01
This book offers readers a clear guide to implementing engineering applications with FPGAs, from the mathematical description to the hardware synthesis, including discussion of VHDL programming and co-simulation issues. Coverage includes FPGA realizations such as: chaos generators that are described from their mathematical models; artificial neural networks (ANNs) to predict chaotic time series, for which a discussion of different ANN topologies is included, with different learning techniques and activation functions; random number generators (RNGs) that are realized using different chaos generators, and discussions of their maximum Lyapunov exponent values and entropies. Finally, optimized chaotic oscillators are synchronized and realized to implement a secure communication system that processes black and white and grey-scale images. In each application, readers will find VHDL programming guidelines and computer arithmetic issues, along with co-simulation examples with Active-HDL and Simulink. Readers will b...
Kügler, Philipp; Bulelzai, M A K; Erhardt, André H
2017-04-04
Early afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). EADs are caused by drugs, oxidative stress or ion channel disease, and they are considered as potential precursors to cardiac arrhythmias in recent attempts to redefine the cardiac drug safety paradigm. The irregular behaviour of EADs observed in experiments has been previously attributed to chaotic EAD dynamics under periodic pacing, made possible by a homoclinic bifurcation in the fast subsystem of the deterministic AP system of differential equations. In this article we demonstrate that a homoclinic bifurcation in the fast subsystem of the action potential model is neither a necessary nor a sufficient condition for the genesis of chaotic EADs. We rather argue that a cascade of period doubling (PD) bifurcations of limit cycles in the full AP system paves the way to chaotic EAD dynamics across a variety of models including a) periodically paced and spontaneously active cardiomyocytes, b) periodically paced and non-active cardiomyocytes as well as c) unpaced and spontaneously active cardiomyocytes. Furthermore, our bifurcation analysis reveals that chaotic EAD dynamics may coexist in a stable manner with fully regular AP dynamics, where only the initial conditions decide which type of dynamics is displayed. EADs are a potential source of cardiac arrhythmias and hence are of relevance both from the viewpoint of drug cardiotoxicity testing and the treatment of cardiomyopathies. The model-independent association of chaotic EADs with period doubling cascades of limit cycles introduced in this article opens novel opportunities to study chaotic EADs by means of bifurcation control theory and inverse bifurcation analysis. Furthermore, our results may shed new light on the synchronization and propagation of chaotic EADs in homogeneous and heterogeneous multicellular and cardiac tissue preparations.
Chaplygin sleigh with periodically oscillating internal mass
Bizyaev, Ivan A.; Borisov, Alexey V.; Kuznetsov, Sergey P.
2017-09-01
We consider the movement of Chaplygin sleigh on a plane that is a solid body with imposed nonholonomic constraint, which excludes the possibility of motions transversal to the constraint element (“knife-edge”), and complement the model with an attached mass, periodically oscillating relatively to the main platform of the sleigh. Numerical simulations indicate the occurrence of either unrestricted acceleration of the sleigh, or motions with bounded velocities and momenta, depending on parameters. We note the presence of phenomena characteristic to nonholonomic systems with complex dynamics; in particular, attractors occur responsible for chaotic motions. In addition, quasiperiodic regimes take place similar to those observed in conservative nonlinear dynamics.
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.
Long, Zhili; Wang, Rui; Fang, Jiwen; Dai, Xufei; Li, Zuohua
2017-07-01
Piezoelectric actuators invariably exhibit hysteresis nonlinearities that tend to become significant under the open-loop condition and could cause oscillations and errors in nanometer-positioning tasks. Chaotic map modified particle swarm optimization (MPSO) is proposed and implemented to identify the Prandtl-Ishlinskii model for piezoelectric actuators. Hysteresis compensation is attained through application of an inverse Prandtl-Ishlinskii model, in which the parameters are formulated based on the original model with chaotic map MPSO. To strengthen the diversity and improve the searching ergodicity of the swarm, an initial method of adaptive inertia weight based on a chaotic map is proposed. To compare and prove that the swarm's convergence occurs before stochastic initialization and to attain an optimal particle swarm optimization algorithm, the parameters of a proportional-integral-derivative controller are searched using self-tuning, and the simulated results are used to verify the search effectiveness of chaotic map MPSO. The results show that chaotic map MPSO is superior to its competitors for identifying the Prandtl-Ishlinskii model and that the inverse Prandtl-Ishlinskii model can provide hysteresis compensation under different conditions in a simple and effective manner.
Chaotic interactions of self-replicating RNA.
Forst, C V
1996-03-01
A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.
Image Encryption and Chaotic Cellular Neural Network
Peng, Jun; Zhang, Du
Machine learning has been playing an increasingly important role in information security and assurance. One of the areas of new applications is to design cryptographic systems by using chaotic neural network due to the fact that chaotic systems have several appealing features for information security applications. In this chapter, we describe a novel image encryption algorithm that is based on a chaotic cellular neural network. We start by giving an introduction to the concept of image encryption and its main technologies, and an overview of the chaotic cellular neural network. We then discuss the proposed image encryption algorithm in details, which is followed by a number of security analyses (key space analysis, sensitivity analysis, information entropy analysis and statistical analysis). The comparison with the most recently reported chaos-based image encryption algorithms indicates that the algorithm proposed in this chapter has a better security performance. Finally, we conclude the chapter with possible future work and application prospects of the chaotic cellular neural network in other information assurance and security areas.
Qualitative feature extractions of chaotic systems
International Nuclear Information System (INIS)
Vicha, T.; Dohnal, M.
2008-01-01
The theory of chaos offers useful tools for systems analysis. However, models of complex systems are based on a network of inconsistent, space and uncertain knowledge items. Traditional quantitative methods of chaos analysis are therefore not applicable. The paper by the same authors [Vicha T, Dohnal M. Qualitative identification of chaotic systems behaviours. Chaos, Solitons and Fractals, in press, [Log. No. 601019] ] presents qualitative interpretation of some chaos concepts. There are only three qualitative values positive/increasing, negative/decreasing and zero/constant. It means that any set of qualitative multidimensional descriptions of unsteady state behaviours is discrete and finite. A finite upper limit exists for the total number of qualitatively distinguishable scenarios. A set of 21 published chaotic models is solved qualitatively and 21 sets of all existing qualitative scenarios are presented. The intersection of all 21 scenario sets is empty. There is no such a behaviour which is common for all 21 models. The set of 21 qualitative models (e.g. Lorenz, Roessler) can be used to compare chaotic behaviours of an unknown qualitative model with them to evaluate if its chaotic behaviours is close to e.g. Lorenz chaotic model and how much
Pei, Yan
2015-01-01
We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.
2015-01-01
We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed. PMID:25879067
Directory of Open Access Journals (Sweden)
Yan Pei
2015-01-01
Full Text Available We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC algorithm, interactive chaotic evolution (ICE that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.
Generalized projective synchronization of a unified chaotic system
International Nuclear Information System (INIS)
Yan Jianping; Li Changpin
2005-01-01
In the present paper, a simple but efficient control technique of the generalized projective synchronization is applied to a unified chaotic system. Numerical simulations show that this method works very well, which can also be applied to other chaotic systems
The Hausdorff measure of chaotic sets of adjoint shift maps
Energy Technology Data Exchange (ETDEWEB)
Wang Huoyun [Department of Mathematics of Guangzhou University, Guangzhou 510006 (China)]. E-mail: wanghuoyun@sina.com; Song Wangan [Department of Computer, Huaibei Coal Industry Teacher College, Huaibei 235000 (China)
2006-11-15
In this paper, the size of chaotic sets of adjoint shift maps is estimated by Hausdorff measure. We prove that for any adjoint shift map there exists a finitely chaotic set with full Hausdorff measure.
A new chaotic algorithm for image encryption
International Nuclear Information System (INIS)
Gao Haojiang; Zhang Yisheng; Liang Shuyun; Li Dequn
2006-01-01
Recent researches of image encryption algorithms have been increasingly based on chaotic systems, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper presents a new nonlinear chaotic algorithm (NCA) which uses power function and tangent function instead of linear function. Its structural parameters are obtained by experimental analysis. And an image encryption algorithm in a one-time-one-password system is designed. The experimental results demonstrate that the image encryption algorithm based on NCA shows advantages of large key space and high-level security, while maintaining acceptable efficiency. Compared with some general encryption algorithms such as DES, the encryption algorithm is more secure
Describing chaotic attractors: Regular and perpetual points
Dudkowski, Dawid; Prasad, Awadhesh; Kapitaniak, Tomasz
2018-03-01
We study the concepts of regular and perpetual points for describing the behavior of chaotic attractors in dynamical systems. The idea of these points, which have been recently introduced to theoretical investigations, is thoroughly discussed and extended into new types of models. We analyze the correlation between regular and perpetual points, as well as their relation with phase space, showing the potential usefulness of both types of points in the qualitative description of co-existing states. The ability of perpetual points in finding attractors is indicated, along with its potential cause. The location of chaotic trajectories and sets of considered points is investigated and the study on the stability of systems is shown. The statistical analysis of the observing desired states is performed. We focus on various types of dynamical systems, i.e., chaotic flows with self-excited and hidden attractors, forced mechanical models, and semiconductor superlattices, exhibiting the universality of appearance of the observed patterns and relations.
Chaotic behavior learning of Chua's circuit
International Nuclear Information System (INIS)
Sun Jian-Cheng
2012-01-01
Least-square support vector machines (LS-SVM) are applied for learning the chaotic behavior of Chua's circuit. The system is divided into three multiple-input single-output (MISO) structures and the LS-SVM are trained individually. Comparing with classical approaches, the proposed one reduces the structural complexity and the selection of parameters is avoided. Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation. Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua's circuit state variables, and exhibit the chaotic attractors under the autonomous working mode
Semi-classical quantization of chaotic billiards
International Nuclear Information System (INIS)
Smilansky, U.
1992-02-01
The semi-classical quantization of chaotic billiards will be developed using scattering theory approach. This will be used to introduce and explain the inherent difficulties in the semi-classical quantization of chaos, and to show some of the modern tools which were developed recently to overcome these difficulties. To this end, we shall first obtain a semi-classical secular equation which is based on a finite number of classical periodic orbits. We shall use it to derive some spectral properties, and in particular to investigate the relationship between spectral statistics of quantum chaotic systems and the predictions of random-matrix theory. We shall finally discuss an important family of chaotic billiard, whose statistics does not follow any of the canonical ensembles, (GOE,GUE,...) but rather, corresponds to a new universality class. (author)
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
Circuit simulation and physical implementation for a memristor-based colpitts oscillator
Deng, Hongmin; Wang, Dongping
2017-03-01
This paper implements two kinds of memristor-based colpitts oscillators, namely, the circuit where the memristor is added into the feedback network of the oscillator in parallel and series, respectively. First, a MULTISIM simulation circuit for the memristive colpitts oscillator is built, where an emulator constructed by some off-the-shelf components is utilized to replace the memristor. Then the physical system is implemented in terms of the MULTISIM simulation circuit. Circuit simulation and experimental study show that this memristive colpitts oscillator can exhibit periodic, quasi-periodic, and chaotic behaviors with certain parameter's variances. Besides, in a sense, the circuit is robust with circuit parameters and device types.
Directory of Open Access Journals (Sweden)
Paulius Palevicius
2014-01-01
Full Text Available Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.
Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas
2014-01-01
Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms. PMID:24451467
Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas
2014-01-21
Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.
Graf, Rudolf F
1996-01-01
This series of circuits provides designers with a quick source for oscillator circuits. Why waste time paging through huge encyclopedias when you can choose the topic you need and select any of the specialized circuits sorted by application?This book in the series has 250-300 practical, ready-to-use circuit designs, with schematics and brief explanations of circuit operation. The original source for each circuit is listed in an appendix, making it easy to obtain additional information.Ready-to-use circuits.Grouped by application for easy look-up.Circuit source listing
Chaotic Flows Correlation effects and coherent structures
Bakunin, Oleg G
2011-01-01
The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.
Higgs vacuum stability and modified chaotic inflation
Energy Technology Data Exchange (ETDEWEB)
Saha, Abhijit Kumar, E-mail: abhijit.saha@iitg.ernet.in; Sil, Arunansu, E-mail: asil@iitg.ernet.in
2017-02-10
The issue of electroweak vacuum stability is studied in presence of a scalar field which participates in modifying the minimal chaotic inflation model. It is shown that the threshold effect on the Higgs quartic coupling originating from the Higgs–inflaton sector interaction can essentially make the electroweak vacuum stable up to the Planck scale. On the other hand we observe that the new physics parameters in this combined framework are enough to provide deviation from the minimal chaotic inflation predictions so as to keep it consistent with recent observation by Planck 2015.
Chaotic behavior of a quantum waveguide
Energy Technology Data Exchange (ETDEWEB)
Pérez-Aguilar, H., E-mail: hiperezag@yahoo.com [Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mújica S/N 58030, Morelia, Michoacán (Mexico); Mendoza-Suárez, A.; Tututi, E.S. [Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mújica S/N 58030, Morelia, Michoacán (Mexico); Herrera-González, I.F. [Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla (Mexico)
2013-02-15
In this work we consider an infinite quantum waveguide composed of two periodic, hard walls, one-dimensional rippled surfaces. We find that, under certain conditions, the proposed system presents some traces of quantum chaos, when the corresponding classical limit has chaotic behavior. Thus, it is possible to obtain disordered probability densities in a system with smooth surfaces. When the system has chaotic behavior we show numerically that the correlation length of the autocorrelation function of the probability density goes to zero. To corroborate some properties obtained for infinite waveguide that are physically admissible, we study the corresponding finite version of this system.
Chaotic behavior of a quantum waveguide
International Nuclear Information System (INIS)
Pérez-Aguilar, H.; Mendoza-Suárez, A.; Tututi, E.S.; Herrera-González, I.F.
2013-01-01
In this work we consider an infinite quantum waveguide composed of two periodic, hard walls, one-dimensional rippled surfaces. We find that, under certain conditions, the proposed system presents some traces of quantum chaos, when the corresponding classical limit has chaotic behavior. Thus, it is possible to obtain disordered probability densities in a system with smooth surfaces. When the system has chaotic behavior we show numerically that the correlation length of the autocorrelation function of the probability density goes to zero. To corroborate some properties obtained for infinite waveguide that are physically admissible, we study the corresponding finite version of this system
Searching of Chaotic Elements in Hydrology
Directory of Open Access Journals (Sweden)
Sorin VLAD
2014-03-01
Full Text Available Chaos theory offers new means of understanding and prediction of phenomena otherwise considered random and unpredictable. The signatures of chaos can be isolated by performing nonlinear analysis of the time series available. The paper presents the results obtained by conducting a nonlinear analysis of the time series of daily Siret river flow (located in the North-Eastern part of Romania. The time series analysis is recorded starting with January 1999 to July 2009. The attractor is embedded in the reconstructed phase space then the chaotic dynamics is revealed computing the chaotic invariants - correlation dimension and the maximum Lyapunov Exponent.
A time-delayed method for controlling chaotic maps
International Nuclear Information System (INIS)
Chen Maoyin; Zhou Donghua; Shang Yun
2005-01-01
Combining the repetitive learning strategy and the optimality principle, this Letter proposes a time-delayed method to control chaotic maps. This method can effectively stabilize unstable periodic orbits within chaotic attractors in the sense of least mean square. Numerical simulations of some chaotic maps verify the effectiveness of this method
Chaotic correlations in barrier billiards with arbitrary barriers
International Nuclear Information System (INIS)
Osbaldestin, A H; Adamson, L N C
2013-01-01
We study autocorrelation functions in symmetric barrier billiards for golden mean trajectories with arbitrary barriers. Renormalization analysis reveals the presence of a chaotic invariant set and thus that, for a typical barrier, there are chaotic correlations. The chaotic renormalization set is the analogue of the so-called orchid that arises in a generalized Harper equation. (paper)
Empirically characteristic analysis of chaotic PID controlling particle swarm optimization.
Yan, Danping; Lu, Yongzhong; Zhou, Min; Chen, Shiping; Levy, David
2017-01-01
Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles' search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles' premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO.
Recognizing chaotic states in stadium billiard by calculating gyration radius
Directory of Open Access Journals (Sweden)
M. Barezi
2006-12-01
Full Text Available Nowadays study of chaotic quantum billiards because of their relation to Nano technology. In this paper distribution of zeros of wave function on the boundary of two circular and stadium billiards are investigated. By calculating gyration radius for these points chaotic and non-chaotic states are distinguished.
Synchronization of two different chaotic systems via nonlinear ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: This work reports the synchronization of a pair of four chaotic systems via nonlinear control technique. This method has been found to be easy to implement and effective especially on two different chaotic systems. We paired four chaotic systems out of which one is new and we have six possible pairs.
Crenelated fast oscillatory outputs of a two-delay electro-optic oscillator.
Weicker, Lionel; Erneux, Thomas; Jacquot, Maxime; Chembo, Yanne; Larger, Laurent
2012-02-01
An electro-optic oscillator subject to two distinct delayed feedbacks has been designed to develop pronounced broadband chaotic output. Its route to chaos starts with regular pulsating gigahertz oscillations that we investigate both experimentally and theoretically. Of particular physical interest are the transitions to various crenelated fast time-periodic oscillations, prior to the onset of chaotic regimes. The two-delay problem is described mathematically by two coupled delay-differential equations, which we analyze by using multiple-time-scale methods. We show that the interplay of a large delay and a relatively small delay is responsible for the onset of fast oscillations modulated by a slowly varying square-wave envelope. As the bifurcation parameter progressively increases, this envelope undergoes a sequence of bifurcations that corresponds to successive fixed points of a sine map.
Generation of chaotic radiation in a driven traveling wave tube amplifier with time-delayed feedback
International Nuclear Information System (INIS)
Marchewka, Chad; Larsen, Paul; Bhattacharjee, Sudeep; Booske, John; Sengele, Sean; Ryskin, Nikita; Titov, Vladimir
2006-01-01
The application of chaos in communications and radar offers new and interesting possibilities. This article describes investigations on the generation of chaos in a traveling wave tube (TWT) amplifier and the experimental parameters responsible for sustaining stable chaos. Chaos is generated in a TWT amplifier when it is made to operate in a highly nonlinear regime by recirculating a fraction of the TWT output power back to the input in a delayed feedback configuration. A driver wave provides a constant external force to the system making it behave like a forced nonlinear oscillator. The effects of the feedback bandwidth, intensity, and phase are described. The study illuminates the different transitions to chaos and the effect of parameters such as the frequency and intensity of the driver wave. The detuning frequency, i.e., difference frequency between the driver wave and the natural oscillation of the system, has been identified as being an important physical parameter for controlling evolution to chaos. Among the observed routes to chaos, besides the more common period doubling, a new route called loss of frequency locking occurs when the driving frequency is adjacent to a natural oscillation mode. The feedback bandwidth controls the nonlinear dynamics of the system, particularly the number of natural oscillation modes. A computational model has been developed to simulate the experiments and reasonably good agreement is obtained between them. Experiments are described that demonstrate the feasibility of chaotic communications using two TWTs, where one is operated as a driven chaotic oscillator and the other as a time-delayed, open-loop amplifier
Generation of chaotic radiation in a driven traveling wave tube amplifier with time-delayed feedback
Marchewka, Chad; Larsen, Paul; Bhattacharjee, Sudeep; Booske, John; Sengele, Sean; Ryskin, Nikita; Titov, Vladimir
2006-01-01
The application of chaos in communications and radar offers new and interesting possibilities. This article describes investigations on the generation of chaos in a traveling wave tube (TWT) amplifier and the experimental parameters responsible for sustaining stable chaos. Chaos is generated in a TWT amplifier when it is made to operate in a highly nonlinear regime by recirculating a fraction of the TWT output power back to the input in a delayed feedback configuration. A driver wave provides a constant external force to the system making it behave like a forced nonlinear oscillator. The effects of the feedback bandwidth, intensity, and phase are described. The study illuminates the different transitions to chaos and the effect of parameters such as the frequency and intensity of the driver wave. The detuning frequency, i.e., difference frequency between the driver wave and the natural oscillation of the system, has been identified as being an important physical parameter for controlling evolution to chaos. Among the observed routes to chaos, besides the more common period doubling, a new route called loss of frequency locking occurs when the driving frequency is adjacent to a natural oscillation mode. The feedback bandwidth controls the nonlinear dynamics of the system, particularly the number of natural oscillation modes. A computational model has been developed to simulate the experiments and reasonably good agreement is obtained between them. Experiments are described that demonstrate the feasibility of chaotic communications using two TWTs, where one is operated as a driven chaotic oscillator and the other as a time-delayed, open-loop amplifier.
The variation of the density functions on chaotic spheres in chaotic space-like Minkowski space time
International Nuclear Information System (INIS)
El-Ahmady, A.E.
2007-01-01
In this article we introduce types of chaotic spheres in chaotic space-like Minkowski space time M n+1 . The variations of the density functions under the folding of these chaotic spheres are defined. The foldings restriction imposed on the density function are also discussed. The relations between the folding of geometry and pure chaotic manifolds are deduced. Some theorems concerning these relations are presented
International Nuclear Information System (INIS)
Kingni, Sifeu Takougang; Pham, Viet-Thanh; Jafari, Sajad; Woafo, Paul
2017-01-01
A three-dimensional autonomous chaotic system with an infinite number of equilibrium points located on a line and a hyperbola is proposed in this paper. To analyze the dynamical behaviors of the proposed system, mathematical tools such as Routh-Hurwitz criteria, Lyapunov exponents and bifurcation diagram are exploited. For a suitable choice of the parameters, the proposed system can generate periodic oscillations and chaotic attractors of different shapes such as bistable and monostable chaotic attractors. In addition, an electronic circuit is designed and implemented to verify the feasibility of the proposed system. A good qualitative agreement is shown between the numerical simulations and the Orcard-PSpice results. Moreover, the fractional-order form of the proposed system is studied using analog and numerical simulations. It is found that chaos, periodic oscillations and periodic spiking exist in this proposed system with order less than three. Then an electronic circuit is designed for the commensurate fractional order α = 0.98, from which we can observe that a chaotic attractor exists in the fractional-order form of the proposed system. Finally, the problem of drive-response generalized projective synchronization of the fractional-order form of the chaotic proposed autonomous system is considered.
Quantum infinite square well with an oscillating wall
International Nuclear Information System (INIS)
Glasser, M.L.; Mateo, J.; Negro, J.; Nieto, L.M.
2009-01-01
A linear matrix equation is considered for determining the time dependent wave function for a particle in a one-dimensional infinite square well having one moving wall. By a truncation approximation, whose validity is checked in the exactly solvable case of a linearly contracting wall, we examine the cases of a simple harmonically oscillating wall and a non-harmonically oscillating wall for which the defining parameters can be varied. For the latter case, we examine in closer detail the dependence on the frequency changes, and we find three regimes: an adiabatic behabiour for low frequencies, a periodic one for high frequencies, and a chaotic behaviour for an intermediate range of frequencies.
One dimension harmonic oscillator
International Nuclear Information System (INIS)
Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Franck.
1977-01-01
The importance of harmonic oscillator in classical and quantum physics, eigenvalues and eigenstates of hamiltonian operator are discussed. In complement are presented: study of some physical examples of harmonic oscillators; study of stationnary states in the /x> representation; Hermite polynomials; resolution of eigenvalue equation of harmonic oscillator by polynomial method; isotope harmonic oscillator with three dimensions; charged harmonic oscillator in uniform electric field; quasi classical coherent states of harmonic oscillator; eigenmodes of vibration of two coupled harmonic oscillators; vibration modus of a continuous physical system (application to radiation: photons); vibration modus of indefinite linear chain of coupled harmonic oscillators (phonons); one-dimensional harmonic oscillator in thermodynamic equilibrium at temperature T [fr
Parameter and state estimation of experimental chaotic systems using synchronization
Quinn, John C.; Bryant, Paul H.; Creveling, Daniel R.; Klein, Sallee R.; Abarbanel, Henry D. I.
2009-07-01
We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously and we explore them using experiments and simulations with the chaotic Colpitts oscillator as an example system. We explore the impact of model imperfection on the ability to extract valid information from an experimental system. We compare two optimization methods: an initial value method and a constrained method. Each of these involves coupling the model equations to the experimental data in order to regularize the chaotic motions on the synchronization manifold. We explore both time-dependent and time-independent coupling and discuss the use of periodic impulse coupling. We also examine both optimized and fixed (or manually adjusted) coupling. For the case of an optimized time-dependent coupling function u(t) we find a robust structure which includes sharp peaks and intervals where it is zero. This structure shows a strong correlation with the location in phase space and appears to depend on noise, imperfections of the model, and the Lyapunov direction vectors. For time-independent coupling we find the counterintuitive result that often the optimal rms error in fitting the model to the data initially increases with coupling strength. Comparison of this result with that obtained using simulated data may provide one measure of model imperfection. The constrained method with time-dependent coupling appears to have benefits in synchronizing long data sets with minimal impact, while the initial value method with time-independent coupling tends to be substantially faster, more flexible, and easier to use. We also describe a method of coupling which is useful for sparse experimental data sets. Our use of the Colpitts oscillator allows us to explore in detail the case of a system with one positive Lyapunov exponent. The methods we explored are easily
Power oscillation damping controller
DEFF Research Database (Denmark)
2012-01-01
A power oscillation damping controller is provided for a power generation device such as a wind turbine device. The power oscillation damping controller receives an oscillation indicating signal indicative of a power oscillation in an electricity network and provides an oscillation damping control...
International Nuclear Information System (INIS)
Akhiezer, A.I.; Davydov, L.N.; Spol'nik, Z.A.
1976-01-01
Oscillations of a nonideal crystal are studied, in which macroscopic defects (pores) form a hyperlattice. It is shown that alongside with acoustic and optical phonons (relative to the hyperlattice), in such a crystal oscillations of the third type are possible which are a hydridization of sound oscillations of atoms and surface oscillations of a pore. Oscillation spectra of all three types were obtained
Chaotic behaviour of photonic crystals resonators
Di Falco, A.; Liu, C.; Krauss, T. F.; Fratalocchi, Andrea
2015-01-01
We show here theoretically and experimentally how chaotic Photonic Crystal resonators can be used for en- ergy harvesting applications and the demonstration of fundamental theories, like the onset of superradiance in quantum systems. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Controlling chaotic systems via nonlinear feedback control
International Nuclear Information System (INIS)
Park, Ju H.
2005-01-01
In this article, a new method to control chaotic systems is proposed. Using Lyapunov method, we design a nonlinear feedback controller to make the controlled system be stabilized. A numerical example is given to illuminate the design procedure and advantage of the result derived
Economic dispatch using chaotic bat algorithm
International Nuclear Information System (INIS)
Adarsh, B.R.; Raghunathan, T.; Jayabarathi, T.; Yang, Xin-She
2016-01-01
This paper presents the application of a new metaheuristic optimization algorithm, the chaotic bat algorithm for solving the economic dispatch problem involving a number of equality and inequality constraints such as power balance, prohibited operating zones and ramp rate limits. Transmission losses and multiple fuel options are also considered for some problems. The chaotic bat algorithm, a variant of the basic bat algorithm, is obtained by incorporating chaotic sequences to enhance its performance. Five different example problems comprising 6, 13, 20, 40 and 160 generating units are solved to demonstrate the effectiveness of the algorithm. The algorithm requires little tuning by the user, and the results obtained show that it either outperforms or compares favorably with several existing techniques reported in literature. - Highlights: • The chaotic bat algorithm, a new metaheuristic optimization algorithm has been used. • The problem solved – the economic dispatch problem – is nonlinear, discontinuous. • It has number of equality and inequality constraints. • The algorithm has been demonstrated to be applicable on high dimensional problems.
Chaotic magnetic field line in toroidal plasmas
International Nuclear Information System (INIS)
Hatori, Tadatsugu; Abe, Yoshihiko; Urata, Kazuhiro; Irie, Haruyuki.
1989-05-01
This is an introductory review of chaotic magnetic field line in plasmas, together with some new results, with emphasis on the long-time tail and the fractional Brownian motion of the magnetic field line. The chaotic magnetic field line in toroidal plasmas is a typical chaotic phenomena in the Hamiltonian dynamical systems. The onset of stochasticity induced by a major magnetic perturbation is thought to cause a macroscopic rapid phenomena called the current disruption in the tokamak discharges. Numerical simulations on the basis of magnetohydrodynamics reveal in fact the disruptive phenomena. Some dynamical models which include the area-preserving mapping such as the standard mapping, and the two-wave Hamiltonian system can model the stochastic magnetic field. Theoretical results with use of the functional integral representation are given regarding the long-time tail on the basis of the radial twist mapping. It is shown that application of renormalization group technique to chaotic orbit in the two-wave Hamiltonian system proves decay of the velocity autocorrelation function with the power law. Some new numerical results are presented which supports these theoretical results. (author)
Analyzing and improving a chaotic encryption method
International Nuclear Information System (INIS)
Wu Xiaogang; Hu Hanping; Zhang Baoliang
2004-01-01
To resist the return map attack [Phys. Rev. Lett. 74 (1995) 1970] presented by Perez and Cerdeira, Shouliang Bu and Bing-Hong Wang proposed a simple method to improve the security of the chaotic encryption by modulating the chaotic carrier with an appropriately chosen scalar signal in [Chaos, Solitons and Fractals 19 (2004) 919]. They maintained that this modulating strategy not only preserved all appropriate information required for synchronizing chaotic systems but also destroyed the possibility of the phase space reconstruction of the sender dynamics such as a return map. However, a critical defect does exist in this scheme. This paper gives a zero-point autocorrelation method, which can recover the parameters of the scalar signal from the modulated signal. Consequently, the messages will be extracted from the demodulated chaotic carrier by using return map. Based on such a fact, an improved scheme is presented to obtain higher security, and the numerical simulation indicates the improvement of the synchronizing performance as well
Study of chaos in chaotic satellite systems
Indian Academy of Sciences (India)
Lyapunov exponents are estimated. From these studies, chaosin satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the ...
Entanglement production in quantized chaotic systems
Indian Academy of Sciences (India)
Abstract. Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical ...
Entanglement production in quantized chaotic systems
Indian Academy of Sciences (India)
Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies.
Cryptanalysis of a chaotic secure communication system
International Nuclear Information System (INIS)
Alvarez, G.; Montoya, F.; Romera, M.; Pastor, G.
2003-01-01
Recently a chaotic encryption system has been proposed by P. Garcia et al. It represents an improvement over an algorithm previously presented by some of the same authors. In this Letter, several weaknesses of the new cryptosystem are pointed out and four successful cryptanalytic attacks are described
Chaotic digital communication by encoding initial conditions.
Xiaofeng, Gong; Xingang, Wang; Meng, Zhan; Lai, C H
2004-06-01
We investigate the possibility to improve the noise performance of a chaotic digital communication scheme by utilizing further dynamical information. We show that by encoding the initial information of the chaotic carrier according to the transmitting bits, extra redundance can be introduced into the segments of chaotic signals corresponding to the consecutive bits. Such redundant information can be exploited effectively at the receiver end to improve the noise performance of the system. Compared to other methods (e.g., differential chaos shift keying), straightforward application of the proposed modulation/demodulation scheme already provides significant performance gain in the low signal-to-noise ratio (SNR) region. Furthermore, maximum likelihood precleaning procedure based on the Viterbi algorithm can be applied before the demodulation step to overcome the performance degradation in the high SNR region. The study indicates that it is possible to improve the noise performance of the chaotic digital communication scheme if further dynamics information is added to the system. (c) 2004 American Institute of Physics
Quantum Statistical Operator and Classically Chaotic Hamiltonian ...
African Journals Online (AJOL)
Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...
Chaotic behaviour of photonic crystals resonators
Di Falco, A.
2015-02-08
We show here theoretically and experimentally how chaotic Photonic Crystal resonators can be used for en- ergy harvesting applications and the demonstration of fundamental theories, like the onset of superradiance in quantum systems. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Linking Chaotic Advection with Subsurface Biogeochemical Processes
Mays, D. C.; Freedman, V. L.; White, S. K.; Fang, Y.; Neupauer, R.
2017-12-01
This work investigates the extent to which groundwater flow kinematics drive subsurface biogeochemical processes. In terms of groundwater flow kinematics, we consider chaotic advection, whose essential ingredient is stretching and folding of plumes. Chaotic advection is appealing within the context of groundwater remediation because it has been shown to optimize plume spreading in the laminar flows characteristic of aquifers. In terms of subsurface biogeochemical processes, we consider an existing model for microbially-mediated reduction of relatively mobile uranium(VI) to relatively immobile uranium(IV) following injection of acetate into a floodplain aquifer beneath a former uranium mill in Rifle, Colorado. This model has been implemented in the reactive transport code eSTOMP, the massively parallel version of STOMP (Subsurface Transport Over Multiple Phases). This presentation will report preliminary numerical simulations in which the hydraulic boundary conditions in the eSTOMP model are manipulated to simulate chaotic advection resulting from engineered injection and extraction of water through a manifold of wells surrounding the plume of injected acetate. This approach provides an avenue to simulate the impact of chaotic advection within the existing framework of the eSTOMP code.
Comment on two papers of chaotic synchronization
International Nuclear Information System (INIS)
Li Lixiang; Peng Haipeng; Wang Xiangdong; Yang Yixian
2004-01-01
This Letter comments on two papers of chaotic synchronization, namely [Phys. Rev. Lett. 76 (1996) 1232] and [Phys. Lett. A 321 (2004) 50]. We find that some statements in the two papers are incorrect by numerical simulations. The consequence of the incorrectness is analyzed as well
Adaptive projective synchronization between different chaotic ...
Indian Academy of Sciences (India)
Numerical simulation results are performed to explain the effectiveness and feasibility of ... analysis of nonlinear dynamics have gained immense popularity during the last few ... applications of projective synchronization is in secure communication [31] due to ... of uncertain chaotic systems using adaptive control method.
Review Article: Hazards of Chaotic Importation, Certification ...
African Journals Online (AJOL)
Review Article: Hazards of Chaotic Importation, Certification, Distribution and Marketing of Medical Laboratory Consumables in Nigeria. BC Nlemadim. Abstract. No abstract. Journal of Medical Laboratory Science Vol.12(2) 2003: 25 - 27. Full Text: EMAIL FULL TEXT EMAIL FULL TEXT · DOWNLOAD FULL TEXT ...
Chaos Noise on Phase of Van Der Pol Oscillator
Directory of Open Access Journals (Sweden)
Xian He Huang
2010-12-01
Full Text Available Phase noise is the most important parameter in many oscillators. In this paper, based on nonlinear stochastic differential equation for phase noise analysis approach is proposed. And then discusses and compares the influence of two different sources of noise in the Van Der Pol oscillator adopted this method. One source of noise is a white noise process, which is a genuinely stochastic process; the other source of noise is actually a deterministic system, which exhibits chaotic behavior in some regions. The behavior of the oscillator under different conditions is investigated numerically. It is shown that the phase noise of the oscillator is affected more by noise arising from chaos than by noise arising from the genuine stochastic process at the same noise intensity.
A new control strategy of SMES for mitigating subsynchronous oscillations
Energy Technology Data Exchange (ETDEWEB)
Farahani, Mohsen, E-mail: m.farahani@basu.ac.ir [Bu-Ali Sina University, Department of Electrical Engineering, Hamedan-Iran (Iran, Islamic Republic of)
2012-12-14
This paper proposes a new strategy to mitigate the subsynchronous oscillations in power systems compensated by series capacitors via control of active power of superconducting magnetic energy storage (SMES) unit. The strategy is based on the generator acceleration signal. So, the SMES absorbs or generates the energy imbalance caused by different disturbances in the power system and suppresses the subsynchronous oscillations. The chaotic optimization algorithm (COA) is used to achieve the optimal parameter of the proposed controller. To validate the capability of the SMES in damping oscillations, some simulations with different disturbances are performed on the first model of IEEE second benchmark model. All the simulation results show that the subsynchronous resonance as well as low frequency oscillation (LFO) is satisfactorily mitigated by the SMES controlled by the proposed strategy.
A new control strategy of SMES for mitigating subsynchronous oscillations
International Nuclear Information System (INIS)
Farahani, Mohsen
2012-01-01
This paper proposes a new strategy to mitigate the subsynchronous oscillations in power systems compensated by series capacitors via control of active power of superconducting magnetic energy storage (SMES) unit. The strategy is based on the generator acceleration signal. So, the SMES absorbs or generates the energy imbalance caused by different disturbances in the power system and suppresses the subsynchronous oscillations. The chaotic optimization algorithm (COA) is used to achieve the optimal parameter of the proposed controller. To validate the capability of the SMES in damping oscillations, some simulations with different disturbances are performed on the first model of IEEE second benchmark model. All the simulation results show that the subsynchronous resonance as well as low frequency oscillation (LFO) is satisfactorily mitigated by the SMES controlled by the proposed strategy.
New robust chaotic system with exponential quadratic term
International Nuclear Information System (INIS)
Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)
Building Chaotic Model From Incomplete Time Series
Siek, Michael; Solomatine, Dimitri
2010-05-01
This paper presents a number of novel techniques for building a predictive chaotic model from incomplete time series. A predictive chaotic model is built by reconstructing the time-delayed phase space from observed time series and the prediction is made by a global model or adaptive local models based on the dynamical neighbors found in the reconstructed phase space. In general, the building of any data-driven models depends on the completeness and quality of the data itself. However, the completeness of the data availability can not always be guaranteed since the measurement or data transmission is intermittently not working properly due to some reasons. We propose two main solutions dealing with incomplete time series: using imputing and non-imputing methods. For imputing methods, we utilized the interpolation methods (weighted sum of linear interpolations, Bayesian principle component analysis and cubic spline interpolation) and predictive models (neural network, kernel machine, chaotic model) for estimating the missing values. After imputing the missing values, the phase space reconstruction and chaotic model prediction are executed as a standard procedure. For non-imputing methods, we reconstructed the time-delayed phase space from observed time series with missing values. This reconstruction results in non-continuous trajectories. However, the local model prediction can still be made from the other dynamical neighbors reconstructed from non-missing values. We implemented and tested these methods to construct a chaotic model for predicting storm surges at Hoek van Holland as the entrance of Rotterdam Port. The hourly surge time series is available for duration of 1990-1996. For measuring the performance of the proposed methods, a synthetic time series with missing values generated by a particular random variable to the original (complete) time series is utilized. There exist two main performance measures used in this work: (1) error measures between the actual
Optimized chaotic Brillouin dynamic grating with filtered optical feedback.
Zhang, Jianzhong; Li, Zhuping; Wu, Yuan; Zhang, Mingjiang; Liu, Yi; Li, Mengwen
2018-01-16
Chaotic Brillouin dynamic gratings (BDGs) have special advantages such as the creation of single, permanent and localized BDG. However, the periodic signals induced by conventional optical feedback (COF) in chaotic semiconductor lasers can lead to the generation of spurious BDGs, which will limit the application of chaotic BDGs. In this paper, filtered optical feedback (FOF) is proposed to eliminate spurious BDGs. By controlling the spectral width of the optical filter and its detuning from the laser frequency, semiconductor lasers with FOF operate in the suppression region of the time-delay signature, and chaotic outputs serving as pump waves are then utilized to generate the chaotic BDG in a polarization maintaining fiber. Through comparative analysis of the COF and FOF schemes, it has been demonstrated that spurious BDGs are effectively eliminated and that the reflection characterization of the chaotic BDG is improved. The influence of FOF on the reflection and gain spectra of the chaotic BDG is analyzed as well.
International Nuclear Information System (INIS)
Peng Yafu
2009-01-01
In this paper, a robust intelligent sliding model control (RISMC) scheme using an adaptive recurrent cerebellar model articulation controller (RCMAC) is developed for a class of uncertain nonlinear chaotic systems. This RISMC system offers a design approach to drive the state trajectory to track a desired trajectory, and it is comprised of an adaptive RCMAC and a robust controller. The adaptive RCMAC is used to mimic an ideal sliding mode control (SMC) due to unknown system dynamics, and a robust controller is designed to recover the residual approximation error for guaranteeing the stable characteristic. Moreover, the Taylor linearization technique is employed to derive the linearized model of the RCMAC. The all adaptation laws of the RISMC system are derived based on the Lyapunov stability analysis and projection algorithm, so that the stability of the system can be guaranteed. Finally, the proposed RISMC system is applied to control a Van der Pol oscillator, a Genesio chaotic system and a Chua's chaotic circuit. The effectiveness of the proposed control scheme is verified by some simulation results with unknown system dynamics and existence of external disturbance. In addition, the advantages of the proposed RISMC are indicated in comparison with a SMC system
Nonlinear dynamics of drops and bubbles and chaotic phenomena
Trinh, Eugene H.; Leal, L. G.; Feng, Z. C.; Holt, R. G.
1994-01-01
Nonlinear phenomena associated with the dynamics of free drops and bubbles are investigated analytically, numerically and experimentally. Although newly developed levitation and measurement techniques have been implemented, the full experimental validation of theoretical predictions has been hindered by interfering artifacts associated with levitation in the Earth gravitational field. The low gravity environment of orbital space flight has been shown to provide a more quiescent environment which can be utilized to better match the idealized theoretical conditions. The research effort described in this paper is a closely coupled collaboration between predictive and guiding theoretical activities and a unique experimental program involving the ultrasonic and electrostatic levitation of single droplets and bubbles. The goal is to develop and to validate methods based on nonlinear dynamics for the understanding of the large amplitude oscillatory response of single drops and bubbles to both isotropic and asymmetric pressure stimuli. The first specific area on interest has been the resonant coupling between volume and shape oscillatory modes isolated gas or vapor bubbles in a liquid host. The result of multiple time-scale asymptotic treatment, combined with domain perturbation and bifurcation methods, has been the prediction of resonant and near-resonant coupling between volume and shape modes leading to stable as well as chaotic oscillations. Experimental investigations of the large amplitude shape oscillation modes of centimeter-size single bubbles trapped in water at 1 G and under reduced hydrostatic pressure, have suggested the possibility of a low gravity experiment to study the direct coupling between these low frequency shape modes and the volume pulsation, sound-radiating mode. The second subject of interest has involved numerical modeling, using the boundary integral method, of the large amplitude shape oscillations of charged and uncharged drops in the presence
Oscillators - a simple introduction
DEFF Research Database (Denmark)
Lindberg, Erik
2013-01-01
Oscillators are kernel components of electrical and electronic circuits. Discussion of history, mechanisms and design based on Barkhausens observation. Discussion of a Wien Bridge oscillator based on the question: Why does this circuit oscillate ?......Oscillators are kernel components of electrical and electronic circuits. Discussion of history, mechanisms and design based on Barkhausens observation. Discussion of a Wien Bridge oscillator based on the question: Why does this circuit oscillate ?...
DEFF Research Database (Denmark)
Lindberg, Erik
1997-01-01
In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear wit...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos....
DEFF Research Database (Denmark)
Stockmarr, Leila
2013-01-01
Vi bygger som besatte mure og barrierer for at holde flygtninge ude og tæmme de negative konsekvenser af den neoliberale globalisering.......Vi bygger som besatte mure og barrierer for at holde flygtninge ude og tæmme de negative konsekvenser af den neoliberale globalisering....
Chaotic behavior of a Watt-type predator-prey system with impulsive control strategy
International Nuclear Information System (INIS)
Wang, Xiaoqin; Wang Weiming; Lin Xiaolin
2008-01-01
In this paper, by using theories and methods of ecology and ODE, a predator-prey system with Watt-type functional response and impulsive perturbations on the predator is established. It proves that there exists a locally asymptotically stable prey-eradication periodic solution when the impulse period is less than some critical value, otherwise, the system can be permanent. Further, by using the method of computer simulation, the influences of the impulsive perturbations on the inherent oscillation are investigated, which shows the more complex dynamics of the system we considered, such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, period doubling bifurcation, symmetry-breaking pitchfork bifurcation, period-halving bifurcation and crisis, etc. It will be useful for studying the dynamical complexity of ecosystems
DEFF Research Database (Denmark)
Rasmussen, Rune; H. Jensen, Mogens; L. Heltberg, Mathias
2017-01-01
Previous studies have suggested that changes in extracellular ion concentrations initiate the transition from an activity state that characterizes sleep in cortical neurons to states that characterize wakeful- ness. However, because neuronal activity and extra- cellular ion concentrations...... are interdependent, isolating their unique roles during sleep-wake transitions is not possible in vivo. Here, we extend the Averaged-Neuron model and demonstrate that, although changes in extracellular ion concentrations occur concurrently, decreasing the conductance of calcium-dependent potassium channels initiates...... the transition from sleep to wakefulness. We find that sleep is governed by stable, self-sustained oscillations in neuronal firing patterns, whereas the quiet awake state and active awake state are both governed by irregular oscillations and chaotic dynamics; transitions between these separable awake states...
High power RF oscillator with Marx generators
International Nuclear Information System (INIS)
Murase, Hiroshi; Hayashi, Izumi
1980-01-01
A method to maintain RF oscillation by using many Marx generators was proposed and studied experimentally. Many charging circuits were connected to an oscillator circuit, and successive pulsed charging was made. This successive charging amplified and maintained the RF oscillation. The use of vacuum gaps and high power silicon diodes improved the characteristics of RF current cut-off of the circuit. The efficiency of the pulsed charging from Marx generators to a condenser was theoretically investigated. The theoretical result showed the maximum efficiency of 0.98. The practical efficiency obtained by using a proposed circuit with a high power oscillator was in the range 0.50 to 0.56. The obtained effective output power of the RF pulses was 11 MW. The maximum holding time of the RF pulses was about 21 microsecond. (Kato, T.)
Chaotic dynamics and diffusion in a piecewise linear equation
International Nuclear Information System (INIS)
Shahrear, Pabel; Glass, Leon; Edwards, Rod
2015-01-01
Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems
Chaotic dynamics and diffusion in a piecewise linear equation
Shahrear, Pabel; Glass, Leon; Edwards, Rod
2015-03-01
Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.
Chaotic motion in axially symmetric potentials with oblate quadrupole deformation
Energy Technology Data Exchange (ETDEWEB)
Letelier, Patricio S. [Departamento de Matematica Aplicada, IMECC, Universidade Estadual de Campinas, 13083-859, Campinas, SP (Brazil); Ramos-Caro, Javier, E-mail: javier@ime.unicamp.br [Departamento de Matematica Aplicada, IMECC, Universidade Estadual de Campinas, 13083-859, Campinas, SP (Brazil); Lopez-Suspes, Framsol, E-mail: framsol@gmail.com [Facultad de Telecomunicaciones, Universidad Santo Tomas and Escuela de Fisica, Universidad Industrial de Santander, Bucaramanga (Colombia)
2011-10-03
By computing the Poincare's surfaces of section and Lyapunov exponents, we study the effect of introducing an oblate quadrupole in the dynamics associated with two generic spherical potentials of physical interest: the central monopole and the isotropic harmonic oscillator. In the former case we find saddle points in the effective potential, in contrast to the statements presented by Gueron and Letelier in [E. Gueron, P.S. Letelier, Phys. Rev. E 63 (2001) 035201]. The results we show in the second case have application in nuclear or atomic physics. In particular, we find values of oblate deformation leading to a disappearance of shell structure in the single-particle spectrum. -- Highlights: → We find chaotic motion around a monopole with oblate quadrupole deformation. → This corrects the statements introduced in [E. Gueron, P.S. Letelier, Phys. Rev. E 63 (2001) 035201]. → We present an alternative model for the potential due to an oblate deformed nuclei. → This leads to stochastic regions in the phase space of classical orbits. → It suggests that the shell structure of single-particle spectrum tends to disappear.
Implementation of chaotic secure communication systems based on OPA circuits
International Nuclear Information System (INIS)
Huang, C.-K.; Tsay, S.-C.; Wu, Y.-R.
2005-01-01
In this paper, we proposed a novel three-order autonomous circuit to construct a chaotic circuit with double scroll characteristic. The design idea is to use RLC elements and a nonlinear resistor. The one of salient features of the chaotic circuit is that the circuit with two flexible breakpoints of nonlinear element, and the advantage of the flexible breakpoint is that it increased complexity of the dynamical performance. Here, if we take a large and suitable breakpoint value, then the chaotic state can masking a large input signal in the circuit. Furthermore, we proposed a secure communication hyperchaotic system based on the proposed chaotic circuits, where the chaotic communication system is constituted by a chaotic transmitter and a chaotic receiver. To achieve the synchronization between the transmitter and the receiver, we are using a suitable Lyapunov function and Lyapunov theorem to design the feedback control gain. Thus, the transmitting message masked by chaotic state in the transmitter can be guaranteed to perfectly recover in the receiver. To achieve the systems performance, some basic components containing OPA, resistor and capacitor elements are used to implement the proposed communication scheme. From the viewpoints of circuit implementation, this proposed chaotic circuit is superior to the Chua chaotic circuits. Finally, the test results containing simulation and the circuit measurement are shown to demonstrate that the proposed method is correct and feasible
International Nuclear Information System (INIS)
Perez Polo, Manuel F.; Perez Molina, Manuel; Gil Chica, Javier
2009-01-01
This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing's oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.
Energy Technology Data Exchange (ETDEWEB)
Perez Polo, Manuel F. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)], E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia. UNED, C/Boyero 12-1A, Alicante 03007 (Spain)], E-mail: ma_perez_m@hotmail.com; Gil Chica, Javier [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)], E-mail: gil@dfists.ua.es
2009-02-15
This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing's oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.
Chaotic coordinates for the Large Helical Device
Energy Technology Data Exchange (ETDEWEB)
Hudson, S. R., E-mail: shudson@pppl.gov [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543 (United States); Suzuki, Y. [National Institute for Natural Sciences, National Institute for Fusion Sciences, 322-6 Oroshi, Toki, 509-5292 (Japan)
2014-10-15
The theory of quadratic-flux-minimizing (QFM) surfaces is reviewed, and numerical techniques that allow high-order QFM surfaces to be efficiently constructed for experimentally relevant, non-integrable magnetic fields are described. As a practical example, the chaotic edge of the magnetic field in the Large Helical Device (LHD) is examined. A precise technique for finding the boundary surface is implemented, the hierarchy of partial barriers associated with the near-critical cantori is constructed, and a coordinate system, which we call chaotic coordinates, that is based on a selection of QFM surfaces is constructed that simplifies the description of the magnetic field, so that flux surfaces become “straight” and islands become “square.”.
Communicating via robust synchronization of chaotic lasers
International Nuclear Information System (INIS)
Lopez-Gutierrez, R.M.; Posadas-Castillo, C.; Lopez-Mancilla, D.; Cruz-Hernandez, C.
2009-01-01
In this paper, the robust synchronization problem for coupled chaotic Nd:YAG lasers is addressed. We resort to complex systems theory to achieve chaos synchronization. Based on stability theory, it is shown that the state trajectories of the perturbed error synchronization are ultimately bounded, provided the unperturbed synchronization error system is exponentially stable, and some conditions on the bounds of the perturbation terms are satisfied. So that, encoding, transmission, and decoding in chaotic optical communications are presented. We analyze the transmission and recovery of encrypted information when parameter mismatches are considered. Computer simulations are provided to show the effectiveness of this robustness synchronization property, we present the encrypted transmission of image messages, and we show that, the transmitted image is faithfully recovered.
Communicating via robust synchronization of chaotic lasers
Energy Technology Data Exchange (ETDEWEB)
Lopez-Gutierrez, R.M. [Engineering Faculty, Baja California Autonomous University (UABC), Km. 103 Carret. Tij-Ens., 22860 Ensenada, B.C. (Mexico); Posadas-Castillo, C. [Engineering Faculty, Baja California Autonomous University (UABC), Km. 103 Carret. Tij-Ens., 22860 Ensenada, B.C. (Mexico); FIME, Autonomous University of Nuevo Leon (UANL), Pedro de Alba, S.N., Cd. Universitaria, San Nicolas de los Garza, NL (Mexico); Lopez-Mancilla, D. [Departamento de Ciencias Exactas y Tecnologicas, Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG), Enrique Diaz de Leon s/n, 47460 Lagos de Moreno, Jal. (Mexico); Cruz-Hernandez, C. [Electronics and Telecommunications Department, Scientific Research and Advanced Studies of Ensenada (CICESE), Km. 107 Carret. Tij-Ens., 22860 Ensenada, B.C. (Mexico)], E-mail: ccruz@cicese.mx
2009-10-15
In this paper, the robust synchronization problem for coupled chaotic Nd:YAG lasers is addressed. We resort to complex systems theory to achieve chaos synchronization. Based on stability theory, it is shown that the state trajectories of the perturbed error synchronization are ultimately bounded, provided the unperturbed synchronization error system is exponentially stable, and some conditions on the bounds of the perturbation terms are satisfied. So that, encoding, transmission, and decoding in chaotic optical communications are presented. We analyze the transmission and recovery of encrypted information when parameter mismatches are considered. Computer simulations are provided to show the effectiveness of this robustness synchronization property, we present the encrypted transmission of image messages, and we show that, the transmitted image is faithfully recovered.
Cryptanalysis of a spatiotemporal chaotic cryptosystem
International Nuclear Information System (INIS)
Rhouma, Rhouma; Belghith, Safya
2009-01-01
This paper proposes three different attacks on a recently proposed chaotic cryptosystem in [Li P, Li Z, Halang WA, Chen G. A stream cipher based on a spatiotemporal chaotic system. Chaos, Solitons and Fractals 2007;32:1867-76]. The cryptosystem under study displays weakness in the generation of the keystream. The encryption is made by generating a keystream mixed with blocks generated from the plaintext. The so obtained keystream remains unchanged for every encryption procedure. Moreover, its generation does neither depend on the plaintext nor on the ciphertext, that's to say, the keystream remains unchangeable for every plaintext with the same length. Guessing the keystream leads to guessing the key. This paper presents three possible attacks able to break the whole cryptosystem based on this drawback in generating the keystream.
Enhanced energy storage in chaotic optical resonators
Liu, Changxu; Di Falco, Andrea; Molinari, Diego P.; Khan, Yasser; Ooi, Boon S.; Krauss, Thomas F.; Fratalocchi, Andrea
2013-01-01
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability, which makes it difficult to predict or explain experimental results. Conversely, we demonstrate here how chaos can be used to enhance the ability of an optical resonator to store energy. We combine analytic theory with ab initio simulations and experiments in photonic-crystal resonators to show that a chaotic resonator can store six times more energy than its classical counterpart of the same volume. We explain the observed increase by considering the equipartition of energy among all degrees of freedom of the chaotic resonator (that is, the cavity modes) and discover a convergence of their lifetimes towards a single value. A compelling illustration of the theory is provided by enhanced absorption in deformed polystyrene microspheres. © 2013 Macmillan Publishers Limited. All rights reserved.
Exact solutions to chaotic and stochastic systems
González, J. A.; Reyes, L. I.; Guerrero, L. E.
2001-03-01
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.
International Nuclear Information System (INIS)
Theiler, J.; Eubank, S.
1993-01-01
A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ''bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed
Enhanced energy storage in chaotic optical resonators
Liu, Changxu
2013-05-05
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability, which makes it difficult to predict or explain experimental results. Conversely, we demonstrate here how chaos can be used to enhance the ability of an optical resonator to store energy. We combine analytic theory with ab initio simulations and experiments in photonic-crystal resonators to show that a chaotic resonator can store six times more energy than its classical counterpart of the same volume. We explain the observed increase by considering the equipartition of energy among all degrees of freedom of the chaotic resonator (that is, the cavity modes) and discover a convergence of their lifetimes towards a single value. A compelling illustration of the theory is provided by enhanced absorption in deformed polystyrene microspheres. © 2013 Macmillan Publishers Limited. All rights reserved.
Bearing Health Assessment Based on Chaotic Characteristics
Directory of Open Access Journals (Sweden)
Chen Lu
2013-01-01
Full Text Available Vibration signals extracted from rotating parts of machinery carry a lot of useful information about the condition of operating machine. Due to the strong non-linear, complex and non-stationary characteristics of vibration signals from working bearings, an accurate and reliable health assessment method for bearing is necessary. This paper proposes to utilize the selected chaotic characteristics of vibration signal for health assessment of a bearing by using self-organizing map (SOM. Both Grassberger-Procaccia algorithm and Takens' theory are employed to calculate the characteristic vector which includes three chaotic characteristics, such as correlation dimension, largest Lyapunov exponent and Kolmogorov entropy. After that, SOM is used to map the three corresponding characteristics into a confidence value (CV which represents the health state of the bearing. Finally, a case study based on vibration datasets of a group of testing bearings was conducted to demonstrate that the proposed method can reliably assess the health state of bearing.
Control of hyper-chaotic system
International Nuclear Information System (INIS)
Yin Xunhe; Feng Rupeng
2000-01-01
The approach based on the exact linearization via feedback is used for controlling Roessler hyper-chaos. A controller for hyper-chaos Roessler is designed by using the approach. The method is used to realize global stabilization and to control hyper-chaotic motion not only to any unstable equilibrium point but also to any desired periodic orbit. Simulation results presented here prove the feasibility of the method, and its robustness is analyzed numerically
Collectivity and chaoticity in nuclear dynamics
International Nuclear Information System (INIS)
Zelevinsky, V.G.
1992-01-01
Collective and chaotic features of nuclear dynamics are discussed using simple criteria of complexity of wave functions and their coherence with respect to specific operators. Various physical phenomena are considered in this connection: - coherent interaction of collective modes; - fragmentation and spreading widths; - mixing of compound states and dynamical enhancement; - mean field as a smooth component of complicated dynamics; - coupling through continuum and collectivization of widths; - structure of giant resonances; - statistical properties of unstable states as generalization of canonical random matrix ensembles. (orig.)
Extraction of dynamical equations from chaotic data
International Nuclear Information System (INIS)
Rowlands, G.; Sprott, J.C.
1991-02-01
A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs
Chaos control of Chen chaotic dynamical system
International Nuclear Information System (INIS)
Yassen, M.T.
2003-01-01
This paper is devoted to study the problem of controlling chaos in Chen chaotic dynamical system. Two different methods of control, feedback and nonfeedback methods are used to suppress chaos to unstable equilibria or unstable periodic orbits (UPO). The Lyapunov direct method and Routh-Hurwitz criteria are used to study the conditions of the asymptotic stability of the steady states of the controlled system. Numerical simulations are presented to show these results
Cryptanalysis of an ergodic chaotic cipher
International Nuclear Information System (INIS)
Alvarez, G.; Montoya, F.; Romera, M.; Pastor, G.
2003-01-01
In recent years, a growing number of cryptosystems based on chaos have been proposed, many of them fundamentally flawed by a lack of robustness and security. In this Letter, we offer our results after having studied the security and possible attacks on a very interesting cipher algorithm based on the logistic map's ergodicity property. This algorithm has become very popular recently, as it has been taken as the development basis of new chaotic cryptosystems
Chaotic inflation with metric and matter perturbations
International Nuclear Information System (INIS)
Feldman, H.A.; Brandenberger, R.H.
1989-01-01
A perturbative scheme to analyze the evolution of both metric and scalar field perturbations in an expanding universe is developed. The scheme is applied to study chaotic inflation with initial metric and scalar field perturbations present. It is shown that initial gravitational perturbations with wavelength smaller than the Hubble radius rapidly decay. The metric simultaneously picks up small perturbations determined by the matter inhomogeneities. Both are frozen in once the wavelength exceeds the Hubble radius. (orig.)
A nonlinear optimal control approach for chaotic finance dynamics
Rigatos, G.; Siano, P.; Loia, V.; Tommasetti, A.; Troisi, O.
2017-11-01
A new nonlinear optimal control approach is proposed for stabilization of the dynamics of a chaotic finance model. The dynamic model of the financial system, which expresses interaction between the interest rate, the investment demand, the price exponent and the profit margin, undergoes approximate linearization round local operating points. These local equilibria are defined at each iteration of the control algorithm and consist of the present value of the systems state vector and the last value of the control inputs vector that was exerted on it. The approximate linearization makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. The truncation of higher order terms in the Taylor series expansion is considered to be a modelling error that is compensated by the robustness of the control loop. As the control algorithm runs, the temporary equilibrium is shifted towards the reference trajectory and finally converges to it. The control method needs to compute an H-infinity feedback control law at each iteration, and requires the repetitive solution of an algebraic Riccati equation. Through Lyapunov stability analysis it is shown that an H-infinity tracking performance criterion holds for the control loop. This implies elevated robustness against model approximations and external perturbations. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven.
Characterizing the chaotic nature of ocean ventilation
MacGilchrist, Graeme A.; Marshall, David P.; Johnson, Helen L.; Lique, Camille; Thomas, Matthew
2017-09-01
Ventilation of the upper ocean plays an important role in climate variability on interannual to decadal timescales by influencing the exchange of heat and carbon dioxide between the atmosphere and ocean. The turbulent nature of ocean circulation, manifest in a vigorous mesoscale eddy field, means that pathways of ventilation, once thought to be quasi-laminar, are in fact highly chaotic. We characterize the chaotic nature of ventilation pathways according to a nondimensional "filamentation number," which estimates the reduction in filament width of a ventilated fluid parcel due to mesoscale strain. In the subtropical North Atlantic of an eddy-permitting ocean model, the filamentation number is large everywhere across three upper ocean density surfaces—implying highly chaotic ventilation pathways—and increases with depth. By mapping surface ocean properties onto these density surfaces, we directly resolve the highly filamented structure and confirm that the filamentation number captures its spatial variability. These results have implications for the spreading of atmospherically-derived tracers into the ocean interior.
Transient chaotic transport in dissipative drift motion
Energy Technology Data Exchange (ETDEWEB)
Oyarzabal, R.S. [Pós-Graduação em Ciências/Física, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR (Brazil); Szezech, J.D. [Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR (Brazil); Batista, A.M., E-mail: antoniomarcosbatista@gmail.com [Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR (Brazil); Souza, S.L.T. de [Departamento de Física e Matemática, Universidade Federal de São João del Rei, 36420-000, Ouro Branco, MG (Brazil); Caldas, I.L. [Instituto de Física, Universidade de São Paulo, 05315-970, São Paulo, SP (Brazil); Viana, R.L. [Departamento de Física, Universidade Federal do Paraná, 81531-990, Curitiba, PR (Brazil); Sanjuán, M.A.F. [Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid (Spain)
2016-04-22
Highlights: • We consider a situation for which a chaotic transient is present in the dynamics of the two-wave model with damping. • The damping in plasma models can be a way for study a realistic behavior of confinement due the collisional effect. • The escape time as a function of the damping obey a power-law scaling. • We have made a qualitative transport analysis with a simple model that can be useful for more complete models. • We have shown that the pattern of the basin of attraction depends on the damping parameter. - Abstract: We investigate chaotic particle transport in magnetised plasmas with two electrostatic drift waves. Considering dissipation in the drift motion, we verify that the removed KAM surfaces originate periodic attractors with their corresponding basins of attraction. We show that the properties of the basins depend on the dissipation and the space-averaged escape time decays exponentially when the dissipation increases. We find positive finite time Lyapunov exponents in dissipative drift motion, consequently the trajectories exhibit transient chaotic transport. These features indicate how the transient plasma transport depends on the dissipation.
Banknote authentication using chaotic elements technology
Ambadiyil, Sajan; P. S., Krishnendu; Mahadevan Pillai, V. P.; Prabhu, Radhakrishna
2017-10-01
The counterfeit banknote is a growing threat to the society since the advancements in the field of computers, scanners and photocopiers, as they have made the duplication process for banknote much simpler. The fake note detection systems developed so far have many drawbacks such as high cost, poor accuracy, unavailability, lack of user-friendliness and lower effectiveness. One possible solution to this problem could be the use of a system uniquely linked to the banknote itself. In this paper, we present a unique identification and authentication process for the banknote using chaotic elements embedded in it. A chaotic element means that the physical elements are formed from a random process independent from human intervention. The chaotic elements used in this paper are the random distribution patterns of such security fibres set into the paper pulp. A unique ID is generated from the fibre pattern obtained from UV image of the note, which can be verified by any person who receives the banknote to decide whether the banknote is authentic or not. Performance analysis of the system is also studied in this paper.
Wave dynamics of regular and chaotic rays
International Nuclear Information System (INIS)
McDonald, S.W.
1983-09-01
In order to investigate general relationships between waves and rays in chaotic systems, I study the eigenfunctions and spectrum of a simple model, the two-dimensional Helmholtz equation in a stadium boundary, for which the rays are ergodic. Statistical measurements are performed so that the apparent randomness of the stadium modes can be quantitatively contrasted with the familiar regularities observed for the modes in a circular boundary (with integrable rays). The local spatial autocorrelation of the eigenfunctions is constructed in order to indirectly test theoretical predictions for the nature of the Wigner distribution corresponding to chaotic waves. A portion of the large-eigenvalue spectrum is computed and reported in an appendix; the probability distribution of successive level spacings is analyzed and compared with theoretical predictions. The two principal conclusions are: 1) waves associated with chaotic rays may exhibit randomly situated localized regions of high intensity; 2) the Wigner function for these waves may depart significantly from being uniformly distributed over the surface of constant frequency in the ray phase space
Chaotic Fluid Mixing in Crystalline Sphere Arrays
Turuban, Regis; Lester, Daniel; Meheust, Yves; Le Borgne, Tanguy
2017-11-01
We study the Lagrangian dynamics of steady 3D Stokes flow over simple cubic (SC) and body-centered cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media (e.g. open pore networks), with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices share the same symmetry point group, these differences are explained in terms of their space groups, and we find that a glide symmetry of the BCC lattice generates chaotic mixing. These insights are used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation, and point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures. The authors acknowledge the support of ERC project ReactiveFronts (648377).
Chaotic spectra: How to extract dynamic information
International Nuclear Information System (INIS)
Taylor, H.S.; Gomez Llorente, J.M.; Zakrzewski, J.; Kulander, K.C.
1988-10-01
Nonlinear dynamics is applied to chaotic unassignable atomic and molecular spectra with the aim of extracting detailed information about regular dynamic motions that exist over short intervals of time. It is shown how this motion can be extracted from high resolution spectra by doing low resolution studies or by Fourier transforming limited regions of the spectrum. These motions mimic those of periodic orbits (PO) and are inserts into the dominant chaotic motion. Considering these inserts and the PO as a dynamically decoupled region of space, resonant scattering theory and stabilization methods enable us to compute ladders of resonant states which interact with the chaotic quasi-continuum computed in principle from basis sets placed off the PO. The interaction of the resonances with the quasicontinuum explains the low resolution spectra seen in such experiments. It also allows one to associate low resolution features with a particular PO. The motion on the PO thereby supplies the molecular movements whose quantization causes the low resolution spectra. Characteristic properties of the periodic orbit based resonances are discussed. The method is illustrated on the photoabsorption spectrum of the hydrogen atom in a strong magnetic field and on the photodissociation spectrum of H 3 + . Other molecular systems which are currently under investigation using this formalism are also mentioned. 53 refs., 10 figs., 2 tabs
Chaotic Fluid Mixing in Crystalline Sphere Arrays
Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.
2017-12-01
We study the Lagrangian dynamics of steady 3D Stokes flow over simple cubic (SC) and body-centered cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media (e.g. open pore networks), with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices share the same symmetry point group, these differences are explained in terms of their space groups, and we find that a glide symmetry of the BCC lattice generates chaotic mixing. These insight are used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation, and point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures.
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)
Temperature oscillations in methanol partial oxidation reactor for the production of hydrogen
Energy Technology Data Exchange (ETDEWEB)
Kim, Jinsu; Byeon, Jeonguk; Seo, Il Gyu; Lee, Hyun Chan; Kim, Dong Hyun; Lee, Jietae [Kyungpook National University, Daegu (Korea, Republic of)
2013-04-15
Methanol partial oxidation (POX) is a well-known reforming reaction for the production of hydrogen from methanol. Since POX is relatively fast and highly exothermic, this reforming method will be efficient for the fast start-up and load-following operation. However, POX generates hot spots around catalyst and even oscillations in the reactor temperature. These should be relieved for longer operations of the reactor without catalyst degradations. For this, temperature oscillations in a POX reactor are investigated experimentally. Various patterns of temperature oscillations according to feed flow rates of reactants and reactor temperatures are obtained. The bifurcation phenomena from regular oscillations to chaotic oscillations are found as the methanol flow rate increases. These experimental results can be used for theoretical analyses of oscillations and for designing safe reforming reactors.
Temperature oscillations in methanol partial oxidation reactor for the production of hydrogen
International Nuclear Information System (INIS)
Kim, Jinsu; Byeon, Jeonguk; Seo, Il Gyu; Lee, Hyun Chan; Kim, Dong Hyun; Lee, Jietae
2013-01-01
Methanol partial oxidation (POX) is a well-known reforming reaction for the production of hydrogen from methanol. Since POX is relatively fast and highly exothermic, this reforming method will be efficient for the fast start-up and load-following operation. However, POX generates hot spots around catalyst and even oscillations in the reactor temperature. These should be relieved for longer operations of the reactor without catalyst degradations. For this, temperature oscillations in a POX reactor are investigated experimentally. Various patterns of temperature oscillations according to feed flow rates of reactants and reactor temperatures are obtained. The bifurcation phenomena from regular oscillations to chaotic oscillations are found as the methanol flow rate increases. These experimental results can be used for theoretical analyses of oscillations and for designing safe reforming reactors
A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps
International Nuclear Information System (INIS)
Behnia, S.; Akhshani, A.; Ahadpour, S.; Mahmodi, H.; Akhavan, A.
2007-01-01
In recent years, a growing number of discrete chaotic cryptographic algorithms have been proposed. However, most of them encounter some problems such as the lack of robustness and security. In this Letter, we introduce a new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps. The system is a measurable dynamical system with an interesting property of being either ergodic or having stable period-one fixed point. They bifurcate from a stable single periodic state to chaotic one and vice versa without having usual period-doubling or period-n-tippling scenario. Also, we present the KS-entropy of this maps with respect to control parameter. This algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security
Normal form and synchronization of strict-feedback chaotic systems
International Nuclear Information System (INIS)
Wang, Feng; Chen, Shihua; Yu Minghai; Wang Changping
2004-01-01
This study concerns the normal form and synchronization of strict-feedback chaotic systems. We prove that, any strict-feedback chaotic system can be rendered into a normal form with a invertible transform and then a design procedure to synchronize the normal form of a non-autonomous strict-feedback chaotic system is presented. This approach needs only a scalar driving signal to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, the Roessler chaotic system is taken as a concrete example to illustrate the procedure of designing without transforming a strict-feedback chaotic system into its normal form. Numerical simulations are also provided to show the effectiveness and feasibility of the developed methods
Video encryption using chaotic masks in joint transform correlator
Saini, Nirmala; Sinha, Aloka
2015-03-01
A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest-Shamir-Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique.
Video encryption using chaotic masks in joint transform correlator
International Nuclear Information System (INIS)
Saini, Nirmala; Sinha, Aloka
2015-01-01
A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest–Shamir–Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique. (paper)
Hash function based on piecewise nonlinear chaotic map
International Nuclear Information System (INIS)
Akhavan, A.; Samsudin, A.; Akhshani, A.
2009-01-01
Chaos-based cryptography appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an algorithm for one-way hash function construction based on piecewise nonlinear chaotic map with a variant probability parameter is proposed. Also the proposed algorithm is an attempt to present a new chaotic hash function based on multithreaded programming. In this chaotic scheme, the message is connected to the chaotic map using probability parameter and other parameters of chaotic map such as control parameter and initial condition, so that the generated hash value is highly sensitive to the message. Simulation results indicate that the proposed algorithm presented several interesting features, such as high flexibility, good statistical properties, high key sensitivity and message sensitivity. These properties make the scheme a suitable choice for practical applications.
Fractional order control and synchronization of chaotic systems
Vaidyanathan, Sundarapandian; Ouannas, Adel
2017-01-01
The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional contro...
Anti-synchronization between different chaotic complex systems
International Nuclear Information System (INIS)
Liu Ping; Liu Shutang
2011-01-01
Many studies on the anti-synchronization of nonlinear real dynamic systems have been carried out, whereas the anti-synchronization of chaotic complex systems has not been studied extensively. In this work, the anti-synchronization between a new chaotic complex system and a complex Lorenz system and that between a new chaotic complex system and a complex Lue system were separately investigated by active control and nonlinear control methods, and explicit expressions were derived for the controllers that are used to achieve the anti-synchronization of chaotic complex systems. These expressions were tested numerically and excellent agreement was found. Concerning the new chaotic complex system, we discuss its dynamical properties including dissipation, chaotic behavior, fixed points, and their stability and invariance.
Blue breath holding is benign.
Stephenson, J B
1991-01-01
In their recent publication in this journal, Southall et al described typical cyanotic breath holding spells, both in otherwise healthy children and in those with brainstem lesions and other malformations. Their suggestions regarding possible autonomic disturbances may require further study, but they have adduced no scientific evidence to contradict the accepted view that in the intact child blue breath holding spells are benign. Those families in which an infant suffers an 'apparently life t...
Parameter-Independent Dynamical Behaviors in Memristor-Based Wien-Bridge Oscillator
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Ning Wang
2017-01-01
Full Text Available This paper presents a novel memristor-based Wien-bridge oscillator and investigates its parameter-independent dynamical behaviors. The newly proposed memristive chaotic oscillator is constructed by linearly coupling a nonlinear active filter composed of memristor and capacitor to a Wien-bridge oscillator. For a set of circuit parameters, phase portraits of a double-scroll chaotic attractor are obtained by numerical simulations and then validated by hardware experiments. With a dimensionless system model and the determined system parameters, the initial condition-dependent dynamical behaviors are explored through bifurcation diagrams, Lyapunov exponents, and phase portraits, upon which the coexisting infinitely many attractors and transient chaos related to initial conditions are perfectly offered. These results are well verified by PSIM circuit simulations.
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
Research on dynamic characteristics of new chaotic-advection fins
International Nuclear Information System (INIS)
Kong Songtao; Dong Qiwu; Liu Minshan; Zhu Qing
2007-01-01
Analysis and the numerical simulation has confirmed that the flow is of the chaotic advection in the flow channel of the new fin. The chaotic advection results in stronger mixing under low Re, and thus enhances the heat transfer and anti-scaling ability. The new fin provides the beneficial exploration to the concept of chaotic advection which applies to the plate-fin heat exchanger. (authors)
A novel block cryptosystem based on iterating a chaotic map
International Nuclear Information System (INIS)
Xiang Tao; Liao Xiaofeng; Tang Guoping; Chen Yong; Wong, Kwok-wo
2006-01-01
A block cryptographic scheme based on iterating a chaotic map is proposed. With random binary sequences generated from the real-valued chaotic map, the plaintext block is permuted by a key-dependent shift approach and then encrypted by the classical chaotic masking technique. Simulation results show that performance and security of the proposed cryptographic scheme are better than those of existing algorithms. Advantages and security of our scheme are also discussed in detail
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.
Empirically characteristic analysis of chaotic PID controlling particle swarm optimization
Yan, Danping; Lu, Yongzhong; Zhou, Min; Chen, Shiping; Levy, David
2017-01-01
Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles’ search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles’ premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO. PMID:28472050
Empirically characteristic analysis of chaotic PID controlling particle swarm optimization.
Directory of Open Access Journals (Sweden)
Danping Yan
Full Text Available Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO, we herein propose a chaotic proportional integral derivative (PID controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles' search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles' premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA and PSO.
A combination chaotic system and application in color image encryption
Parvaz, R.; Zarebnia, M.
2018-05-01
In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based on new chaotic system. Also this encryption algorithm can be used for gray scale or binary images. The experimental results of the encryption algorithm show that the encryption algorithm is secure and practical.
Chaos synchronization of a unified chaotic system via partial linearization
International Nuclear Information System (INIS)
Yu Yongguang; Li Hanxiong; Duan Jian
2009-01-01
A partial linearization method is proposed for realizing the chaos synchronization of an unified chaotic system. Through synchronizing partial state of the chaotic systems can result in the synchronization of their entire states, and the resulting controller is singularity free. The results can be easily extended to the synchronization of other similar chaotic systems. Simulation results are conducted to show the effectiveness of the method.
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.
On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization
International Nuclear Information System (INIS)
Lu Zhao; Shieh Leangsan; Chen GuanRong
2003-01-01
This paper presents a novel Lyapunov-based control approach which utilizes a Lyapunov function of the nominal plant for robust tracking control of general multi-input uncertain nonlinear systems. The difficulty of constructing a control Lyapunov function is alleviated by means of predefining an optimal sliding mode. The conventional schemes for constructing sliding modes of nonlinear systems stipulate that the system of interest is canonical-transformable or feedback-linearizable. An innovative approach that exploits a chaotic optimizing algorithm is developed thereby obtaining the optimal sliding manifold for the control purpose. Simulations on the uncertain chaotic Chen's system illustrate the effectiveness of the proposed approach
On periodic and chaotic regions in the Mandelbrot set
International Nuclear Information System (INIS)
Pastor, G.; Romera, M.; Alvarez, G.; Arroyo, D.; Montoya, F.
2007-01-01
We show here in a graphic and simple way the relation between the periodic and chaotic regions in the Mandelbrot set. Since the relation between the periodic and chaotic regions in a one-dimensional (1D) quadratic set is already well known, we shall base on it to extend the results to the Mandelbrot set. We shall see that in the same way as the hyperbolic components of the period-doubling cascade determines the chaotic bands structure in 1D quadratic sets, the periodic region determines the chaotic region in the Mandelbrot set
Closed-loop suppression of chaos in nonlinear driven oscillators
Aguirre, L. A.; Billings, S. A.
1995-05-01
This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.
Coexisting chaotic attractors in a single neuron model with adapting feedback synapse
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong
2005-01-01
In this paper, we consider the nonlinear dynamical behavior of a single neuron model with adapting feedback synapse, and show that chaotic behaviors exist in this model. In some parameter domain, we observe two coexisting chaotic attractors, switching from the coexisting chaotic attractors to a connected chaotic attractor, and then switching back to the two coexisting chaotic attractors. We confirm the chaoticity by simulations with phase plots, waveform plots, and power spectra
Different types of bursting calcium oscillations in non-excitable cells
International Nuclear Information System (INIS)
Perc, Matjaz; Marhl, Marko
2003-01-01
In the paper different types of bursting Ca 2+ oscillations are presented. We analyse bursting behaviour in four recent mathematical models for Ca 2+ oscillations in non-excitable cells. Separately, regular, quasi-periodic, and chaotic bursting Ca 2+ oscillations are classified into several subtypes. The classification is based on the dynamics of separated fast and slow subsystems, the so-called fast-slow burster analysis. For regular bursting Ca 2+ oscillations two types of bursting are specified: Point-Point and Point-Cycle bursting. In particular, the slow passage effect, important for the Hopf-Hopf and SubHopf-SubHopf bursting subtypes, is explained by local divergence calculated for the fast subsystem. Quasi-periodic bursting Ca 2+ oscillations can be found in only one of the four studied mathematical models and appear via a homoclinic bifurcation with a homoclinic torus structure. For chaotic bursting Ca 2+ oscillations, we found that bursting patterns resulting from the period doubling root to chaos considerably differ from those appearing via intermittency and have to be treated separately. The analysis and classification of different types of bursting Ca 2+ oscillations provides better insight into mechanisms of complex intra- and intercellular Ca 2+ signalling. This improves our understanding of several important biological phenomena in cellular signalling like complex frequency-amplitude signal encoding and synchronisation of intercellular signal transduction between coupled cells in tissue
Symmetric encryption algorithms using chaotic and non-chaotic generators: A review.
Radwan, Ahmed G; AbdElHaleem, Sherif H; Abd-El-Hafiz, Salwa K
2016-03-01
This paper summarizes the symmetric image encryption results of 27 different algorithms, which include substitution-only, permutation-only or both phases. The cores of these algorithms are based on several discrete chaotic maps (Arnold's cat map and a combination of three generalized maps), one continuous chaotic system (Lorenz) and two non-chaotic generators (fractals and chess-based algorithms). Each algorithm has been analyzed by the correlation coefficients between pixels (horizontal, vertical and diagonal), differential attack measures, Mean Square Error (MSE), entropy, sensitivity analyses and the 15 standard tests of the National Institute of Standards and Technology (NIST) SP-800-22 statistical suite. The analyzed algorithms include a set of new image encryption algorithms based on non-chaotic generators, either using substitution only (using fractals) and permutation only (chess-based) or both. Moreover, two different permutation scenarios are presented where the permutation-phase has or does not have a relationship with the input image through an ON/OFF switch. Different encryption-key lengths and complexities are provided from short to long key to persist brute-force attacks. In addition, sensitivities of those different techniques to a one bit change in the input parameters of the substitution key as well as the permutation key are assessed. Finally, a comparative discussion of this work versus many recent research with respect to the used generators, type of encryption, and analyses is presented to highlight the strengths and added contribution of this paper.
Transition from amplitude to oscillation death in a network of oscillators
International Nuclear Information System (INIS)
Nandan, Mauparna; Hens, C. R.; Dana, Syamal K.; Pal, Pinaki
2014-01-01
We report a transition from a homogeneous steady state (HSS) to inhomogeneous steady states (IHSSs) in a network of globally coupled identical oscillators. We perturb a synchronized population of oscillators in the network with a few local negative or repulsive mean field links. The whole population splits into two clusters for a certain number of repulsive mean field links and a range of coupling strength. For further increase of the strength of interaction, these clusters collapse into a HSS followed by a transition to IHSSs where all the oscillators populate either of the two stable steady states. We analytically determine the origin of HSS and its transition to IHSS in relation to the number of repulsive mean-field links and the strength of interaction using a reductionism approach to the model network. We verify the results with numerical examples of the paradigmatic Landau-Stuart limit cycle system and the chaotic Rössler oscillator as dynamical nodes. During the transition from HSS to IHSSs, the network follows the Turing type symmetry breaking pitchfork or transcritical bifurcation depending upon the system dynamics
Transition from amplitude to oscillation death in a network of oscillators
Energy Technology Data Exchange (ETDEWEB)
Nandan, Mauparna [Dr. B. C. Roy Engineering College, Durgapur 713206 (India); Department of Mathematics, National Institute of Technology, Durgapur 713209 (India); Hens, C. R.; Dana, Syamal K. [CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India); Pal, Pinaki [Department of Mathematics, National Institute of Technology, Durgapur 713209 (India)
2014-12-01
We report a transition from a homogeneous steady state (HSS) to inhomogeneous steady states (IHSSs) in a network of globally coupled identical oscillators. We perturb a synchronized population of oscillators in the network with a few local negative or repulsive mean field links. The whole population splits into two clusters for a certain number of repulsive mean field links and a range of coupling strength. For further increase of the strength of interaction, these clusters collapse into a HSS followed by a transition to IHSSs where all the oscillators populate either of the two stable steady states. We analytically determine the origin of HSS and its transition to IHSS in relation to the number of repulsive mean-field links and the strength of interaction using a reductionism approach to the model network. We verify the results with numerical examples of the paradigmatic Landau-Stuart limit cycle system and the chaotic Rössler oscillator as dynamical nodes. During the transition from HSS to IHSSs, the network follows the Turing type symmetry breaking pitchfork or transcritical bifurcation depending upon the system dynamics.
Feature Selection via Chaotic Antlion Optimization.
Directory of Open Access Journals (Sweden)
Hossam M Zawbaa
Full Text Available Selecting a subset of relevant properties from a large set of features that describe a dataset is a challenging machine learning task. In biology, for instance, the advances in the available technologies enable the generation of a very large number of biomarkers that describe the data. Choosing the more informative markers along with performing a high-accuracy classification over the data can be a daunting task, particularly if the data are high dimensional. An often adopted approach is to formulate the feature selection problem as a biobjective optimization problem, with the aim of maximizing the performance of the data analysis model (the quality of the data training fitting while minimizing the number of features used.We propose an optimization approach for the feature selection problem that considers a "chaotic" version of the antlion optimizer method, a nature-inspired algorithm that mimics the hunting mechanism of antlions in nature. The balance between exploration of the search space and exploitation of the best solutions is a challenge in multi-objective optimization. The exploration/exploitation rate is controlled by the parameter I that limits the random walk range of the ants/prey. This variable is increased iteratively in a quasi-linear manner to decrease the exploration rate as the optimization progresses. The quasi-linear decrease in the variable I may lead to immature convergence in some cases and trapping in local minima in other cases. The chaotic system proposed here attempts to improve the tradeoff between exploration and exploitation. The methodology is evaluated using different chaotic maps on a number of feature selection datasets. To ensure generality, we used ten biological datasets, but we also used other types of data from various sources. The results are compared with the particle swarm optimizer and with genetic algorithm variants for feature selection using a set of quality metrics.
Complex dynamics of a new 3D Lorenz-type autonomous chaotic ...
Indian Academy of Sciences (India)
Newautonomous chaotic system; chaotic attractors; Lyapunov stability theory; ultimate ... College of Mathematics and Statistics, Chongqing Technology and Business ... College of Electronic and Information Engineering, Southwest University, ...
Chaotic behaviour induced by space charge
International Nuclear Information System (INIS)
Lagniel, J.M.
1994-01-01
In numerous non-linear dynamical systems studied in various disciplines (fluid dynamics, celestial mechanisms, chemistry, biology, economy, ecology...), chaotic motions are generated by the dynamics itself whereas no random force is present. This phenomenon, already studied in the particle accelerator field to understand the beam-beam effect, is also observed in numerical experiments on space-charge dominated beams. Stochasticity threshold and halo formation are discussed for a continuous focusing channel (1D beam) and for a FODO channel (2D beam) with the possibility to take into account the defocusing effects of RF gaps localized between the quadrupoles. (authors). 7 refs., 4 figs
Hash function based on chaotic map lattices.
Wang, Shihong; Hu, Gang
2007-06-01
A new hash function system, based on coupled chaotic map dynamics, is suggested. By combining floating point computation of chaos and some simple algebraic operations, the system reaches very high bit confusion and diffusion rates, and this enables the system to have desired statistical properties and strong collision resistance. The chaos-based hash function has its advantages for high security and fast performance, and it serves as one of the most highly competitive candidates for practical applications of hash function for software realization and secure information communications in computer networks.
Experimental pulse synchronisation of two chaotic circuits
Fortuna, L; Rizzo, A
2003-01-01
In this work a novel synchronisation scheme for chaotic systems is presented. Taking inspiration from the system decomposition approach, the master and slave are connected via a switch which allows to alternate the signal fed into the slave between the master signal and the slave signal itself. The switching frequency has been taken into account as a control parameter to characterise the synchronisation properties of the system. Experimental results, performed on real Chua's circuits, confirm the validity of the approach, emphasising the fact that synchronisation is achieved for switching frequencies greater than a certain threshold.
Mechanical analysis of Chen chaotic system
International Nuclear Information System (INIS)
Liang, Xiyin; Qi, Guoyuan
2017-01-01
The Chen chaotic system is transformed into Kolmogorov type system, which is decomposed into four types of torques: inertial torque, internal torque, dissipation and external torque. By the combinations of different torques, five cases are studied to discover key factors of chaos generation and the physical meaning. The conversion among Hamiltonian energy, kinetic energy and potential energy is investigated in these five cases. The relationship between the energies and the parameters is studied. It concludes that the combination of these four types of torques is necessary conditions to produce chaos, and any combination of three types of torques cannot produce chaos in Chen system.
Noise-Induced Riddling in Chaotic Systems
International Nuclear Information System (INIS)
Lai, Y.; Grebogi, C.
1996-01-01
Recent works have considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. We show that riddling can be induced by arbitrarily small random noise even if the attractor is transversely unstable, and we obtain universal scaling laws for noise-induced riddling. Our results imply that the phenomenon of riddling can be more prevalent than expected before, as noise is practically inevitable in dynamical systems. copyright 1996 The American Physical Society
Unitarity and irreversibility in chaotic systems
International Nuclear Information System (INIS)
Hasegawa, H.H.; Saphir, W.C.
1992-01-01
We analyze the spectral properties of the Perron-Frobenius operator U, associated with some simple highly chaotic maps. We obtain a spectral decomposition of U in terms of generalized eigenfunctions of U and its adjoint. The corresponding eigenvalues are related to the decay rates of correlation functions and have magnitude less than one, so that physically measurable quantities manifestly approach equilibrium. To obtain decaying eigenstates of unitary and isometric operators it is necessary to extend the Hilbert-space formulation of dynamical systems. We describe and illustrate a method to obtain the decomposition explicitly
Chaotic behavior in the Henon mapping
Energy Technology Data Exchange (ETDEWEB)
Marotto, F R [Drexel Univ., Philadelphia, PA (USA). Dept. of Mathematics
1979-01-01
In a previous work Henon investigated a two-dimensional difference equation which was motivated by a hydrodynamical system of Lorenz. Numerically solving this equation indicated for certain parameter values the existence of a 'strange attractor', i.e., a region in the plane which attracts bounded solutions and in which solutions wander erratically. In the present work it is shown that this behavior is related to the mathematical concept of 'chaos'. Using general methods previously developed, it is proven analytically that for some parameter values the mapping has a transversal homoclinic orbit, which implies the existence of the chaotic behavior observed by Henon.
A dynamic modification to sneutrino chaotic inflation
International Nuclear Information System (INIS)
Saha, Abhijit Kumar; Sil, Arunansu
2015-01-01
We consider a right-handed scalar neutrino as the inflaton which carries a gravitational coupling with a supersymmetric QCD sector responsible for breaking supersymmetry dynamically. The framework suggests an inflaton potential which is a deformed version of the quadratic chaotic inflation leading to a flatter potential. We find that this deformation results a sizable tensor to scalar ratio which falls within the allowed region by PLANCK 2015. At the same time supersymmetry breaking at the end of inflation can naturally be induced in this set-up. The symmetries required to construct the framework allows the neutrino masses and mixing to be of right order.
On the quantization of classically chaotic system
International Nuclear Information System (INIS)
Godoy, N.F. de.
1988-01-01
Some propeties of a quantization in terms of observables of a classically chaotic system, which exhibits a strange are studied. It is shown in particular that convenient expected values of some observables have the correct classical limit and that in these cases the limits ℎ → O and t → ∞ (t=time) rigorously comute. This model was alternatively quantized by R.Graham in terms of Wigner function. The Graham's analysis is completed a few points, in particular, we find out a remarkable analogy with general results about the semi-classical limit of Wigner function. Finally the expected values obtained by both methods of quantization were compared. (author) [pt
Parametric number covariance in quantum chaotic spectra.
Vinayak; Kumar, Sandeep; Pandey, Akhilesh
2016-03-01
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.
Chaotic combustion in spark ignition engines
International Nuclear Information System (INIS)
Wendeker, Miroslaw; Czarnigowski, Jacek; Litak, Grzegorz; Szabelski, Kazimierz
2003-01-01
We analyse the combustion process in a spark ignition engine using the experimental data of an internal pressure during the combustion process and show that the system can be driven to chaotic behaviour. Our conclusion is based on the observation of unperiodicity in the time series, suitable stroboscopic maps and a complex structure of a reconstructed strange attractor. This analysis can explain that in some circumstances the level of noise in spark ignition engines increases considerably due to nonlinear dynamics of a combustion process
Experimental pulse synchronisation of two chaotic circuits
International Nuclear Information System (INIS)
Fortuna, L.; Frasca, M.; Rizzo, A.
2003-01-01
In this work a novel synchronisation scheme for chaotic systems is presented. Taking inspiration from the system decomposition approach, the master and slave are connected via a switch which allows to alternate the signal fed into the slave between the master signal and the slave signal itself. The switching frequency has been taken into account as a control parameter to characterise the synchronisation properties of the system. Experimental results, performed on real Chua's circuits, confirm the validity of the approach, emphasising the fact that synchronisation is achieved for switching frequencies greater than a certain threshold
Designing synchronization schemes for chaotic fractional-order unified systems
International Nuclear Information System (INIS)
Wang Junwei; Zhang Yanbin
2006-01-01
Synchronization in chaotic fractional-order differential systems is studied both theoretically and numerically. Two schemes are designed to achieve chaos synchronization of so-called unified chaotic systems and the corresponding numerical algorithms are established. Some sufficient conditions on synchronization are also derived based on the Laplace transformation theory. Computer simulations are used for demonstration
Horseshoes in a Chaotic System with Only One Stable Equilibrium
Huan, Songmei; Li, Qingdu; Yang, Xiao-Song
To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.
Active control versus recursive backstepping control of a chaotic ...
African Journals Online (AJOL)
In this paper active controllers and recursive backstepping controllers are designed for a third order chaotic system. The performances of these controllers in the control of the dynamics of the chaotic system are investigated numerically and are found to be effective. Comparison of their transient performances show that the ...
Modification for collection of master-slave synchronized chaotic systems
International Nuclear Information System (INIS)
Guo Rongwei; Li Gang
2009-01-01
In this paper, based on the adaptive-feedback control method, we synchronize two identical chaotic systems. In comparison with the previous methods such as the open-plus-closed-loop (OPCL) method, the present control scheme is simple, and therefore it is easily implemented in practice. At last, a group of chaotic systems are used to demonstrate the effectiveness of this method.
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.
Regular and Chaotic Regimes in Scalar Field Cosmology
Directory of Open Access Journals (Sweden)
Alexey V. Toporensky
2006-03-01
Full Text Available A transient chaos in a closed FRW cosmological model with a scalar field is studied. We describe two different chaotic regimes and show that the type of chaos in this model depends on the scalar field potential. We have found also that for sufficiently steep potentials or for potentials with large cosmological constant the chaotic behavior disappears.
PSO algorithm enhanced with Lozi Chaotic Map - Tuning experiment
Energy Technology Data Exchange (ETDEWEB)
Pluhacek, Michal; Senkerik, Roman; Zelinka, Ivan [Tomas Bata University in Zlín, Faculty of Applied Informatics Department of Informatics and Artificial Intelligence nám. T.G. Masaryka 5555, 760 01 Zlín (Czech Republic)
2015-03-10
In this paper it is investigated the effect of tuning of control parameters of the Lozi Chaotic Map employed as a chaotic pseudo-random number generator for the particle swarm optimization algorithm. Three different benchmark functions are selected from the IEEE CEC 2013 competition benchmark set. The Lozi map is extensively tuned and the performance of PSO is evaluated.
Transition to a pair of chaotic symmetric flows
International Nuclear Information System (INIS)
Chen Zhimin; Price, W.G.
2006-01-01
The complexity of transition to chaotic flow is discussed. It is shown that many different bifurcation processes may coexist and join together to excite the chaotic flow. The profile of this nonlinear dynamical behaviour is developed on the basis of a four-mode truncation model
Chaos synchronization between two different chaotic dynamical systems
International Nuclear Information System (INIS)
Park, Ju H.
2006-01-01
This work presents chaos synchronization between two different chaotic systems by nonlinear control laws. First, synchronization problem between Genesio system and Rossler system has been investigated, and then the similar approach is applied to the synchronization problem between Genesio system and a new chaotic system developed recently in the literature. The control performances are verified by two numerical examples
The Smallest Transistor-Based Nonautonomous Chaotic Circuit
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, Arunas
2005-01-01
A nonautonomous chaotic circuit based on one transistor, two capacitors, and two resistors is described. The mechanism behind the chaotic performance is based on “disturbance of integration.” The forward part and the reverse part of the bipolar transistor are “fighting” about the charging...
A new chaotic Hopfield network with piecewise linear activation function
International Nuclear Information System (INIS)
Peng-Sheng, Zheng; Wan-Sheng, Tang; Jian-Xiong, Zhang
2010-01-01
This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters
Lag synchronization of chaotic systems with time-delayed linear
Indian Academy of Sciences (India)
In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems.
Towards generalized synchronization of strictly different chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Femat, R. [Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Apdo. Postal 3-90, 78291 Tangamanga, San Luis Potosi S.L.P. (Mexico)]. E-mail: rfemat@ipicyt.edu.mx; Kocarev, L. [Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0402 (United States)]. E-mail: lkocarev@ucsd.edu; Gerven, L. van [Department of Mechanical Engineering, Technische Universiteit Eindhoven (Netherlands); Monsivais-Perez, M.E. [Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Camino a la Presa San Jose 2055, 78216 Lomas 4a Sec., San Luis Potosi S.L.P. (Mexico)
2005-07-11
This contribution addresses the problem of the generalized synchronization (GS) in different chaotic systems, and departs from chaotic systems in a triangular from, which can be derived from Lie derivatives. A state-feedback (full knowledge of both master and slave systems) scheme is designed, which achieves GS. The work includes illustrative examples; moreover an experimental setup is used to corroborate the obtained results.
Secure Image Encryption Based On a Chua Chaotic Noise Generator
Directory of Open Access Journals (Sweden)
A. S. Andreatos
2013-10-01
Full Text Available This paper presents a secure image cryptography telecom system based on a Chua's circuit chaotic noise generator. A chaotic system based on synchronised Master–Slave Chua's circuits has been used as a chaotic true random number generator (CTRNG. Chaotic systems present unpredictable and complex behaviour. This characteristic, together with the dependence on the initial conditions as well as the tolerance of the circuit components, make CTRNGs ideal for cryptography. In the proposed system, the transmitter mixes an input image with chaotic noise produced by a CTRNG. Using thresholding techniques, the chaotic signal is converted to a true random bit sequence. The receiver must be able to reproduce exactly the same chaotic noise in order to subtract it from the received signal. This becomes possible with synchronisation between the two Chua's circuits: through the use of specific techniques, the trajectory of the Slave chaotic system can be bound to that of the Master circuit producing (almost identical behaviour. Additional blocks have been used in order to make the system highly parameterisable and robust against common attacks. The whole system is simulated in Matlab. Simulation results demonstrate satisfactory performance, as well as, robustness against cryptanalysis. The system works with both greyscale and colour jpg images.
Chaotic scattering of two identical point vortex pairs revisited
DEFF Research Database (Denmark)
Tophøj, Laust Emil Hjerrild; Aref, Hassan
2008-01-01
A new numerical exploration suggests that the motion of two vortex pairs, with constituent vortices all of the same absolute circulation, displays chaotic scattering regimes. The mechanisms leading to chaotic scattering are different from the “slingshot effect” identified by Price [Phys. Fluids A...
Nonlinear observer based phase synchronization of chaotic systems
International Nuclear Information System (INIS)
Meng Juan; Wang Xingyuan
2007-01-01
This Letter analyzes the phase synchronization problem of autonomous chaotic systems. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations further demonstrate the effectiveness of the proposed phase synchronization scheme
Adaptive control and synchronization of a fractional-order chaotic ...
Indian Academy of Sciences (India)
In this paper, the chaotic dynamics of a three-dimensional fractional-order chaotic sys- tem is investigated. ... So, the fractional description is closer to reality. One of the ..... For the augmented systems (14) and (16), the candidate function can.
PSO algorithm enhanced with Lozi Chaotic Map - Tuning experiment
International Nuclear Information System (INIS)
Pluhacek, Michal; Senkerik, Roman; Zelinka, Ivan
2015-01-01
In this paper it is investigated the effect of tuning of control parameters of the Lozi Chaotic Map employed as a chaotic pseudo-random number generator for the particle swarm optimization algorithm. Three different benchmark functions are selected from the IEEE CEC 2013 competition benchmark set. The Lozi map is extensively tuned and the performance of PSO is evaluated
A novel chaotic encryption scheme based on arithmetic coding
International Nuclear Information System (INIS)
Mi Bo; Liao Xiaofeng; Chen Yong
2008-01-01
In this paper, under the combination of arithmetic coding and logistic map, a novel chaotic encryption scheme is presented. The plaintexts are encrypted and compressed by using an arithmetic coder whose mapping intervals are changed irregularly according to a keystream derived from chaotic map and plaintext. Performance and security of the scheme are also studied experimentally and theoretically in detail
Ma, Hongbin
2015-01-01
This book presents the fundamental fluid flow and heat transfer principles occurring in oscillating heat pipes and also provides updated developments and recent innovations in research and applications of heat pipes. Starting with fundamental presentation of heat pipes, the focus is on oscillating motions and its heat transfer enhancement in a two-phase heat transfer system. The book covers thermodynamic analysis, interfacial phenomenon, thin film evaporation, theoretical models of oscillating motion and heat transfer of single phase and two-phase flows, primary factors affecting oscillating motions and heat transfer, neutron imaging study of oscillating motions in an oscillating heat pipes, and nanofluid’s effect on the heat transfer performance in oscillating heat pipes. The importance of thermally-excited oscillating motion combined with phase change heat transfer to a wide variety of applications is emphasized. This book is an essential resource and learning tool for senior undergraduate, gradua...
A New Simple Chaotic Circuit Based on Memristor
Wu, Renping; Wang, Chunhua
In this paper, a new memristor is proposed, and then an emulator built from off-the-shelf solid state components imitating the behavior of the proposed memristor is presented. Multisim simulation and breadboard experiment are done on the emulator, exhibiting a pinched hysteresis loop in the voltage-current plane when the emulator is driven by a periodic excitation voltage. In addition, a new simple chaotic circuit is designed by using the proposed memristor and other circuit elements. It is exciting that this circuit with only a linear negative resistor, a capacitor, an inductor and a memristor can generate a chaotic attractor. The dynamical behaviors of the proposed chaotic system are analyzed by Lyapunov exponents, phase portraits and bifurcation diagrams. Finally, an electronic circuit is designed to implement the chaotic system. For the sake of simple circuit topology, the proposed chaotic circuit can be easily manufactured at low cost.