Modeling of Coupled Chaotic Oscillators
Energy Technology Data Exchange (ETDEWEB)
Lai, Y. [Departments of Physics and Astronomy and of Mathematics, University of Kansas, Lawrence, Kansas 66045 (United States); Grebogi, C. [Institute for Plasma Research, Department of Mathematics, Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)
1999-06-01
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} {ital 1999} {ital 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 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...... the interacting chaotic oscillators causes a shift of the synchronization manifold. The presence of a coupling asymmetry is found to lead to further modifications of the destabilization process. Finally, the paper considers the problem of partial synchronization in a system of four coupled Rossler oscillators...
Simple driven chaotic oscillators with complex variables.
Marshall, Delmar; Sprott, J C
2009-03-01
Despite a search, no chaotic driven complex-variable oscillators of the form z+f(z)=e(iOmegat) or z+f(z)=e(iOmegat) are found, where f is a polynomial with real coefficients. It is shown that, for analytic functions f(z), driven complex-variable oscillators of the form z+f(z)=e(iOmegat) cannot have chaotic solutions. Seven simple driven chaotic oscillators of the form z+f(z,z)=e(iOmegat) with polynomial f(z,z) are given. Their chaotic attractors are displayed, and Lyapunov spectra are calculated. Attractors for two of the cases have symmetry across the x=-y line. The systems' behavior with Omega as a control parameter in the range of Omega=0.1-2.0 is examined, revealing cases of period doubling, intermittency, chaotic transients, and period adding as routes to chaos. Numerous cases of coexisting attractors are also observed.
Chaotic coupling synchronization of hyperchaotic oscillators
Institute of Scientific and Technical Information of China (English)
Zou Yan-Li; Zhu Jie; Chen Guan-Rong
2005-01-01
In this paper, two kinds of chaotic coupling synchronization schemes are presented. The synchronizability of the coupled hyperchaotic oscillators is proved mathematically and the numerical simulation is also carried out. The numerical calculation of the largest conditional Lyapunov exponent shows that in a given range of coupling strengths,chaotic-coupling synchronization is quicker than the typical continuous-coupling synchronization.
Autonomous Duffing-Holmes Type Chaotic Oscillator
DEFF Research Database (Denmark)
Tamaševičius, A.; Bumelienė, S.; Kirvaitis, R.
2009-01-01
We have designed and built a novel Duffing type autonomous 3rd-order chaotic oscillator. In comparison with the common non-autonomous DuffingHolmes type oscillator the autonomous circuit has an internal positive feedback loop instead of an external periodic drive source. In addition...
Quantum noise-induced chaotic oscillations
Bag, Bidhan Chandra; Ray, Deb Shankar
1999-01-01
We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxiliary Hamiltonian manifests itself as an additional fluctuational degree of freedom which may induce chaotic and regular oscillations in a nonlinear oscillator.
Quantum noise-induced chaotic oscillations
Bag, B C; Bag, Bidhan Chandra; Ray, Deb Shankar
1999-01-01
We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxilliary Hamiltonian manifests itself as an additional fluctuational degree of freedom which may induce chaotic and regular oscillations in a nonlinear oscillator.
Amplitude envelope synchronization in coupled chaotic oscillators.
Gonzalez-Miranda, J M
2002-03-01
A peculiar type of synchronization has been found when two Van der Pol-Duffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.
Energy Technology Data Exchange (ETDEWEB)
Sabavath, Gopi Kishan; Banerjee, I.; Mahapatra, S. K., E-mail: skmahapatra@bitmesra.ac.in [Plasma Laboratory, Department of Physics, Birla Institute of Technology-Mesra, Ranchi 835215 (India); Shaw, Pankaj Kumar; Sekar Iyengar, A. N. [Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064 (India)
2015-08-15
Floating potential fluctuations from a direct current magnetron sputtering plasma have been analysed using time series analysis techniques like phase space plots, power spectra, frequency bifurcation plot, etc. The system exhibits quasiperiodic-chaotic-quasiperiodic-chaotic transitions as the discharge voltage was increased. The transitions of the fluctuations, quantified using the largest Lyapunov exponent, have been corroborated by Hurst exponent and the Shannon entropy. The Shannon entropy is high for quasiperiodic and low for chaotic oscillations.
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 negative...
Spice Modeling of the Vilnius Chaotic Oscillator
Peters, R D
2005-01-01
``A simple chaotic oscillator for educational purposes'' was recently described in the literature [1]. In addition to their hardware description, the authors of this paper generated a bifurcation diagram from the model equations presented in their paper. In the present treatment of their circuit the `simulation program for integrated circuit engineering' (Spice) has been used to generate some insightful graphs that were not shown by the Lithuania group.
Institute of Scientific and Technical Information of China (English)
SHI Zhi-Guo; RAN Li-Xin; CHEN Kang-Sheng
2005-01-01
@@ We demonstrate multiplexing chaotic signals generated by two totally different dynamic systems (one is a Colpitts oscillator and the other is a Chua circuit) using dual synchronization and propose a method to select the proper coupling parameters. In the response systems, the cross coupling method is used, in which the voltage difference between the sum of two master oscillators and one slave oscillator is converted to current and then feed into the other slave oscillator. The result in this letter offers a potential multiuser coherent chaotic communication scheme where different chaotic oscillators can be used in one system.
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.
Chaotic synchronization of two complex nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Gamal M. [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)], E-mail: gmahmoud@aun.edu.eg; Mahmoud, Emad E. [Department of Mathematics, Faculty of Science, Sohag University (Egypt)], E-mail: emad_eluan@yahoo.com; Farghaly, Ahmed A. [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)], E-mail: ahmed_1_66@yahoo.com; Aly, Shaban A. [Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511 (Egypt)], E-mail: shhaly12@yahoo.com
2009-12-15
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.
Control of partial synchronization in chaotic oscillators
Indian Academy of Sciences (India)
R Banerjee; E Padmanaban; S K Dana
2015-02-01
A design of coupling is proposed to control partial synchronization in two chaotic oscillators in a driver–response mode. A control of synchrony between one response variables is made possible (a transition from a complete synchronization to antisynchronization via amplitude death and vice versa without loss of synchrony) keeping the other pairs of variables undisturbed in their pre-desired states of coherence. Further, one of the response variables can be controlled so as to follow the dynamics of an external signal (periodic or chaotic) while keeping the coherent status of other variables unchanged. The stability of synchronization is established using the Hurwitz matrix criterion. Numerical example of an ecological foodweb model is presented. The control scheme is demonstrated in an electronic circuit of the Sprott system.
Recursive backstepping control of chaotic Duffing oscillators
Energy Technology Data Exchange (ETDEWEB)
Harb, Ahmad M. [Jordan University of Science and Technology, EE Department, P.O. Box 3030, Irbid (Jordan)]. E-mail: aharb@just.edu.jo; Zaher, Ashraf A. [Oakland University, School of Engineering and Computer Science, ESE Department, DHE 137, Rochester, MI 48309 (United States); Al-Qaisia, Ahmad A. [University of Jordan, ME Department, Amman (Jordan); Zohdy, Mohammad A. [Oakland University, School of Engineering and Computer Science, ESE Department, DHE 137, Rochester, MI 48309 (United States)
2007-10-15
In this paper, the dynamics of a forced Duffing oscillator is studied by means of modern nonlinear, bifurcation and chaos theories and shows that the system is ultimately experiencing chaos. The main objective is to characterize and control chaotic behavior. A nonlinear recursive backstepping controller is proposed and the transient performance is investigated. Systematic following of a reference model is introduced. Robustness problems as well as ways to tune the controller parameters are examined. Simulation results are submitted for the uncontrolled and controlled cases, verifying the effectiveness of the proposed controller. Finally a discussion and conclusions are given with possible future extensions.
Automatic simulation of 1D and 2D chaotic oscillators
Energy Technology Data Exchange (ETDEWEB)
Tlelo-Cuautle, E; Munoz-Pacheco, J-M [Department of Electronics, INAOE, Luis Enrique Erro No. 1, Tonantzintla, Puebla, 72840 MEXICO (Mexico)], E-mail: e.tlelo@ieee.org, E-mail: mpacheco@inaoep.mx
2008-02-15
A new method is introduced for automatic simulation of three kinds of chaotic oscillators: Chua's circuit, generalized Chua's circuit and chaotic oscillator implemented with saturated functions. The former generates the double-scroll, and the others 1D n-scroll attractors. The third chaotic oscillator is modified to generate 2D n-scrolls attractors. The oscillators are modelled by applying state variables and piecewise-linear approximation. Basically, the method computes the eigenvalues of the oscillators to begin time simulation and to make control of step-size automatically.
Periodic Oscillations within the Chaotic Region in Finite Piezoelectric Structures
Bettucci, A.; Biagioni, A.; D'Orazio, A.; Passeri, D.
2008-06-01
We report experimental observation of a window of periodic oscillations within the chaotic oscillations of a finite piezoelectric structure electrically forced with a frequency equal to—or close to—a normal mode. Continuously sampled spectra of the oscillation as the level of the driving voltage is increased, reveal the general behaviour of the system as well as features that suggest that the periodic oscillation forms a distinct island within the chaotic region in the parameter space. A period-doubling sequence routing to chaotic oscillations is also observed.
Autonomous third-order duffing-holmes type chaotic oscillator
DEFF Research Database (Denmark)
Lindberg, Erik; Tamaseviciute, E; Mykolaitis, G
2009-01-01
A novel Duffing-Holmes type autonomous chaotic oscillator is described. In comparison with the well-known nonautonomous Duffing-Holmes circuit it lacks the external periodic drive, but includes two extra linear feedback subcircuits, namely a direct positive feedback loop, and an inertial negative...... 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...... are presented. The Lyapunov exponents calculated from the rate equations confirm dynamical nature of chaotic oscillations....
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...... synchronization are found to significantly reduce the degree of multiscality. The influence of external noise on the possibility of distinguishing the various chaotic states is considered....
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.
Frequency-locked chaotic opto-RF oscillator
Thorette, Aurélien; Brunel, Marc; Vallet, Marc
2016-01-01
A driven opto-RF oscillator, consisting of a dual-frequency laser (DFL) submitted to frequency-shifted feedback, is studied experimentally and numerically in a chaotic regime. Precise control of the reinjection strength and detuning permits to isolate a parameter region of bounded-phase chaos, where the opto-RF oscillator is frequency-locked to the master oscillator, in spite of chaotic phase and intensity oscillations. Robust experimental evidence of this synchronization regime is found and phase noise spectra allows to compare phase-locking and bounded-phase chaos regimes. In particular, it is found that the long-term phase stability of the master oscillator is well transferred to the opto-RF oscillator even in the chaotic regime.
Frequency-locked chaotic opto-RF oscillator.
Thorette, Aurélien; Romanelli, Marco; Brunel, Marc; Vallet, Marc
2016-06-15
A driven opto-RF oscillator, consisting of a dual-frequency laser (DFL) submitted to frequency-shifted feedback, is experimentally and numerically studied in a chaotic regime. Precise control of the reinjection strength and detuning permits isolation of a parameter region of bounded-phase chaos, where the opto-RF oscillator is frequency-locked to the master oscillator, in spite of chaotic phase and intensity oscillations. Robust experimental evidence of this synchronization regime is found, and phase noise spectra allow us to compare phase-locking and bounded-phase chaos regimes. In particular, it is found that the long-term phase stability of the master oscillator is well transferred to the opto-RF oscillator, even in the chaotic regime.
Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators
Hramov, Alexander E.; ALEXEY A. KORONOVSKII
2005-01-01
A new behavior type of unidirectionally coupled chaotic oscillators near the generalized synchronization transition has been detected. It has been shown that the generalized synchronization appearance is preceded by the intermitted behavior: close to threshold parameter value the coupled chaotic systems demonstrate the generalized synchronization most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous bursts. This type of th...
Inhomogeneous stationary and oscillatory regimes in coupled chaotic oscillators.
Liu, Weiqing; Volkov, Evgeny; Xiao, Jinghua; Zou, Wei; Zhan, Meng; Yang, Junzhong
2012-09-01
The dynamics of linearly coupled identical Lorenz and Pikovsky-Rabinovich oscillators are explored numerically and theoretically. We concentrate on the study of inhomogeneous stable steady states ("oscillation death (OD)" phenomenon) and accompanying periodic and chaotic regimes that emerge at an appropriate choice of the coupling matrix. The parameters, for which OD occurs, are determined by stability analysis of the chosen steady state. Three model-specific types of transitions to and from OD are observed: (1) a sharp transition to OD from a nonsymmetric chaotic attractor containing random intervals of synchronous chaos; (2) transition to OD from the symmetry-breaking chaotic regime created by negative coupling; (3) supercritical bifurcation of OD into inhomogeneous limit cycles and further evolution of the system to inhomogeneous chaotic regimes that coexist with complete synchronous chaos. These results may fill a gap in the understanding of the mechanism of OD in coupled chaotic systems.
A Simple RLCC-Diode-Opamp Chaotic Oscillator
San-Um, Wimol; Suksiri, Bandhit; Ketthong, Patinya
This paper presents a simple autonomous chaotic oscillator. The design method is primarily based on a linear oscillator constructed by a closed loop connection of two building blocks, i.e. an inverting active integrator and a passive second-order LC integrator. A diode is inserted in parallel to the two building blocks for inducing chaos. The mathematical model reveals a set of three-dimensional ordinary differential equations, containing seven terms with four constants and an exponential nonlinearity. The dynamics properties are investigated in terms of an equilibrium point, Jacobian matrix, chaotic attractors, bifurcation, Lyapunov exponents, and chaotic waveforms in time domain. The proposed chaotic oscillator potentially exhibits complex dynamical behaviors through the utilization of only six minimal electronic components.
Experimental Synchronization of two Integrated Multi-scroll Chaotic Oscillators
Directory of Open Access Journals (Sweden)
J.M. Muñoz-Pacheco
2014-06-01
Full Text Available Chaotic oscillators have been implemented with a wide variety of discrete electronic devices and quite few realizations using integrated circuit technology. This article describes the synchronization of two chaotic oscillators already fabricated with complementary metal-oxide-semiconductor (CMOS integrated circuit technology of 0.5um and generating 3- and 5-scrolls. In order to attain the synchronization, we use a master-slave topology with unidirectional coupling. Within this context, a system parameter iterates until the correlation coefficient computed between the chaotic signals generated by the master and slave systems approximates to unity. For the following parameter, its value depends on the standard deviations from the individual signals contrary to previous one. By combining those statistical relationships according to the number of system parameters, we can synchronize integrated chaotic oscillators. Theoretical model simulations of two chaotic oscillators generating 3- and 5-scrolls, and experimental results for two integrated 3-scroll chaotic oscillators validate this approach. Stability and error analysis are also included.
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.
A transient-chaotic autoassociative network (TCAN) based on Lee oscillators.
Lee, R T
2004-09-01
In the past few decades, neural networks have been extensively adopted in various applications ranging from simple synaptic memory coding to sophisticated pattern recognition problems such as scene analysis. Moreover, current studies on neuroscience and physiology have reported that in a typical scene segmentation problem our major senses of perception (e.g., vision, olfaction, etc.) are highly involved in temporal (or what we call "transient") nonlinear neural dynamics and oscillations. This paper is an extension of the author's previous work on the dynamic neural model (EGDLM) of memory processing and on composite neural oscillators for scene segmentation. Moreover, it is inspired by the work of Aihara et al. and Wang on chaotic neural oscillators in pattern association. In this paper, the author proposes a new transient chaotic neural oscillator, namely the "Lee oscillator," to provide temporal neural coding and an information processing scheme. To illustrate its capability for memory association, a chaotic autoassociative network, namely the Transient-Chaotic Auto-associative Network (TCAN) was constructed based on the Lee oscillator. Different from classical autoassociators such as the celebrated Hopfield network, which provides a "time-independent" pattern association, the TCAN provides a remarkable progressive memory association scheme [what we call "progressive memory recalling" (PMR)] during the transient chaotic memory association. This is exactly consistent with the latest research in psychiatry and perception psychology on dynamic memory recalling schemes.
FPGA realization of multi-scroll chaotic oscillators
Tlelo-Cuautle, E.; Rangel-Magdaleno, J. J.; Pano-Azucena, A. D.; Obeso-Rodelo, P. J.; Nunez-Perez, J. C.
2015-10-01
Chaotic oscillators have been realized using field-programmable gate arrays (FPGAs) showing good results. However, only 2-scrolls have been observed experimentally, and all reported works use commercially-available software tools for FPGA synthesis. In this manner, as a first contribution we show the FPGA realization of two multi-scroll chaotic oscillators that are characterized by their maximum Lyapunov exponent (MLE) for generating from 2- to 6-scrolls. The first multi-scroll chaotic oscillator is based on saturated function series and the second on Chua's circuit. As a second contribution, we show their hardware realization by applying two numerical methods: Forward Euler (FE) and Runge Kutta (RK). The advantage of realizing those multi-scroll chaotic oscillators is that one can avoid the use of multiplier entities, thus optimizing FPGA resources and increasing the processing speed, as we show by realizing single constant multiplication (SCM) blocks. The experiments are verified by performing co-simulation for an FPGA Spartan 3 of Xilinx. Finally, experimental results are shown for different values of MLE (already optimized) for both multi-scroll chaotic oscillators, and the FPGA used resources are listed for generating 6-scrolls when applying FE and RK.
An open plus nonlinear closed loop control of chaotic oscillators
Institute of Scientific and Technical Information of China (English)
陈立群
2002-01-01
An open plus nonlinear closed loop control law is presented for chaotic oscillations described by a set of non-autonomous second-order ordinary differential equations. It is proven that the basins of entrainment are global whenthe right-hand sides of the equations are given by arbitrary polynomial functions. The forced Duffing oscillator and theforced van der Pol oscillator are treated as numerical examples to demonstrate the applications of the method.
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.
Phase multistability of synchronous chaotic oscillations
Directory of Open Access Journals (Sweden)
T. E. Vadivasova
2000-01-01
Full Text Available The paper describes the sequence of bifurcations leading to multistability of periodic and chaotic synchronous attractors for the coupled Rössler systems which individually demonstrate the Feigenbaum route to chaos. We investigate how a frequency mismatch affects this phenomenon. The role of a set of coexisting synchronous regimes in the transitions to and between different forms of synchronization is studied.
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.
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
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 and technology, is illustrated through concrete examples of coupled biological cell models.
Chaotic Colpitts Oscillator for the Ultrahigh Frequency Range
DEFF Research Database (Denmark)
Tamasevicius, A.; Mykolaitis, G.; Bumeliene, S.
2006-01-01
PSpice simulation and experimental results demonstrating chaotic performance of the Colpitts oscillator in the ultrahigh frequency (300–1000 MHz) range are presented.Various combinations of the resonance tank parameters are considered to achieve a fundamental frequency as high as possible...
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.
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 and t...... and technology, is illustrated through concrete examples of coupled biological cell models....
DEFF Research Database (Denmark)
Isaeva, Olga B.; Kuznetsov, Sergey P.; Mosekilde, Erik
2011-01-01
The paper proposes an approach to constructing feasible examples of dynamical systems with hyperbolic chaotic attractors based on the successive transfer of excitation between two pairs of self-oscillators that are alternately active. An angular variable that measures the relations of the current...
Simulation and Experimental Realization of Multi-Scroll Chaotic Oscillators
Directory of Open Access Journals (Sweden)
E. T. Cuautle
2013-09-01
Full Text Available This article shows the simulation and experimental realization of a multi-scroll chaotic oscillator based on saturated nonlinear function (SNLF series. First, the simulation is performed by MATLAB using the mathematical description of the oscillator. At this step, it is shown how to increase the number of scrolls by augmenting the SNLF. Second, the mathematical description is implemented with electronic devices and simulated by using the behavioral model of commercially available operational amplifiers. The circuit simulation of the multi-scroll chaotic oscillator is performed showing how to generate even and odd number of scrolls. Finally, the simulated circuit is realized experimentally and the results confirm good agreement with theoretical simulations.
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.
Generation of chaotic oscillations in auto-oscillator based on avalanche transit-time diode
Myasin, E. A.
2012-01-01
Time series of chaotic oscillations have been observed for the first time in an auto-oscillator for the 8-mm wavelength range based on an avalanche transit-time diode. The noise generator based on this diode has been used as a signal source for a noise radar prototype.
Extraction of periodic signals in chaotic secure communication using Duffing oscillators
Institute of Scientific and Technical Information of China (English)
Wang Yun-Cai; Zhao Qing-Chun; Wang An-Bang
2008-01-01
This paper presents a novel approach to extract the periodic signals masked by a chaotic carrier. It verifies that the driven Duffing oscillator is immune to the chaotic carrier and sensitive to certain periodic signals. A preliminary detection scenario illustrates that the frequency and amplitude of the hidden sine wave signal can be extracted from the chaotic carrier by numerical simulation. The obtained results indicate that the hidden messages in chaotic secure communication can be eavesdropped utilizing Duffing oscillators.
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.
Regular nonlinear response of the driven Duffing oscillator to chaotic time series
Institute of Scientific and Technical Information of China (English)
YuanYe; Li Yue; Danilo P. Mandic; Yang Bao-Jun
2009-01-01
Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated.
Directory of Open Access Journals (Sweden)
Junwei Sun
2014-01-01
Full Text Available Some important dynamical properties of the memristor chaotic oscillator system have been studied in the paper. A novel hybrid dislocated control method and a general hybrid projective dislocated synchronization scheme have been realized for memristor chaotic oscillator system. The paper firstly presents hybrid dislocated control method for stabilizing chaos to the unstable equilibrium point. Based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization has been studied for the drive memristor chaotic oscillator system and the same response memristor chaotic oscillator system. For the different dimensions, the memristor chaotic oscillator system and the other chaotic system have realized general hybrid projective dislocated synchronization. Numerical simulations are given to show the effectiveness of these methods.
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.
Chaotic Solutions of a Typical Nonlinear Oscillator in a Double Potential Trap
Institute of Scientific and Technical Information of China (English)
FANG Jian-Shu
2003-01-01
We have obtained a general unstable chaotic solution of a typical nonlinear oscillator in a double potential trap with weak periodic perturbations by using the direct perturbation method. Theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding chaotic region and orbits in parameter space are described by numerical simulations.
Chaotic oscillator detection system about weak signals in spot welding
Institute of Scientific and Technical Information of China (English)
Kai-lei SONG; Zhen LUO; Feng YE; Xin-xin TANG; Shu-xian YUAN
2009-01-01
Spot welding is an efficient and shortcut processing method used in plate, and its quality detection is very important. However, there are many factors affecting the spot welding quality. Because of the low precision of traditional detection methods, spot welding has seldom been used in the aerospace industry which requires high welding quality. In this article, we give a new weak signal detection model based on chaotic oscillators. Using Melnikov methods and Lyapunov exponent, we can determine the critical values when the system enters in and out of chaos. Through lots of numerical simulations, it can be found that the lowest value of the weak sinusoidal signal the system can detect reach 10-11, and its signal-to-noise ratio (SNR) is = 126 dB. Compared with other detection methods, chaos oscillator detection system not only has a lower threshold value, but also is easy to implement in practice. This model thus has good application prospects.
Memcapacitor model and its application in a chaotic oscillator
Guang-Yi, Wang; Bo-Zhen, Cai; Pei-Pei, Jin; Ti-Ling, Hu
2016-01-01
A memcapacitor is a new type of memory capacitor. Before the advent of practical memcapacitor, the prospective studies on its models and potential applications are of importance. For this purpose, we establish a mathematical memcapacitor model and a corresponding circuit model. As a potential application, based on the model, a memcapacitor oscillator is designed, with its basic dynamic characteristics analyzed theoretically and experimentally. Some circuit variables such as charge, flux, and integral of charge, which are difficult to measure, are observed and measured via simulations and experiments. Analysis results show that besides the typical period-doubling bifurcations and period-3 windows, sustained chaos with constant Lyapunov exponents occurs. Moreover, this oscillator also exhibits abrupt chaos and some novel bifurcations. In addition, based on the digital signal processing (DSP) technology, a scheme of digitally realizing this memcapacitor oscillator is provided. Then the statistical properties of the chaotic sequences generated from the oscillator are tested by using the test suit of the National Institute of Standards and Technology (NIST). The tested randomness definitely reaches the standards of NIST, and is better than that of the well-known Lorenz system. Project supported by the National Natural Science Foundation of China (Grant Nos. 61271064, 61401134, and 60971046), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LZ12F01001 and LQ14F010008), and the Program for Zhejiang Leading Team of S&T Innovation, China (Grant No. 2010R50010).
Chaos and chaotic control in a fractional-order electronic oscillator
Gao, Xin; Yu, Jue-Bang
2005-05-01
In this paper, we study the chaotic behaviours in a fractional-order chaotic electronic oscillator. We find that chaos exists in the fractional-order electronic oscillator with an order being less than 3. In addition, we numerically simulate the continuance of the chaotic behaviours in the electronic oscillator with orders ranging from 2.8 to 3.2. Finally, we further investigate the method of controlling a fractional-order electronic oscillator based on adaptive backstepping. Numerical simulations show the effectiveness and feasibility of this approach.
Chaos and chaotic control in a fractional-order electronic oscillator
Institute of Scientific and Technical Information of China (English)
Gao Xin; Yu Jue-Bang
2005-01-01
In this paper, we study the chaotic behaviours in a fractional-order chaotic electronic oscillator. We find that chaos exists in the fractional-order electronic oscillator with an order being less than 3. In addition, we numerically simulate the continuance of the chaotic behaviours in the electronic oscillator with orders ranging from 2.8 to 3.2. Finally, we further investigate the method of controlling a fractional-order electronic oscillator based on adaptive backstepping.Numerical simulations show the effectiveness and feasibility of this approach.
Synchronization of networks of chaotic oscillators: Structural and dynamical datasets
Directory of Open Access Journals (Sweden)
Ricardo Sevilla-Escoboza
2016-06-01
Full Text Available We provide the topological structure of a series of N=28 Rössler chaotic oscillators diffusively coupled through one of its variables. The dynamics of the y variable describing the evolution of the individual nodes of the network are given for a wide range of coupling strengths. Datasets capture the transition from the unsynchronized behavior to the synchronized one, as a function of the coupling strength between oscillators. The fact that both the underlying topology of the system and the dynamics of the nodes are given together makes this dataset a suitable candidate to evaluate the interplay between functional and structural networks and serve as a benchmark to quantify the ability of a given algorithm to extract the structural network of connections from the observation of the dynamics of the nodes. At the same time, it is possible to use the dataset to analyze the different dynamical properties (randomness, complexity, reproducibility, etc. of an ensemble of oscillators as a function of the coupling strength.
Chaotic, regular and unbounded behaviour in the elastic impact oscillator
Lamba, H
1993-01-01
A discontinuous area-preserving mapping derived from a sinusoidally-forced impacting system is studied. This system, the elastic impact oscillator, is very closely related to the accelerator models of particle physics such as the Fermi map. The discontinuity in the mapping is due to grazing which can have a surprisingly large effect upon the phase space. In particular, at the boundary of the stochastic sea, the discontinuity set and its images can act as a partial barrier which allows trajectories to move between chaotic and regular regions. The system at higher energies is also analysed and Moser's invariant curve theorem is used to find sufficient conditions for the existence of invariant curves that bound the energy of the motion. Finally the behaviour of the system under more general periodic forcing is briefly investigated.
Kondrashov, A. V.; Ustinov, A. B.; Kalinikos, B. A.; Demokritov, S. O.
2016-11-01
This paper reports the first experimental study of broadband chaotic nonlinear spin- wave excitations which is formed through development of four-wave parametric processes in active ring oscillator based on metallized ferrite film. We find that an increase in the oscillation power leads to Hopf bifurcations sequence. Monochromatic, periodic quasi-periodic and chaotic excitations are observed. Spectra of the chaotic excitations consist of series of chaotic bands separated well in frequency. Parameters of the chaotic attractors are discussed.
Chaotic oscillations of structures in mechanical engineering; Kikai kozo no kaosu shindo
Energy Technology Data Exchange (ETDEWEB)
Nagai, K. [Gunma University, Gunma (Japan). Faculty of Engineering; Yamaguchi, T.
1998-07-01
This paper describes the chaotic oscillations which are irregular unsteady oscillations of structures generated in mechanical engineering. The chaotic oscillations are apt to generate when the kinetic system contains both the stable balance and unstable balance in it at the same time. When an external force acts on the thin-walled structure of vehicle with a large portable volume, the chaotic oscillation response is generated with a dynamic snap through phenomenon. As a result of the numerical analysis using a simple model, the chaotic oscillation has non-linear characteristics. When a load is applied to the system, the snap through buckling occurs. For verifying the chaotic characteristics, are usually used the frequency distribution in which the chaotic oscillation response is analyzed using Fourier series expansion, Poincare map in which a series of points of displacement and velocity of the phase curve synchronized with the cycle of exciting force are extracted and mapped on a phase plane, or Lyapunov exponent which is a rate of continuous change in the distance between two points on the phase curve. The maximum Lyapunov exponent is calculated from the rate of change in the distance between the basic phase curve and the near-by phase curve. Thus, the chaotic oscillation can be determined. 31 refs., 7 figs.
Directory of Open Access Journals (Sweden)
HAITAO CUIa
2004-01-01
Full Text Available The current oscillations of a copper electrode in trichloroacetic acid solutions were studied in this paper. The Cu/CCl3COOH system is a new electrochemical oscillator, showing rich dynamic behaviour on two controllable parameters: the trichloroacetic acid concentration (cCCl3COOH and the imposed potential (E. Phase trajectories were reconstructed from time series using time delay methods in order that the complex oscillations could be analyzed. Five kinds of oscillations, periodic and quasiperiodic, mixed-mode, aperiodic, small amplitude and chaotic current oscillations, were observed. The EDS (energy dispersive spectroscopy technique was used to analyze the elemental composition of the film formed on the surface of the copper electrode after the current oscillations.
Lee, C; Zhu, X; Gao, K; Hai, W; Duan Yi Shi; Liu, W K; Lee, Chaohong; Shi, Lei; Zhu, Xiwen; Gao, Kelin; Hai, Wenhua; Duan, Yiwu; Liu, Wing-Ki
2001-01-01
We have investigated the chaotic atomic population oscillations between two coupled Bose-Einstein condensates (BEC) with time-dependent asymmetric trap potential. In the perturbative regime, the population oscillations can be described by the Duffing equation, and the chaotic oscillations near the separatrix solution are analyzed. The sufficient-necessary conditions for stable oscillations depend on the physical parameters and initial conditions sensitively. The first-order necessary condition indicates that the Melnikov function is equal to zero, so the stable oscillations are Melnikov chaotic. For the ordinary parameters and initial conditions, the chaotic dynamics is simulated with numerical calculation. If the damping is absent, with the increasing of the trap asymmetry, the regular oscillations become chaotic gradually, the corresponding stroboscopic Poincare sections (SPS) vary from a single island to more islands, and then the chaotic sea. For the completely chaotic oscillations, the long-term localiza...
Chaotic oscillations in a map-based model of neural activity.
Courbage, M; Nekorkin, V I; Vdovin, L V
2007-12-01
We propose a discrete time dynamical system (a map) as a phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find conditions under which this map has an invariant region on the phase plane, containing a chaotic attractor. This attractor creates chaotic spiking-bursting oscillations of the model. We also show various regimes of other neural activities (subthreshold oscillations, phasic spiking, etc.) derived from the proposed model.
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.
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. PMID:28796797
Persistent currents for interacting electrons in ballistic/chaotic billiards
Zelyak, Oleksandr; Murthy, Ganpathy
2005-03-01
We study persistent currents in a quantum billiard enclosing a magnetic flux φ by analytical and numerical methods. We concentrate on the family of Robnik-Berry billiards generated by conformal maps of the unit disk. We study the persistent current as a function of magnetic flux and parameters of the billiard in the chaotic regime. We include Fermi-liquid interactions in a mean-field approach, justified by the recent large-N approach[1] for ballistic/chaotic quantum dots. [1] G. Murthy, R. Shankar, D. Herman, and H. Mathur, Phys. Rev. B 69, 075321 (2004); G. Murthy, R. Shankar, and H. Mathur, cond-mat/0411280.
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.
Adaptive robust control of chaotic oscillations in power system with excitation limits
Institute of Scientific and Technical Information of China (English)
Wei Du-Qu; Luo Xiao-Shu
2007-01-01
With system parameters falling into a certain area, power system with excitation limits experiences complicated chaotic oscillations which threaten the secure and stable operation of power system. In this paper, to control these unwanted chaotic oscillations, a straightforward adaptive chaos controller based on Lyapunov asymptotical stability theory is designed. Since the presented controller does not need to change the controlled system structure and not to use any information of system except the system state variables, the designed controller is simple and desirable.Simulation results show that the proposed control law is very effective. This work is helpful to maintain the power system's security operation.
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.
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
Energy Technology Data Exchange (ETDEWEB)
Zhang Wei [College of Mechanical Engineering, Beijing University of Technology, Beijing 100022 (China)] e-mail: sandyzhang0@yahoo.com
2005-11-01
This paper presents an analysis of the chaotic motion and its control for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. A new method of controlling chaotic motion for the nonlinear nonplanar oscillations of the cantilever beam, refereed as to the force control approach, is proposed for the first time. The governing nonlinear equations of nonplanar motion under combined parametric and external excitations are obtained. The Galerkin procedure is applied to the governing equation to obtain a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations for the in-plane and out-of-plane modes. The work is focused on the case of 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance-primary resonance for the out-of-plane mode. The method of multiple scales is used to transform the parametrically and externally excited system to the averaged equations which have a constant perturbation force. Based on the averaged equations obtained here, numerical simulation is utilized to discover the periodic and chaotic motions for the nonlinear nonplanar oscillations of the cantilever beam. The numerical results indicate that the transverse excitation in the z direction at the free end can control the chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam. The methodology of controlling chaotic motion by using the transverse excitation is proposed. The transverse excitation in the z direction at the free end may be thought about to be an open-loop control. For the problem investigated in this paper, this approach is an effective methodology of controlling chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam.
Synchronization and quorum sensing in an ensemble of indirectly coupled chaotic oscillators
Li, Bing-Wei; Fu, Chenbo; Zhang, Hong; Wang, Xingang
2012-10-01
The fact that the elements in some realistic systems are influenced by each other indirectly through a common environment has stimulated a new surge of studies on the collective behavior of coupled oscillators. Most of the previous studies, however, consider only the case of coupled periodic oscillators, and it remains unknown whether and to what extent the findings can be applied to the case of coupled chaotic oscillators. Here, using the population density and coupling strength as the tuning parameters, we explore the synchronization and quorum sensing behaviors in an ensemble of chaotic oscillators coupled through a common medium, in which some interesting phenomena are observed, including the appearance of the phase synchronization in the process of progressive synchronization, the various periodic oscillations close to the quorum sensing transition, and the crossover of the critical population density at the transition. These phenomena, which have not been reported for indirectly coupled periodic oscillators, reveal a corner of the rich dynamics inherent in indirectly coupled chaotic oscillators, and are believed to have important implications to the performance and functionality of some realistic systems.
Finite-time synchronization of tunnel-diode-based chaotic oscillators.
Louodop, Patrick; Fotsin, Hilaire; Kountchou, Michaux; Ngouonkadi, Elie B Megam; Cerdeira, Hilda A; Bowong, Samuel
2014-03-01
This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel-diode-based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulations followed by pspice experiment are presented to show the feasibility of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Fotsin, Hilaire [Laboratoire d' Electronique, Departement de Physique, Faculte des Sciences, Universite de Dschang, B.P. 67 Dschang (Cameroon); INPL-CRAN, UMR CNRS-INPL-UHP 7039 ENSEM-2, Avenue de la Foret de Haye-54516, Vandoeuvre-les-Nancy Cedex (France); E-mail: hbfotsin@yahoo.fr; Bowong, Samuel [Laboratoire de Mathematiques Appliquees, Departement de Mathematiques et Informatique, Faculte des sciences, Universite de Douala, B.P. 24157 Douala (Cameroon)] e-mail: sbowong@uycdc.uninet.cm
2006-02-01
This paper deals with the problem of control and synchronization of coupled second-order oscillators showing a chaotic behavior. A classical feedback controller is first used to stabilize the system at its equilibrium. An adaptive observer is then designed to synchronize the states of the master and slave oscillators using a single scalar signal corresponding to an observable state variable of the driving oscillator. An interesting feature of the proposed approach is that it can be used for chaos control as well as synchronization purposes. Numerical simulations results confirming the analytical predictions are shown and pspice simulations are also performed to confirm the efficiency of the proposed control scheme.
Chaotic oscillator containing memcapacitor and meminductor and its dimensionality reduction analysis
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.
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 on the pa...... on the parameters of the nonlinear unit the oscillator operates either in a one-scroll or two-scroll mode. Two positive Lyapunov exponents, found at larger values of the negative slopes of the nonlinear function, characterize the oscillations as hyperchaotic....
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.
Sinusoidal synchronization of a Duffing oscillator with a chaotic pendulum
Energy Technology Data Exchange (ETDEWEB)
Min, Fuhong, E-mail: minfuhong@njnu.edu.cn [School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, Jiangsu 210042 (China); Luo, Albert C.J., E-mail: aluo@siue.edu [Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805 (United States)
2011-08-08
In this Letter, analytical conditions for the sinusoidal synchronization of the pendulum and Duffing oscillator are presented. From the analytical conditions, the invariant domain of such sinusoidal synchronization is determined, and the control parameter map of the synchronicity is achieved. Under specific parameters, numerical illustrations of the partial and full sinusoidal synchronizations of the controlled Duffing oscillator with the pendulum are carried out for a better understanding of such synchronization under specific function constraints. The methodology presented in this Letter is applicable to synchronizations with any specific function constraints. -- Highlights: → Synchronization dynamics of two distinct dynamical systems. → Invariant domain of sinusoidal synchronization. → Partial and full sinusoidal synchronizations. → Analytical conditions for sinusoidal synchronization of the pendulum and Duffing oscillator. → Control parameter map for sinusoidal synchronization of the controlled Duffing oscillator with pendulum.
Symbolic Dynamics and Chaotic Synchronization in Coupled Duffing Oscillators
Gracio, Clara; Caneco, Acilina; Rocha, José
2008-01-01
In this work we discuss the complete synchronization of two identical double-well Duffing oscillators unidirectionally coupled, from the point of view of symbolic dynamics. Working with Poincar´e cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized. We obtained analytically the threshold value of the coupling parameter for the synchronization of two unimodal and two bimodal piecewise linea...
A flux-controlled model of meminductor and its application in chaotic oscillator
Wang, Guang-Yi; Jin, Pei-Pei; Wang, Xiao-Wei; Shen, Yi-Ran; Yuan, Fang; Wang, Xiao-Yuan
2016-09-01
A meminductor is a new type of memory device developed from the memristor. We present a mathematical model of a flux-controlled meminductor and its equivalent circuit model for exploring the properties of the meminductor in a nonlinear circuit. We explore the response characteristics of the meminductor under the exciting signals of sinusoidal, square, and triangular waves by using theoretical analysis and experimental tests, and design a meminductor-based oscillator based on the model. Theoretical analysis and experiments show that the meminductor-based oscillator possesses complex bifurcation behaviors and can generate periodic and chaotic oscillations. A special phenomenon called the co-existent oscillation that can generate multiple oscillations (such as chaotic, periodic oscillations as well as stable equilibrium) with the same parameters and different initial conditions occurs. We also design an analog circuit to realize the meminductor-based oscillator, and the circuit experiment results are in accordance with the theory analysis. Project supported by the National Natural Science Foundation of China (Grant Nos. 61271064, 61401134, and 60971046), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LZ12F01001 and LQ14F010008), and the Program for Zhejiang Leading Team of S&T Innovation, China (Grant No. 2010R50010).
Chaotic mixing and fractals in a geophysical jet current
Budyansky, M V; 10.1016/j.cnsns.2006.05.004
2012-01-01
We model Lagrangian lateral mixing and transport of passive scalars in meandering oceanic jet currents by two-dimensional advection equations with a kinematic stream function with a time-dependent amplitude of a meander imposed. The advection in such a model is known to be chaotic in a wide range of the meander's characteristics. We study chaotic transport in a stochastic layer and show that it is anomalous. The geometry of mixing is examined and shown to be fractal-like. The scattering characteristics (trapping time of advected particles and the number of their rotations around elliptical points) are found to have a hierarchical fractal structure as functions of initial particle's positions. A correspondence between the evolution of material lines in the flow and elements of the fractal is established.
Optimal phase synchronization in networks of phase-coherent chaotic oscillators
Skardal, P. S.; Sevilla-Escoboza, R.; Vera-Ávila, V. P.; Buldú, J. M.
2017-01-01
We investigate the existence of an optimal interplay between the natural frequencies of a group of chaotic oscillators and the topological properties of the network they are embedded in. We identify the conditions for achieving phase synchronization in the most effective way, i.e., with the lowest possible coupling strength. Specifically, we show by means of numerical and experimental results that it is possible to define a synchrony alignment function J (ω ,L ) linking the natural frequencies ωi of a set of non-identical phase-coherent chaotic oscillators with the topology of the Laplacian matrix L, the latter accounting for the specific organization of the network of interactions between oscillators. We use the classical Rössler system to show that the synchrony alignment function obtained for phase oscillators can be extended to phase-coherent chaotic systems. Finally, we carry out a series of experiments with nonlinear electronic circuits to show the robustness of the theoretical predictions despite the intrinsic noise and parameter mismatch of the electronic components.
Synchronization of chaotic oscillations in doped fiber ring lasers
Lewis, C T; Kennel, M B; Buhl, M; Illing, L; Lewis, Clifford Tureman; Abarbanel, Henry D I; Kennel, Matthew B; Buhl, Michael; Illing, Lucas
1999-01-01
We investigate synchronization and subsequently communication using chaotic rare-earth-doped fiber ring lasers, represented by a physically realistic model. The lasers are coupled by transmitting a fraction c of the circulating electric field in the transmitter and injecting it into the optical cavity of the receiver. We then analyze a coupling strategy which relies on modulation of the intensity of the light alone. This avoids problems associated with the polarization and phase of the laser light. We study synchronization as a function of the coupling strength and see excellent convergence, even with small coupling constants. We prove that in an open-loop configuration (c=1) synchronization is guaranteed due to the particular structure of our equations and of the injection method we use for these coupled laser systems. We also analyze the generalized synchronization of these model lasers when there is parameter mismatch between the transmitter and the receiver. We then address communicating information betwe...
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.
Energy Technology Data Exchange (ETDEWEB)
Fotsin, H.B. [Faculte des Sciences, Universite de Dschang, B.P. 067 Dschang (Cameroon)]. E-mail: hbfotsin@yahoo.fr; Woafo, P. [Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon)
2005-06-01
This paper considers the problem of adaptive synchronization and parameter identification of an uncertain chaotic oscillator. Using recent results on adaptive control, we design a controller which enables both the synchronization of two unidirectionally coupled modified Van der Pol-Duffing oscillators and the estimation of unknown parameters of the drive oscillator.
Coupled predator-prey oscillations in a chaotic food web
Beninca, E.; Jöhnk, K.; Heerkloss, R.; Huisman, J.
2009-01-01
Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles
Coupled predator-prey oscillations in a chaotic food web
Benincà, E.; Johnk, K.D.; Heerkloss, R.; Huisman, J.
2009-01-01
Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles
Experimental Realization of a Multiscroll Chaotic Oscillator with Optimal Maximum Lyapunov Exponent
Directory of Open Access Journals (Sweden)
Esteban Tlelo-Cuautle
2014-01-01
Full Text Available Nowadays, different kinds of experimental realizations of chaotic oscillators have been already presented in the literature. However, those realizations do not consider the value of the maximum Lyapunov exponent, which gives a quantitative measure of the grade of unpredictability of chaotic systems. That way, this paper shows the experimental realization of an optimized multiscroll chaotic oscillator based on saturated function series. First, from the mathematical description having four coefficients (a, b, c, d1, an optimization evolutionary algorithm varies them to maximize the value of the positive Lyapunov exponent. Second, a realization of those optimized coefficients using operational amplifiers is given. Herein a, b, c, d1 are implemented with precision potentiometers to tune up to four decimals of the coefficients having the range between 0.0001 and 1.0000. Finally, experimental results of the phase-space portraits for generating from 2 to 10 scrolls are listed to show that their associated value for the optimal maximum Lyapunov exponent increases by increasing the number of scrolls, thus guaranteeing a more complex chaotic behavior.
Experimental realization of a multiscroll chaotic oscillator with optimal maximum Lyapunov exponent.
Tlelo-Cuautle, Esteban; Pano-Azucena, Ana Dalia; Carbajal-Gomez, Victor Hugo; Sanchez-Sanchez, Mauro
2014-01-01
Nowadays, different kinds of experimental realizations of chaotic oscillators have been already presented in the literature. However, those realizations do not consider the value of the maximum Lyapunov exponent, which gives a quantitative measure of the grade of unpredictability of chaotic systems. That way, this paper shows the experimental realization of an optimized multiscroll chaotic oscillator based on saturated function series. First, from the mathematical description having four coefficients (a, b, c, d1 ), an optimization evolutionary algorithm varies them to maximize the value of the positive Lyapunov exponent. Second, a realization of those optimized coefficients using operational amplifiers is given. Herein a, b, c, d1 are implemented with precision potentiometers to tune up to four decimals of the coefficients having the range between 0.0001 and 1.0000. Finally, experimental results of the phase-space portraits for generating from 2 to 10 scrolls are listed to show that their associated value for the optimal maximum Lyapunov exponent increases by increasing the number of scrolls, thus guaranteeing a more complex chaotic behavior.
Weak signal detection based on the information fusion and chaotic oscillator.
Xiang, Xiuqiao; Shi, Baochang
2010-03-01
Based on the chaotic oscillator, a method for weak signal detection using information fusion technology is proposed in this paper. On the one hand, various methods are employed to the amplitude detection of the same weak periodic signal, then the detection outcomes are fused by the adaptive weighted fusion method. On the other hand, during the detection course, information entropy, statistic distance, and Walsh transform are, respectively, used in the state recognition of chaotic oscillator from the viewpoint of time domain or frequency domain, then the recognition results are fused by the k/l fusion method. Numerical results show that the proposed approach detects signal more precisely, identifies state more accurately, and represents information more completely compared with traditional methods.
New Route to Phase Synchronization in Chaotic Oscillators
Kim, I; Kye, W H; Park, Y J; Kim, Inbo; Kim, Chil-Min; Kye, Won-Ho; Park, Young-Jai
1999-01-01
We study a new type of \\pm 2 \\pi irregular phase jumping behavior before the onset of phase synchronization (PS) in a system of two coupled self-sustained hyperchaotic Rössler oscillators. The behavior is understood as a stochastic hopping of an overdamped particle in a potential which has 2 noise through the return map analysis. In \\epsilon_t \\sim \\exp(|\\epsilon_t - \\epsilon|^2), which agrees well with the scaling law obtained from the Fokker- Planck equation.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The chaotic dynamics of a Duffing oscillator with a parametric force is investigated. By using the direct perturbation technique, we analytically obtain the general solution of the 1st-order equation. Through the boundedness condition of the general solution we get the famous Melnikov function predicting the onset of chaos. When the parametric and external forces are strong, numerical simulations show that increasing the amplitude of the parametric or external force can lead the system into chaos via period doubling.
Nonlinear Resistor with Polynomial AV Characteristics and Its Application in Chaotic Oscillator
Directory of Open Access Journals (Sweden)
V. Pospisil
2004-06-01
Full Text Available This paper shows the realization of two terminal devices with anarbitrary polynomial nonlinearity up to the fifth order. The proposeddesign procedure is completely systematic using minimum of components.The very heart of our conception is four-channel four-quadrant analogmultiplier MLT04. The implementation of synthesized nonlinear resistoras a general nonlinearity in chaotic oscillator is also presented andexperimentally verified.
The Radiative Kicked Oscillator A Stochastic Web or Chaotic Attractor ?
Ashkenazy, Yu
1999-01-01
A relativistic charged particle moving in a uniform magnetic field and kicked by an electric field is considered. Under the assumption of small magnetic field, an iterative map is developed. We consider both the case in which no radiation is assumed and the radiative case, using the Lorentz-Dirac equation to describe the motion. Comparison between the non-radiative case and the radiative case shows that in both cases one can observe a stochastic web structure for weak magnetic fields, and, although there are global differences in the result of the map, that both cases are qualitatively similar in their small scale behavior. We also develop an iterative map for strong magnetic fields. In that case the web structure no longer exists; it is replaced by a rich chaotic behavior. It is shown that the particle does not diffuse to infinite energy; it is limited by the boundaries of an attractor (the boundaries are generally much smaller than light velocity). Bifurcation occurs, converging rapidly to Feigenbaum's univ...
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.
Li, Bing-Wei; Cao, Xiao-Zhi; Fu, Chenbo
2017-05-01
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.
Improved Time Response of Stabilization in Synchronization of Chaotic Oscillators Using Mathematica
Directory of Open Access Journals (Sweden)
Mohammad Shahzad
2016-06-01
Full Text Available Chaotic dynamics are an interesting topic in nonlinear science that has been intensively studied during the last three decades due to its wide availability. Motivated by much researches on synchronization, the authors of this study have improved the time response of stabilization when parametrically excited Φ6—Van der Pol Oscillator (VDPO and Φ6—Duffing Oscillator (DO are synchronized identically as well as non-identically (with each other using the Linear Active Control (LAC technique using Mathematica. Furthermore, the authors have synchronized the same pairs of the oscillators using a more robust synchronization with faster time response of stability called Robust Adaptive Sliding Mode Control (RASMC. A comparative study has been done between the previous results of Njah’s work and our results based on Mathematica via LAC. The time response of stabilization of synchronization using RASMC has been discussed.
Gentili, Pier Luigi; Giubila, Maria Sole; Heron, B Mark
2017-02-03
This work demonstrates the computational power of a hydrodynamic photochemical oscillator based on a photochromic naphthopyran, generating aperiodic time series. The chaotic character of the time series is tested by calculating its largest Lyapunov exponent and the correlation dimension of its attractor after building its phase space through the Takens' theorem. Then, the chaotic dynamic is shown to be suitable to implement all the fundamental Boolean two-inputs-one-output logic gates. Finally, the strategy to implement Fuzzy logic systems (FLSs) based on the time series is described. Such FLSs promise to be useful in the field of Computational Linguistics that is concerned with the development of artificial intelligent systems able to transform collections of numerical data in natural language texts.
Che, Yanqiu; Li, Ruixue; Li, Huiyan; Han, Chunxiao; Wang, Jiang; Wei, Xile
2014-01-01
In this paper, we propose a dynamic delayed feedback control approach for desynchronization of chaotic-bursting synchronous activities in an ensemble of globally coupled neuronal oscillators. We demonstrate that the difference signal between an ensemble's mean field and its time delayed state, filtered and fed back to the ensemble, can suppress the self-synchronization in the ensemble. These individual units are decoupled and stabilized at the desired desynchronized states while the stimulation signal reduces to the noise level. The effectiveness of the method is illustrated by examples of two different populations of globally coupled chaotic-bursting neurons. The proposed method has potential for mild, effective and demand-controlled therapy of neurological diseases characterized by pathological synchronization.
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.
Chaotic oscillation and random-number generation based on nanoscale optical-energy transfer
Naruse, Makoto; Kim, Song-Ju; Aono, Masashi; Hori, Hirokazu; Ohtsu, Motoichi
2014-08-01
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.
Chaotic oscillation and random-number generation based on nanoscale optical-energy transfer
Naruse, Makoto; Aono, Masashi; Hori, Hirokazu; Ohtsu, Motoichi
2014-01-01
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 (R...
An open-plus-closed-loop control for chaotic Mathieu-Duffing oscillator
Institute of Scientific and Technical Information of China (English)
Jian-he SHEN; Shu-hui CHEN
2009-01-01
By using the idea of open-plus-closed-loop(OPCL) control, a controller com-posed of an external excitation and a linear feedback is designed to entrain chaotic tra-jectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of this open-plus-closed-loop control is proved by combining the Lyapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations are performed to ver-ify the theoretical results.
Senkerik, Roman; Oplatkova, Zuzana; Zelinka, Ivan; Davendra, Donald; Jasek, Roman
2012-11-01
This research deals with a synthesis of control law for selected discrete chaotic system - logistic equation by means of analytic programming. The novelty of the approach is that a tool for symbolic regression - analytic programming - is used for the purpose of stabilization of higher periodic orbits - oscillations between several values of chaotic system. The paper consists of the descriptions of analytic programming as well as used chaotic system and detailed proposal of cost function used in optimization process. For experimentation, Self-Organizing Migrating Algorithm (SOMA) with analytic programming and Differential evolution (DE) as second algorithm for meta-evolution were used.
Energy Technology Data Exchange (ETDEWEB)
Kengne, Jacques [Laboratoire d' Automatique et Informatique Apliquée (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Bandjoun (Cameroon); Kenmogne, Fabien [Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototype, University of Yaoundé 1, Yaoundé (Cameroon)
2014-12-15
The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by using time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.
Emergent organization of oscillator clusters in coupled self-regulatory chaotic maps
Indian Academy of Sciences (India)
Hiroyasu Ando; Sudeshna Sinha; Kazuyuki Aihara
2008-06-01
Here we introduce a model of parametrically coupled chaotic maps on a one-dimensional lattice. In this model, each element has its internal self-regulatory dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site is adjusted by feedback from its past evolution. Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a power-law distribution. Moreover, we find that the transient dynamics gives rise to a 1/ power spectrum. All these characteristics indicate self-organization and emergent scaling behavior in this system. We also interpret the power-law characteristics of the proposed system from an ecological point of view.
Indian Academy of Sciences (India)
Horacio Castellini; Efta Yudiarsah; Lilia Romanelli; Hilda A Cerdeira
2005-04-01
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 central pattern generator (CPG) in the animal brain. They modeled the CPG by coupling four nonlinear oscillators and found that it was possible to reproduce all symmetries of the gaits by changing the coupling strength. Here we propose to extend this idea using coupled chaotic oscillators synchronized using the Pyragas method in order to characterize the CPG symmetries. We also evaluate the time series behavior when the foot is in contact with the ground: this has potential robotic applications.
Dynamical hysteresis and spatial synchronization in coupled non-identical chaotic oscillators
Indian Academy of Sciences (India)
Awadesh Prasad; Leon D Iasemidis; Shivkumar Sabesan; Kostas Tsakalis
2005-04-01
We identify a novel phenomenon in distinct (namely non-identical) coupled chaotic systems, which we term dynamical hysteresis. This behavior, which appears to be universal, is defined in terms of the system dynamics (quantified for example through the Lyapunov exponents), and arises from the presence of at least two coexisting stable attractors over a finite range of coupling, with a change of stability outside this range. Further characterization via mutual synchronization indices reveals that one attractor corresponds to spatially synchronized oscillators, while the other corresponds to desynchronized oscillators. Dynamical hysteresis may thus help to understand critical aspects of the dynamical behavior of complex biological systems, e.g. seizures in the epileptic brain can be viewed as transitions between different dynamical phases caused by time dependence in the brain's internal coupling.
Abnormal Synchronizing Path of Delay-coupled Chaotic Oscillators on the Edge of Stability
Zhuo, Zhao; Fu, Zhong-Qian
2015-01-01
In this paper, the transition of synchronizing path of delay-coupled chaotic oscillators in a scale-free network is highlighted. Mainly, through the critical transmission delay makes chaotic oscillators be coupled on the edge of stability, we find that the transition of synchronizing path is \\emph{abnormal}, which is characterized by the following evidences: (a) synchronization process starts with low-degree rather than high-degree ones; (b) the high-degree nodes don't undertake the role of hub; (c) the synchronized subnetworks show a poor small-world property as a result of hubs absence; (d) the clustering synchronization behavior emerges even community structure is absent in the scale-free network. This abnormal synchronizing path suggests that the diverse synchronization behaviors occur in the same topology, which implies that the relationship between dynamics and structure of network is much more complicated than the common sense that the structure is the foundation of dynamics. Moreover, it also reveals ...
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.
Two-dimensional Insect Flight on an Air-Water Interface is a Chaotic Oscillator
Mukundarajan, Haripriya; Prakash, Manu
2014-01-01
Two-dimensional flapping wing insect flight on an air-water interface provides a successful foraging strategy to explore an ecological niche on the surface of a pond. However, the complex interplay of surface tension, aerodynamic forces, biomechanics and neural control that enables two-dimensional flight is unknown. Here we report the discovery of two-dimensional flight in the waterlily beetle Galerucella nymphaeae, which is the fastest reported propulsion mode for an insect on a fluid interface. Using kinematics derived from high-speed videography coupled with analytical models, we demonstrate that two-dimensional flight is a chaotic interfacial oscillator, thus significantly constraining the possible range of flight parameters. Discovery of this complex dynamics in two-dimensional flight on time scales similar to neural responses indicates the challenge of evolving active flight control on a fluid interface.
Kengne, J.; Njitacke Tabekoueng, Z.; Fotsin, H. B.
2016-07-01
We perform a systematic analysis of a system consisting of an autonomous third order Duffing-Holmes type chaotic oscillator recently introduced by Tamasevicius et al. (2009). In this type of oscillators, the symmetrical characteristics of the nonlinear component necessary for generating chaotic oscillations is synthesized by using a pair of semiconductor diodes connected in anti-parallel. Based on the Shockley diode equation and a judicious choice of state variables, we derive a smooth mathematical model (involving hyperbolic sine and cosine functions) for a better description of both the regular and chaotic dynamics of the oscillator. The bifurcation analysis shows that chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. More interestingly, some regions of the parameter space corresponding to the coexistence of multiple attractors (e.g. coexistence of four different attractors for the same values of system parameters) are discovered. This striking phenomenon is unique and has not yet been reported previously in an electrical circuit (the universal Chua's circuit included, in spite the immense amount of related research work), and thus represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. Some PSpice simulations of the nonlinear dynamics of the oscillator are carried out to verify the theoretical analysis.
用输入-输出线性化控制混沌振动%Controlling Chaotic Oscillations with Input-Output Linearization
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper, the nonlinear control of chaotic oscillations was investigated by using the input-output linearization control method. The chaotic attitude of a kind of spacecraft was discussed. It is demonstrated that the input-output linearization control law is the nonlinear version of the parametric open-plus-closed-loop control law.
The North-South asymmetry of solar activity: A signature of two coupled chaotic oscillators?
Donner, Reik V.
2010-05-01
The phase-coherent oscillatory dynamics on the 11-year frequency band (Schwabe cycle) is a common feature in all characteristic observables of solar activity. In this work, a wavelet-based framework [1,2] is applied for studying the mutual phase synchronicity of these oscillations. As a problem of specific scientific interest, the variability recorded on both solar hemispheres is systematically studied. It is demonstrated that time-varying phase shifts between the activity on Northern and Southern hemispheres provides a major contribution to the so-called North-South asymmetry (NSA). The presented results indicate that the NSA observations are consistent with the assumption of a different long-term phase diffusion of two weekly chaotic coupled oscillators, which evolve coherently in time. The obtained quantitative results on the variability of interhemispheric phase shifts are critically compared with the outcome of other studies using complementary methods of time series analysis [3]. The statistical reliability and implications of the derived long-term phase shift variability result are discussed. By using sophisticated methods for time series continuation and extrapolation [4], the recently hypothesised relationship between strong phase asynchrony of hemispheric variability and the occurrence of great minima of solar activity [5] is critically reexamined. References: [1] R. Donner, M. Thiel, A&A 475, L33-L36 (2007) [2] R. Donner, in: Nonlinear Time Series Analysis in the Geosciences (ed. by R.V. Donner and S.M. Barbosa), Springer, Berlin, 2008, pp. 355-386 [3] N.V. Zolotova, D.I. Ponyavin, N. Marwan, J. Kurths, A&A 503, 197-201 (2009) [4] C. Komalapriya, M. Thiel, M.C. Romano, N. Marwan, U. Schwarz, J. Kurths, Phys. Rev. E 78, 066217 (2008) [5] N.V. Zolotova, D.I. Ponyavin, A&A 470, L17-L20 (2007)
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.
Hannestad, Steen; Tram, Thomas
2013-01-01
While the cosmic baryon asymmetry has been measured at high accuracy to be 6.1*10^-10, a corresponding lepton asymmetry could be as large as 10^-2 if it hides in the neutrino sector. It has been known for some time that a large asymmetry can be generated from a small initial asymmetry given the existence of a sterile neutrino with a mass less than the mass of the active neutrino. While the magnitude of the final lepton asymmetry is deterministic, its sign has been conjectured to be chaotic in nature. This has been proven in the single momentum approximation, also known as the quantum rate equations, but has up to now not been established using the full momentum dependent quantum kinetic equations. Here we investigate this problem by solving the quantum kinetic equations for a system of 1 active and 1 sterile neutrino on an adaptive grid. We show that by increasing the resolution oscillations in the lepton asymmetry are eliminated and that the sign of the lepton asymmetry is in fact deterministic. This paper a...
Energy Technology Data Exchange (ETDEWEB)
Hannestad, Steen; Hansen, Rasmus Sloth [Department of Physics and Astronomy, University of Aarhus, 8000 Aarhus C (Denmark); Tram, Thomas, E-mail: sth@phys.au.dk, E-mail: rshansen@phys.au.dk, E-mail: thomas.tram@epfl.ch [Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland)
2013-04-01
While the cosmic baryon asymmetry has been measured at high accuracy to be 6.1 × 10{sup −10}, a corresponding lepton asymmetry could be as large as 10{sup −2} if it hides in the neutrino sector. It has been known for some time that such an asymmetry could be generated from a small initial asymmetry given the existence of a sterile neutrino with a mass less than the mass of the active neutrino. While the magnitude of the final lepton asymmetry is deterministic, its sign has been conjectured to be chaotic in nature. This has been proven in the single momentum approximation, also known as the quantum rate equations, but has up to now not been established using the full momentum dependent quantum kinetic equations. Here we investigate this problem by solving the quantum kinetic equations for a system of 1 active and 1 sterile neutrino on an adaptive grid. We show that by increasing the resolution, oscillations in the lepton asymmetry can be eliminated so the sign of the final lepton asymmetry is in fact deterministic. This paper also serves as a launch paper for the adaptive solver LASAGNA which is available at http://users-phys.au.dk/steen.
Everitt, M J; Stiffell, P B; Ralph, J F; Bulsara, A R; Harland, C J
2005-01-01
The driven non-linear duffing osillator is a very good, and standard, example of a quantum mechanical system from which classical-like orbits can be recovered from unravellings of the master equation. In order to generated such trajectories in the phase space of this oscillator in this paper we use a the quantum jumps unravelling together with a suitable application of the correspondence principle. We analyse the measured readout by considering the power spectra of photon counts produced by the quantum jumps. Here we show that localisation of the wave packet from the measurement of the oscillator by the photon detector produces a concomitant structure in the power spectra of the measured output. Furthermore, we demonstrate that this spectral analysis can be used to distinguish between different modes of the underlying dynamics of the oscillator.
Storch, Natalia I.; Lai, Dong
2015-04-01
Many exoplanetary systems containing hot Jupiters (HJs) are found to possess significant misalignment between the spin axis of the host star and the planet's orbital angular momentum axis. A possible channel for producing such misaligned HJs involves Lidov-Kozai oscillations of the planet's orbital eccentricity and inclination driven by a distant binary companion. We have recently shown that a proto-HJ undergoing Lidov-Kozai oscillations can induce chaotic evolution of the spin axis of its host star. Here we explore the origin of the chaotic spin behaviour and its various features in a simplified system where the secular oscillations of the planet's orbit are strictly periodic. Using Hamiltonian perturbation theory, we identify a set of secular spin-orbit resonances in the system, and show that resonance overlaps are responsible for the onset of wide-spread chaos in the evolution of stellar spin axis. The degree of chaos in the system depends on the adiabaticity parameter ɛ, proportional to the ratio of the Lidov-Kozai nodal precession rate and the stellar spin precession rate, and thus depends on the planet mass, semimajor axis and the stellar rotation rate. For systems with zero initial spin-orbit misalignment, our theory successfully explains the occurrence (as a function of ɛ) of large-scale chaotic variation, as well as regions of restricted chaos and quasi-periodic bands. Finally, we discuss a novel `adiabatic resonance advection' phenomenon, in which the spin-orbit misalignment, trapped in a resonance, gradually evolves as ɛ slowly changes. This phenomenon can occur for certain parameter regimes when tidal decay of the planetary orbit is included.
Electronically Tunable Current-Mode Quadrature Oscillator Using Single MCDTA
Directory of Open Access Journals (Sweden)
Y. Li
2010-12-01
Full Text Available This paper presents a modified current differencing transconductance amlpifier (MCDTA and the MCDTA based quadrature oscillator. The oscillator is current-mode and provides current output from high output impedance terminals. The circuit uses only one MCDTA and two grounded capacitors, and is easy to be integrated. Its oscillation frequency can be tuned electronically by tuning bias currents of MCDTA. Finally, frequency error is analyzed. The results of circuit simulations are in agreement with theory.
Analytically solvable chaotic oscillator based on a first-order filter.
Corron, Ned J; Cooper, Roy M; Blakely, Jonathan N
2016-02-01
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.
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.
de Oliveira, G L
2016-01-01
In this work we show a strategy for synchronization of three optoelectronic oscillators (OEO) operating in chaotic regime. Two applications of synchronized OEOs in secure communications are considered. In the first one the OEO is used to produce a pseudo-random bit sequence. The second application is an optical setup for secure transmission of sampled analog signals. Using numerical simulations, we calculated the bit error rate taking into account parameter mismatch noise and Gaussian noise in the input optical power. The conditions for error rate of up to 15% during key generation are shown.
Terahertz Current Oscillation in Wurtzite InN
Institute of Scientific and Technical Information of China (English)
FENG Wei
2012-01-01
Current self-oscillation in doped n+nn+ wurtzite InN diodes driven by a dc electric field is theoretically investigated by solving the time-dependent drift-diffusion model. Current self-oscillation is associated with the negative differential mobility effect in the highly non-parabolic conduction band of InN. A detailed analysis of the dependence of current oscillations on the doping concentration and the applied electric Reid is presented. The current oscillation frequencies can reach up to the terahertz (THz) region. The n+nn+ InN self-oscillating diode may be a promising candidate for THz generation, and the calculation results may guide the design of the devices.%Current self-oscillation in doped n+nn+ wurtzite InN diodes driven by a dc electric field is theoretically investigated by solving the time-dependent drift-diffusion model.Current self-oscillation is associated with the negative differential mobility effect in the highly non-parabolic conduction band of InN.A detailed analysis of the dependence of current oscillations on the doping concentration and the applied electric field is presented.The current oscillation frequencies can reach up to the terahertz (THz) region.The n + nn+ InN self-oscillating diode may be a promising candidate for THz generation,and the calculation results may guide the design of the devices.
Energy Technology Data Exchange (ETDEWEB)
Fotsin, Hilaire [Laboratoire d' electronique, Departement de Physique, Faculte des Sciences, Universite de Dschang, BP 067 Dschang (Cameroon); Laboratoire de Mathematiques Appliquees, Departement de Mathematiques et d' lnformatique, Faculte des sciences, Universite de Douala, BP 24157 Douala (Cameroon); E-mail: hbfotsin@yahoo.fr; Bowong, Samuel [CRAN-INPL-ENSEM-2, Avenue de la Foret de Haye-54516, Vandoeuvre-les-Nancy Cedex (France); E-mail: sbowong@uycdc.uninet.cm; Daafouz, Jamal [Laboratoire de Mathematiques Appliquees, Departement de Mathematiques et d' lnformatique, Faculte des sciences, Universite de Douala, BP 24157 Douala (Cameroon)
2005-10-01
In this paper, chaos synchronization between two chaotic systems consisting of modified Van der Pol-Duffing (MVDPD) and Chua oscillators is studied. Such a problem is related to chaos synchronization of different systems. An adaptive feedback synchronization with two controllers is proposed to ensure global chaos synchronization of the modified Van der Pol-Duffing and Chua circuit oscillators. Numerical simulations show the effectiveness of the proposed control method. Moreover, as an application, the proposed scheme is then applied to secure communication whose process consists of a robust filter that recovers the information signal from the scalar transmitted signal. Also, simulation results verify the proposed scheme's success in the communication application.
Shapes and Statistics of the Rogue Waves Generated by Chaotic Ocean Current
Bayindir, Cihan
2015-01-01
In this study we discuss the shapes and statistics of the rogue (freak) waves emerging due to wave-current interactions. With this purpose, we use a simple governing equation which is a nonlinear Schrodinger equation (NLSE) extended by R. Smith (1976). This extended NLSE accounts for the effects of current gradient on the nonlinear dynamics of the ocean surface near blocking point. Using a split-step scheme we show that the extended NLSE of Smith is unstable against random chaotic perturbation in the current profile. Therefore the monochromatic wave field with unit amplitude turns into a chaotic sea state with many peaks. By comparing the numerical and analytical results, we show that rogue waves due to perturbations in the current profile are in the form of rational rogue wave solutions of the NLSE. We also discuss the effects of magnitude of the chaotic current profile perturbations on the statistics of the rogue wave generation at the ocean surface. The extension term in Smith's extended NLSE causes phase ...
A Simple Current-Mode Quadrature Oscillator Using Single CDTA
Directory of Open Access Journals (Sweden)
D. Biolek
2008-12-01
Full Text Available This article presents a simple current-mode quadrature oscillator using a single Current Differencing Transconductance Amplifier (CDTA as the active element. The oscillation condition and oscillation frequency can be electronically controlled. The circuit structure is very simple, consisting of merely one CDTA, one resistor and two capacitors. The proposed circuit is suitable for IC architecture. The PSpice simulation and experimental results are shown, and the results agree well with the theoretical assumptions.
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.
Hayashi, Kenta; Gotoda, Hiroshi; Gentili, Pier Luigi
2016-05-01
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.
Low Starting Electron Beam Current in Degenerate Band Edge Oscillators
Othman, Mohamed A K; Figotin, Alexander; Capolino, Filippo
2016-01-01
We propose a new principle of operation in vacuum electron-beam-based oscillators that leads to a low beam current for starting oscillations. The principle is based on super synchronous operation of an electron beam interacting with four degenerate electromagnetic modes in a slow-wave structure (SWS). The four mode super synchronous regime is associated with a very special degeneracy condition in the dispersion diagram of a cold periodic SWS called degenerate band edge (DBE). This regime features a giant group delay in the finitelength SWS and low starting-oscillation beam current. The starting beam current is at least an order of magnitude smaller compared to a conventional backward wave oscillator (BWO) of the same length. As a representative example we consider a SWS conceived by a periodically-loaded metallic waveguide supporting a DBE, and investigate starting-oscillation conditions using Pierce theory generalized to coupled transmission lines (CTL). The proposed super synchronism regime can be straightf...
Meinert, F; Mark, M J; Kirilov, E; Lauber, K; Weinmann, P; Gröbner, M; Nägerl, H-C
2014-05-16
We study atomic Bloch oscillations in an ensemble of one-dimensional tilted superfluids in the Bose-Hubbard regime. For large values of the tilt, we observe interaction-induced coherent decay and matter-wave quantum phase revivals of the Bloch oscillating ensemble. We analyze the revival period dependence on interactions by means of a Feshbach resonance. When reducing the value of the tilt, we observe the disappearance of the quasiperiodic phase revival signature towards an irreversible decay of Bloch oscillations, indicating the transition from regular to quantum chaotic dynamics.
Sun, Jitao; Lin, Hai
2008-09-01
This paper investigates the stationary oscillation for an impulsive delayed system which represents a class of nonlinear hybrid systems. First, a new concept of S-stability is introduced for nonlinear impulsive delayed systems. Based on this new concept and fixed point theorem, the relationship between S-stability and stationary oscillation (i.e., existence, uniqueness and global stability of periodic solutions) for the nonlinear impulsive delayed system is explored. It is shown that the nonlinear impulsive delayed system has a stationary oscillation if the system is S-stable. Second, an easily verifiable sufficient condition is then obtained for stationary oscillations of nonautonomous neural networks with both time delays and impulses by using the new criterion. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.
Persistent Currents and Addition Spectrum in Strongly Interacting Chaotic Quantum Dots
Herman, Damir; Mathur, H.; Murthy, Ganpathy
2003-03-01
Murthy and Shankar(Ganpathy Murthy, R. Shankar, Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit), family cond-mat/0209136 have introduced a non-perturbative approach to analyzing the effects of interaction and randomness in chaotic quantum dots in the limit of large Thouless number. Using this framework we study two experimentally observable quantities in the strongly interacting regime. First we compare the Coulomb blockade peak spacing distribution in the strong coupling regime to the distribution in the weak coupling regime (described by the ``universal Hamiltonian''). Second we study persistent currents in mesoscopic rings in the regime of strong interaction.
Chaotic jumps in the generalized first adiabatic invariant in current sheets
Brittnacher, M. J.; Whipple, E. C.
1991-01-01
The present study examines how the changes in the generalized first adiabatic invariant J derived from the separatrix crossing theory can be incorporated into the drift variable approach to generating distribution functions. A method is proposed for determining distribution functions for an ensemble of particles following interaction with the tail current sheet by treating the interaction as a scattering problem characterized by changes in the invariant. Generalized drift velocities are obtained for a 1D tail configuration by using the generalized first invariant. The invariant remained constant except for the discrete changes caused by chaotic scattering as the particles cross the separatrix.
双阱中Duffing振子的混沌行为%Chaotic Behavior of the Duffing Oscillator in a Double-well
Institute of Scientific and Technical Information of China (English)
方见树
2002-01-01
A general unstable chaotic solution of the Duffing oscillator in a double-well with weak periodic perturbations is obtained by using the direct perturbation method in this paper. A theoretical analysis reveals that the stable periodic orbits are embedded in the Melnikov chaotic attractors. The corresponding chaotic region and orbits in parameter space are descrbed by numerical simulations.%利用直接微扰的方法求出了双阱中具有弱周期微扰的Duffing 振子混沌解的一般表达式.理论分析表明, 稳定的周期轨道被嵌在Melnikov 混沌吸引子中.运用数值模拟方法得到了在参数空间中相应的混沌区域和混沌轨道.
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...
Closed-loop transcranial alternating current stimulation of slow oscillations
Directory of Open Access Journals (Sweden)
Wilde Christian
2015-09-01
Full Text Available Transcranial alternating current stimulation (tACS is an emerging non-invasive tool for modulating brain oscillations. There is evidence that weak oscillatory electrical stimulation during sleep can entrain cortical slow oscillations to improve the memory consolidation in rodents and humans. Using a novel method and a custom built stimulation device, automatic stimulation of slow oscillations in-phase with the endogenous activity in a real-time closed-loop setup is possible. Preliminary data from neuroplasticity experiments show a high detection performance of the proposed method, electrical measurements demonstrate the outstanding quality of the presented stimulation device.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we propose a backstepping approach for the synchronization and control of modified Van-der Pol Duffing oscillator circuits.The method is such that one controller function that depends essentially on available circuit parameters that is sufficient to drive the two coupled circuits to a synchronized state as well achieve the global stabilization of the system to its regular dynamics.Numerical simulations are given to demonstrate the effectiveness of the technique.
Application of the Duffing Chaotic Oscillator Model for Early Fault Diagnosis- Ⅰ.Basic Theory
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper, the well-known Duf fing equation and the nonlinear equation describing vibration of the human eardrum are introduced from elastic nonlinear system theory. According to the fact that the human ear can distinguish weak sound with smalldifference, the idea that the Duffing oscillator can be used to detect a weak signal and diagnose early fault of machinery is proposed. In order to obtain a model for weak signaldetection via the Duffing oscillator, the first step is to seek all forms of solutions of theDu f fing equation. The second step is to study global bifurcations of the Du f fing equationusing qualitative analysis theory of a dynamic system. That is to say, a series of bifurcations thresholds of the Duffing equation can be analyzed by the Melnikov function and asubharmonics Melnikov function. Then the three types of bifurcations thresholds varyingwith damping and external exciting amplitude are discussed. The analysis concludes thatthe bifurcation threshold corresponding to the maximum orbit of solutions outside the homoclinic orbit of the Duffing equation can be used to detect a weak signal. Finally, the implementing model of the Du ffing oscillator for weak signal detection is given.
Energy Technology Data Exchange (ETDEWEB)
Tang, Yanmei; Li, Xinli; Bai, Yan [School of Control and Computer Engineering, North China Electric Power University, Beijing (China)
2014-04-11
The measurement of multiphase flow parameters is of great importance in a wide range of industries. In the measurement of multiphase, the signals from the sensors are extremely weak and often buried in strong background noise. It is thus desirable to develop effective signal processing techniques that can detect the weak signal from the sensor outputs. In this paper, two methods, i.e., lock-in-amplifier (LIA) and improved Duffing chaotic oscillator are compared to detect and process the weak signal. For sinusoidal signal buried in noise, the correlation detection with sinusoidal reference signal is simulated by using LIA. The improved Duffing chaotic oscillator method, which based on the Wigner transformation, can restore the signal waveform and detect the frequency. Two methods are combined to detect and extract the weak signal. Simulation results show the effectiveness and accuracy of the proposed improved method. The comparative analysis shows that the improved Duffing chaotic oscillator method can restrain noise strongly since it is sensitive to initial conditions.
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...
四阶忆阻考毕兹混沌振荡器研究%Research on Fourth-Order Memristive Colpitts Chaotic Oscillator
Institute of Scientific and Technical Information of China (English)
徐权; 林毅; 包伯成; 王宁
2016-01-01
By introducing first-order generalized memristor into a third-order Colpitts chaotic oscillator,a new fourth-order memristive Colpitts chaotic oscillator is proposed.The first-order generalized memristor is realized by a full-wave rectifier cascaded with a first-order parallel RC filter.The dynamical model of the memristive Colpitts chaotic oscillator is established,upon which the equilibrium point and its stability are studied.The results indicate that the fourth-order colpitts chaotic oscillator has only one unstable saddle-foci.Furthermore,the dynamics depending on circuit element parameter is investigated.The nonlinear phenomena of chaotic oscillations and periodic limit cycle are illustrated by combining the theoretical analy-sis,numerical simulation and experimental measurement.The experimental measurement and numerical simulation are consistent well,which well verifies the theoretical analysis.%通过在三阶考毕兹混沌振荡器中引入一阶广义忆阻器，提出了一种新颖的四阶忆阻考毕兹混沌振荡器，其中一阶广义忆阻器由二极管桥级联一阶 RC滤波器构成。建立了忆阻考毕兹混沌振荡器的动力学模型，研究了它的平衡点和稳定性，结果表明：四阶忆阻考毕兹混沌振荡器具有唯一的不稳定鞍焦。进一步开展了依赖于电路元件参数的动力学特性研究。采用理论分析、数值仿真和实验验证相结合的方法，对电路展现出的混沌吸引子、周期极限环等复杂的非线性现象进行了研究，实验结果与数值仿真结果相一致，较好地验证了理论分析结果。
Mechanism of Current Oscillations in Gallium Arsenide Photoconductive Semiconductor Switches
Institute of Scientific and Technical Information of China (English)
TIAN Li-Qiang; SHI Wei
2008-01-01
Semi-insulating photoconductive semiconductor switch with an electrode gap of 4mm, triggered by a laser pulse with energy of 0.5mJ, and applied bias of 2.5kV, the periodicity current oscillation with a cycle of 12ns is obtained. It is indicated that the current oscillation is one mode of transferred electron effect, namely quenched domain mode. This mode of trans-electron oscillator is obtained when the instantaneous bias electric field drops below the sustaining field (the minimum electric field required to support the domain) before the domain reaches the anode, which leads to the domain disappears somewhere in the bulk of the switch and away from the ohmic contacts. We mainly analyse the time-dependent characteristic of the mode, the theoretical analysis results are in excellent agreement with the experiment.
Log-Domain Current-mode Quadrature Sinusoidal Oscillator
Directory of Open Access Journals (Sweden)
P. Prommee
2011-09-01
Full Text Available A log-domain current-mode quadrature sinusoidal oscillator based on lossless integrators is presented. The circuit is a direct realization of a first-order differential equation for obtaining the lossy and lossless integrators. Each of the log-domain lossless integrators is realized by using only NPN transistors and a grounded capacitor for achieving low-power and fast response. The proposed oscillator uses two-lossless integrator loop which can be electronically tuned through bias currents. A validated BJT model which is used in SPICE simulation operated from a single power supply as low as 2.5V. The oscillation frequency is controlled over four decades of frequency. The total harmonic distortions for two-phases QSO (12MHz is obtained around 0.93% which enables fully integrated in telecommunication systems. The proposed circuit is also suitable for high-frequency applications. Nonideality studies are included and PSpice simulation results confirm the theoretical results.
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
Energy Technology Data Exchange (ETDEWEB)
Bi, Ping [Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, 500 Dongchuan Rd., Shanghai 200241 (China); Center for Partial Differential Equations, East China Normal University, 500 Dongchuan Rd., Shanghai 200241 (China); Ruan, Shigui, E-mail: ruan@math.miami.edu [Department of Mathematics, University of Miami, Coral Gables, Florida 33124-4250 (United States); Zhang, Xinan [School of Mathematics and Statistics, Central China Normal University, Wuhan 430079 (China)
2014-06-15
In this paper, a tumor and immune system interaction model consisted of two differential equations with three time delays is considered in which the delays describe the proliferation of tumor cells, the process of effector cells growth stimulated by tumor cells, and the differentiation of immune effector cells, respectively. Conditions for the asymptotic stability of equilibria and existence of Hopf bifurcations are obtained by analyzing the roots of a second degree exponential polynomial characteristic equation with delay dependent coefficients. It is shown that the positive equilibrium is asymptotically stable if all three delays are less than their corresponding critical values and Hopf bifurcations occur if any one of these delays passes through its critical value. Numerical simulations are carried out to illustrate the rich dynamical behavior of the model with different delay values including the existence of regular and irregular long periodic oscillations.
Role of asymmetries in the chaotic dynamics of the double-well Duffing oscillator
Indian Academy of Sciences (India)
V Ravichandran; S Jeyakumari; V Chinnathambi; S Rajasekar; M A F Sanjuán
2009-06-01
Duffing oscillator driven by a periodic force with three different forms of asymmetrical double-well potentials is considered. Three forms of asymmetry are introduced by varying the depth of the left-well alone, location of the minimum of the left-well alone and above both the potentials. Applying the Melnikov method, the threshold condition for the occurrence of horseshoe chaos is obtained. The parameter space has regions where transverse intersections of stable and unstable parts of left-well homoclinic orbits alone and right-well orbits alone occur which are not found in the symmetrical system. The analytical predictions are verified by numerical simulation. For a certain range of values of the control parameters there is no attractor in the left-well or in the right-well.
Magnetization oscillations and waves driven by pure spin currents
Demidov, V. E.; Urazhdin, S.; de Loubens, G.; Klein, O.; Cros, V.; Anane, A.; Demokritov, S. O.
2017-02-01
Recent advances in the studies of pure spin currents-flows of angular momentum (spin) not accompanied by the electric currents-have opened new horizons for the emerging technologies based on the electron's spin degree of freedom, such as spintronics and magnonics. The main advantage of pure spin current, as compared to the spin-polarized electric current, is the possibility to exert spin transfer torque on the magnetization in thin magnetic films without the electrical current flow through the material. In addition to minimizing Joule heating and electromigration effects, this enables the implementation of spin torque devices based on the low-loss insulating magnetic materials, and offers an unprecedented geometric flexibility. Here we review the recent experimental achievements in investigations of magnetization oscillations excited by pure spin currents in different nanomagnetic systems based on metallic and insulating magnetic materials. We discuss the spectral properties of spin-current nano-oscillators, and relate them to the spatial characteristics of the excited dynamic magnetic modes determined by the spatially-resolved measurements. We also show that these systems support locking of the oscillations to external microwave signals, as well as their mutual synchronization, and can be used as efficient nanoscale sources of propagating spin waves.
Indian Academy of Sciences (India)
Neetu Gupta; B M Deb
2006-12-01
The quantum dynamics of an electron moving under the Henon–Heiles (HH) potential in the presence of external time-dependent (TD) laser fields of varying intensities have been studied by evolving in real time the unperturbed ground-state wave function (, , ) of the HH oscillator. The TD Schröinger equation is solved numerically and the system is allowed to generate its own wave packet. Two kinds of sensitivities, namely, sensitivity to the initial quantum state and to the Hamiltonian, are examined. 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, distance function and overlap integral (akin to quantum fidelity or Loschmidt echo), in terms of the sensitivity towards an initial state characterized by a mixture of quantum states (wave packet) brought about by small changes in the Hamiltonian, rather than a `pure' quantum state (a single eigenstate). The similarity between the HH potential and atoms/molecules in intense laser fields is also analyzed.
Pérez-Molina, Manuel; Pérez-Polo, Manuel F.
2014-10-01
This paper analyzes a controlled servomechanism with feedback and a cubic nonlinearity by means of the Bogdanov-Takens and Andronov-Poincaré-Hopf bifurcations, from which steady-state, self-oscillating and chaotic behaviors will be investigated using the center manifold theorem. The system controller is formed by a Proportional plus Integral plus Derivative action (PID) that allows to stabilize and drive to a prescribed set point a body connected to the shaft of a DC motor. The Bogdanov-Takens bifurcation is analyzed through the second Lyapunov stability method and the harmonic-balance method, whereas the first Lyapunov value is used for the Andronov-Poincaré-Hopf bifurcation. On the basis of the results deduced from the bifurcation analysis, we show a procedure to select the parameters of the PID controller so that an arbitrary steady-state position of the servomechanism can be reached even in presence of noise. We also show how chaotic behavior can be obtained by applying a harmonical external torque to the device in self-oscillating regime. The advantage of achieving chaotic behavior is that it can be used so that the system reaches a set point inside a strange attractor with a small control effort. The analytical calculations have been verified through detailed numerical simulations.
Energy Technology Data Exchange (ETDEWEB)
Yang Xiaoli [Department of Applied Mathematics, Northwestern Polytechnic University, Xi' an 710072 (China); Department of Mathematics, Shaan' xi Normal University, Xi' an 710062 (China); E-mail: yangxl205@mail.nwpu.edu.cn; Xu Wei [Department of Applied Mathematics, Northwestern Polytechnic University, Xi' an 710072 (China); E-mail: weixu@nwpu.edu.cn; Sun Zhongkui [Department of Applied Mathematics, Northwestern Polytechnic University, Xi' an 710072 (China)
2006-02-01
This paper investigates the chaotic behavior of an extended Duffing Van der pol oscillator in a {phi} {sup 6} potential under additive harmonic and bounded noise excitations for a specific parameter choice. From Melnikov theorem, we obtain the conditions for the existence of homoclinic or heteroclinic bifurcation in the case of the {phi} {sup 6} potential is bounded, which are complemented by the numerical simulations from which we illustrate the bifurcation surfaces and the fractality of the basins of attraction. The results show that the threshold amplitude of bounded noise for onset of chaos will move upwards as the noise intensity increases, which is further validated by the top Lyapunov exponents of the original system. Thus the larger the noise intensity results in the less possible chaotic domain in parameter space. The effect of bounded noise on Poincare maps is also investigated.
Chaotic scattering of pitch angles in the current sheet of the magnetotail
Burkhart, G. R.; Chen, J.
1992-01-01
The modified Harris field model is used to investigate the process of pitch angle scattering by a current sheet. The relationship between the incoming asymptotic pitch angle alpha(in) and the outgoing asymptotic pitch angle alpha(out) is studied from first principles by numerically integrating the equation of motion. Evidence that charged particles undergo chaotic scattering by the current sheet is found. For fixed alpha(in), it is shown that alpha(out) exhibits sensitive dependence on the energy parameter in certain energy ranges. For a fixed energy parameter value in the same energy ranges, alpha(out) sensitively depends on alpha(in). For other energy values, alpha(out) does not show sensitive dependence on alpha(in) for most phase angles. A distribution of alpha(in) is mapped from the asymptotic region to the midplane, and it is found that the resulting particle distribution should have beam structures with well-collimated pitch angles near each resonance energy value. Implications for the particle distribution functions in the earth's magnetotail are discussed.
Generation and control of multi-scroll chaotic attractors in fractional order systems
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M. [Department of Electrical and Computer Engineering, University of Sharjah, P.O. Box 27272, Sharjah (United Arab Emirates)] e-mail: wajdi@sharjah.ac.ae
2005-08-01
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.
Bayindir, Cihan
2016-01-01
In this paper we propose an extended Kundu-Eckhaus equation (KEE) for modeling the dynamics of skewed rogue waves emerging in the vicinity of a wave blocking point due to opposing current. The equation we propose is a KEE with an additional potential term therefore the results presented in this paper can easily be generalized to study the quantum tunneling properties of the rogue waves and ultrashort (femtosecond) pulses of the KEE. In the frame of the extended KEE, we numerically show that the chaotic perturbations of the ocean current trigger the occurrence of the rogue waves on the ocean surface. We propose and implement a split-step scheme and show that the extended KEE that we propose is unstable against random chaotic perturbations in the current profile. These perturbations transform the monochromatic wave field into a chaotic sea state with many peaks. We numerically show that the shapes of rogue waves due to perturbations in the current profile closely follow the form of rational rogue wave solutions...
Laminar and weakly turbulent oceanic gravity currents performing inertial oscillations
Directory of Open Access Journals (Sweden)
A. Wirth
2012-05-01
Full Text Available The small scale dynamics of a weakly turbulent oceanic gravity current is determined. The gravity current considered is initially at rest and adjusts by performing inertial oscillations to a geostrophic mean flow. The dynamics is explored with a hierarchy of mathematical models. The most involved are the fully 3-D Navier-Stokes equations subject to the Boussinesq approximation. A 1-D and 0-D mathematical model of the same gravity current dynamics are systematically derived. Using this hierarchy and the numerical solutions of the mathematical models, the turbulent dynamics at the bottom and the interface is explored and their interaction investigated. Three different regimes of the small scale dynamics of the gravity current are identified, they are characterised by laminar flow, coherent roll vortices and turbulent dynamics with coherent streaks and bursts.
The problem of the rectification of the turbulent fluxes, that is, how to average out the fluctuations and calculate their average influence on the flow, is considered. It is shown that two different regimes of friction are superposed, an Ekman friction applies to the average geostrophic flow and a linear friction, not influenced by rotation, to the inertial oscillations. The combination of the two makes the bulk friction non-local in time for the 0-D model.
The implications of the results for parametrisations of the Ekman dynamics and the small scale turbulent fluxes in the planetary boundary layer are discussed.
Laminar and weakly turbulent oceanic gravity currents performing inertial oscillations
Directory of Open Access Journals (Sweden)
A. Wirth
2011-09-01
Full Text Available The small scale dynamics of a weakly turbulent oceanic gravity current is determined. The gravity current considered is initially at rest and adjusts by performing inertial oscillations to a geostrophic mean flow. The dynamics is explored with a hierarchy of mathematical models. The most involved are the fully 3-D Navier-Stokes equations subject to the Boussinesq approximation. A 1-D and 0-D mathematical model of the same gravity current dynamics are systematically derived. Using this hierarchy and the numerical solutions of the mathematical models, the turbulent dynamics at the bottom and the interface is explored and their interaction investigated. Three different regimes of the small scale dynamics of the gravity current are identified, they are characterised by laminar flow, coherent roll vortices and turbulent dynamics with coherent streaks and bursts.
The problem of the rectification of the turbulent fluxes, that is how to average out the fluctuations and calculate their average influence on the flow is considered. It is shown that two different regimes of friction are superposed, an Ekman friction applies to the average geostrophic flow and a linear friction, not influenced by rotation, to the inertial oscillations. The combination of the two makes the bulk friction non-local in time for the 0-D model. The implications of the results for parametrisations of the Ekman dynamics and the small scale turbulent fluxes in the planetary boundary layer are discussed.
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...
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%.
Synchronization of chaotic systems.
Pecora, Louis M; Carroll, Thomas L
2015-09-01
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.
Synchronization of chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Pecora, Louis M.; Carroll, Thomas L. [U.S. Naval Research Laboratory, Washington, District of Columbia 20375 (United States)
2015-09-15
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.
Nuclear aspects of neutrino energy reconstruction in current oscillation experiments
Energy Technology Data Exchange (ETDEWEB)
Leitner, Tina; Buss, Oliver; Mosel, Ulrich [Institut fuer Theoretische Physik, Universitaet Giessen (Germany); Alvarez-Ruso, Luis [Departamento de Fisica Teorica and IFIC, Universidad de Valencia - CSIC (Spain)
2008-07-01
There is an extensive experimental effort aiming at a precise determination of neutrino oscillation parameters. A critical quantity is the neutrino energy which can not be measured directly but has to be reconstructed from observables. A good knowledge of neutrino-nucleus interactions is thus necessary to minimize the systematic uncertainties in neutrino fluxes, backgrounds and detector responses. A reliable reconstruction has to account for in-medium modifications. We find that in particular final-state interactions inside the target nucleus modify considerably the distributions through rescattering, charge-exchange and absorption. These effects can be simulated with our coupled channel GiBUU transport model where the neutrino first interacts with a bound nucleon producing secondary particles which are then transported out of the nucleus. We consider, besides Fermi motion and Pauli blocking, full in-medium kinematics, mean-field potentials and in-medium spectral functions. In this contribution, we compare the reconstructed quantities obtained within our model to the ones obtained by the current experiments like MiniBooNE, which mostly rely on simple two-body kinematics. We then discuss how these uncertainties influence not only the cross section measurements but also the oscillation results.
Constraining neutrino oscillation parameters with current solar and atmospheric data
Maltoni, M; Tortola, M A; Valle, José W F
2003-01-01
We analyse the impact of recent solar and atmospheric data in the determination of the neutrino oscillation parameters, taking into account that both the solar nu_e and the atmospheric nu_mu may convert to a mixture of active and sterile neutrinos. In addition to the recent SNO neutral current (NC), spectral and day/night data we add the latest 1496-day solar and 1489-day atmospheric Super-K neutrino data samples. By investigating in detail the impact of the recent SNO NC, spectral and day/night data, we confirm the clear preference of the LMA solution of the solar neutrino problem and obtain that the LOW, VAC, SMA solutions are disfavoured with a Delta_chi^2 = 9, 9, 23, respectively. Furthermore, we find that the global solar data constrains the admixture of a sterile neutrino to be less than 45% at 99% CL. A pure sterile solution is ruled out with respect to the active one at 99.996% CL. By performing an improved fit of the atmospheric data, we also update the corresponding regions of oscillation parameters...
Hruby, Vladimir (Inventor); Demmons, Nathaniel (Inventor); Ehrbar, Eric (Inventor); Pote, Bruce (Inventor); Rosenblad, Nathan (Inventor)
2014-01-01
An autonomous method for minimizing the magnitude of plasma discharge current oscillations in a Hall effect plasma device includes iteratively measuring plasma discharge current oscillations of the plasma device and iteratively adjusting the magnet current delivered to the plasma device in response to measured plasma discharge current oscillations to reduce the magnitude of the plasma discharge current oscillations.
Chaotic systems in optical communications
Siuzdak, J.
2016-09-01
Communications application of chaotic oscillations of lasers with optoelectronic feedback was discussed. The possibility of eavesdropping of the transmission was analyzed. It was proved that if the rogue party precisely knows parameters of the chaotic system it may recreate the entire signals solely by observation of the optical signal power causing security breach.
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...
Institute of Scientific and Technical Information of China (English)
魏中磊; 张子强; H.E.Fiedler
1995-01-01
The behavior of synchronization in an open flow dynamical system, especially in an excited wake flow behind a 2-D oscillating circular cylinder with Reynolds number Re ranging from 45 to 200 is presented. The experiment reveals that only under certain conditions can the competition between frequencies of oscillating cylinder and the vortex shedding in the wake flow result in "window of chaos" with the mixed RTN and Feigenbaum scenario in the range of Re<185.
3-flavor oscillations with current and future reactor experiments
Dwyer, Dan
2017-01-01
Nuclear reactors have been a crucial tool for our understanding of neutrinos. The disappearance of electron antineutrinos emitted by nuclear reactors has firmly established that neutrino flavor oscillates, and that neutrinos consequently have mass. The current generation of precision measurements rely on some of the world's most intense reactor facilities to demonstrate that the electron antineutrino mixes with the third antineutrino mass eigenstate (v3-). Accurate measurements of antineutrino energies robustly determine the tiny difference between the masses-squared of the v3- state and the two more closely-spaced v1- and v2- states. These results have given us a much clearer picture of neutrino mass and mixing, yet at the same time open major questions about how to account for these small but non-zero masses in or beyond the Standard Model. These observations have also opened the door for a new generation of experiments which aim to measure the ordering of neutrino masses and search for potential violation of CP symmetry by neutrinos. I will provide a brief overview of this exciting field. Work supported under DOE OHEP DE-AC02-05CH11231.
Periodicity of chaotic solutions
Berezowski, Marek
2016-01-01
The scope of the paper is the analysis of the impact of flow reversal on the dynamics of cascades of reactors. Periodic and chaotic oscillations occur in the analyzed system. There is a dependence between the oscillation period of the state variable of the system without flow reversal and the recurrence period of windows of chaos in the steady-state diagram of the system with flow reversal.
Institute of Scientific and Technical Information of China (English)
2007-01-01
The ferroin-catalyzed Belousov-Zhabotinsky(BZ) reaction,the oxidation of malonic acid by acidic bromate,is the most commonly investigated chemical system for understanding spatial pattern forma-tion. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at low flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy?rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition,it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.
Institute of Scientific and Technical Information of China (English)
ZONG ChunYan; GAO QingYu; WANG YuMei; FENG JiaMin; MAO ShanCheng; ZHANG Lu
2007-01-01
The ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction, the oxidation of malonic acid by acidic bromate, is the most commonly investigated chemical system for understanding spatial pattern formation. Various oscillatory behaviors were found from such as mixed-mode and simple period-doubling oscillations and chaos on both Pt electrode and Br-ISE at high flow rates to mixed-mode oscillations on Br-ISE only at Iow flow rates. The complex dynamic behaviors were qualitatively reproduced with a two-cycle coupling model proposed initially by Gy(o)rgyi and Field. This investigation offered a proper medium for studying pattern formation under complex temporal dynamics. In addition, it also shows that complex oscillations and chaos in the BZ reaction can be extended to other bromate-driven nonlinear reaction systems with different metal catalysts.
Directory of Open Access Journals (Sweden)
Li Jie
2015-01-01
Full Text Available Incipient fault for a gearbox diagnosis is difficult because the signals with low signal-to-noise ratio (SNR are corrupted with background noise. A method based on chaos theory and sampling integral technology will be presented to detect the incipient fault of gearbox according to the characters of the gearbox vibration signals. Sampling integral technology was used to improve the tracking ability of fault signals with lower SNR. The small changes in the sidebands of meshing frequency can be detected by the transformation of chaotic phase diagram and its Hu moment invariants, and on this basis the incipient faults can be diagnosed. The results based on gearboxes experiment justify the effectiveness of the method.
Institute of Scientific and Technical Information of China (English)
孙立莹; 周璇; 常志英
2012-01-01
通过对混沌振子Duffing-Holmes方程及其检测原理的介绍,发现混沌振子对周期小信号具有敏感特性,能够在强噪声环境下实现对微弱周期小信号的检测.Matlab实验仿真和分析证明了采用混沌振子Duffing-Holmes检测微弱周期小信号的可行性.%It is a find that chaotic oscillators is sensitive to faint periodic small signal by introduction about chaotic Duffing-Holmes equation and detection of theory, and it can detect the faint periodic small signal in strong noise background. It was indicted that the detection is feasible, make use of chaotic Duffing-Holmes equation by Matlab simulation result and analysis.
Mechanically-Assisted Current-Induced Switching of the Magnetic Moment in a Torsional Oscillator
Cai, Liufei; Jaafar, Reem; Chudnovsky, Eugene M.
2014-01-01
Switching of the direction of the magnetic moment in a nanomagnet is studied within a modified Slonczewski's model that permits torsional oscillations of the magnet. We show that the latter may inhibit or assist the magnetization switching, depending on parameters. Three regimes have been studied: the switching by torsional oscillations alone, the switching by the spin-polarized current with torsional oscillations permitted, and the magnetization switching by the current combined with the mec...
Simply Adjustable Sinusoidal Oscillator Based on Negative Three-Port Current Conveyors
Directory of Open Access Journals (Sweden)
R. Sotner
2010-09-01
Full Text Available The paper deals with sinusoidal oscillator employing two controlled second-generation negative-current conveyors and two capacitors. The proposed oscillator has a simple circuit configuration. Electronic (voltage adjusting of the oscillation frequency and condition of oscillation are possible. The presented circuit is verified in PSpice utilizing macro models of commercially available negative current conveyors. The circuit is also verified by experimental measurements. Important characteristics and drawbacks of the proposed circuit and influences of real active elements in the designed circuit are discussed in detail.
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.
Self-oscillations of a third order PLL in periodic and chaotic mode and its tracking in a slave PLL
Sarkar, B. C.; Chakraborty, S.
2014-03-01
The dynamics of a third order phase locked loop (PLL) with a resonant low pass filter (LPF) has been studied numerically in the parameter space of the system. The range of stable synchronous operating zone of the PLL, expressed in terms of system and signal parameters, is estimated. The obtained results are in agreement with the analytically predicted results in the literature. The PLL dynamics in the unstable region is found to have a sequence of period doubling bifurcation and chaos. In the master-slave mode of operation of two 3rd order PLLs, the slave PLL can track the periodic as well as chaotic dynamics of the master PLL for a narrow range of effective frequency offset when other design parameters are within the stable zone as predicted for an isolated PLL. The synchronization of the master and slave PLLs in this condition is proved to be a generalized one using the auxiliary slave system approach. Experimental observations on prototype hardware circuits for an isolated PLL and for a master-slave PLL arrangement are also given.
Wang, Chunhua; Lin, Hairong
2015-09-01
In this study, a new versatile active element, namely multifunction current differencing cascaded transconductance amplifier (MCDCTA), is proposed. This device which adopts a simple configuration enjoys the performances of low-voltage, low-input and high-output impedance, wide bandwidth etc. It simplifies the design of the current-mode analog signal processing circuit greatly, especially the design of high-order filter and oscillator circuits. Moreover, an example as a new current-mode multiphase sinusoidal oscillator (MSO) using MCDCTA is described in this paper. The proposed oscillator, which employs only one MCDCTA and minimum grounded passive elements, is easy to be realized. It can provide random n (n being odd or even) output current signals and these output currents are equally spaced in phase all at high output impedance terminals. Its oscillation condition and the oscillation frequency can be adjusted independently, linearly and electronically by controlling the bias currents of MCDCTA. The operation of the proposed oscillator has been testified through PSPICE simulation and experimental results.
Mansingka, Abhinav S.
2013-07-24
This paper introduces fully digital implementations of four different 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 100× higher maximum Lyapunov exponent than the original jerk-equation based chaotic systems. The resulting chaotic output is shown to pass the NIST SP. 800-22 statistical test suite for pseudo-random 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.
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 chaotic systems with parameter driven by a chaotic signal
Energy Technology Data Exchange (ETDEWEB)
Li Guohui [Department of Communication Engineering, Shanghai University, Yanchang Road 149, Shanghai 200072 (China)] e-mail: ghlee@shl63.net
2005-12-01
Chaos control with driving parameter scheme in uncoupled identical chaotic oscillators is presented. By driving the parameter of chaotic systems using external chaotic signal, synchronization and anti-synchronization can be implemented. Numerical simulations show that either synchronization or anti-synchronization can appear depending significantly on initial condition and on driving strength. The proposed method is particularly suited for a variety of chaotic systems, which cannot couple with each other in engineering.
Synchronization of chaotic VCSELs by external chaotic signal parameter modulation
Institute of Scientific and Technical Information of China (English)
Wei Wang; Shenghai Zhang; Xingzhong Qian; Yanbin Wang
2009-01-01
Synchronization of chaotic vertical-cavity surface-emitting lasers (VCSELs) is achieved by external chaotic signal modulation successfully.Simulation indicates that we can get chaos synchronization if the intensity of external chaotic signal is large enough.First of all,we use direct current modulation to achieve the chaos of VCSELs,and determine the laser's chaotic state by analyzing time series of the output and the corresponding power spectrum.And then we achieve synchronization of the two chaotic systems by external chaotic signal parameter modulation.We also find that the larger the modulation intensity is,the easier it is to achieve synchronization for chaotic VCSELs.This approach can also be applied to systems with a number of modulated lasers.
Spin torque and critical currents for magnetic vortex nano-oscillator in nanopillars
Energy Technology Data Exchange (ETDEWEB)
Guslienko, K Y; Gonzalez, J [Dpto. Fisica de Materiales, Universidad del Pais Vasco, 20018 Donostia-San Sebastian (Spain); Aranda, G R, E-mail: sckguslk@ehu.es [Centro de Fisica de Materiales UPV/EHU-CSIC, 20018 San Sebastian (Spain)
2011-04-01
We calculated the main dynamic parameters of the spin polarized current induced magnetic vortex oscillations in nanopillars, such as the range of current density, where vortex steady oscillations exist, the oscillation frequency and orbit radius. We accounted for both the non-linear vortex frequency and non-linear vortex damping. To describe the vortex excitations by the spin polarized current we used a generalized Thiele approach to motion of the vortex core as a collective coordinate. All the calculation results are represented via the free layer sizes, saturation magnetization, and the Gilbert damping. Predictions of the developed model can be checked experimentally.
Directory of Open Access Journals (Sweden)
Hamid Radmanesh
2012-09-01
Full Text Available In this study the effect of MOSA on controlling of the non-conventional ferroresonance overvoltage in the iron core voltage transformer is studied. It is expected that MOSA can generally damp ferroresonance overvoltages. Time-domain study is used to analyze this effect. Study is done on a voltage transformer rated 100VA, 275 kV. The magnetization characteristic of the transformer coil is modeled by a single-parameter twoterm polynomial with q = 7 degree of nonlinearity. Core loss is modeled by linear resistance. Simulation results show that connecting the MOSA in parallel to the voltage transformer, shows a great controlling effect of the ferroresonance oscillations. Phase plane, time domain voltage waveforms, FFT analysis and bifurcation diagrams are also given. Significant effect on settling down to the chaos, the range of parameter values that may lead to ferroresonance overvoltages and controlling these phenomena are obtained and presented.
In vivo assessment of human brain oscillations during application of transcranial electric currents
Soekadar, S.R.; Witkowski, M.; García Cossio, E.; Birbaumer, N.; Robinson, S.E.; Cohen, L.G.
2013-01-01
Brain oscillations reflect pattern formation of cell assemblies’ activity, which is often disturbed in neurological and psychiatric diseases like depression, schizophrenia and stroke. In the neurobiological analysis and treatment of these conditions, transcranial electric currents applied to the
Directory of Open Access Journals (Sweden)
Saraiva R.M.
1997-01-01
Full Text Available Outward current oscillations associated with transient membrane hyperpolarizations were induced in murine macrophage polykaryons by membrane depolarization in the absence of external Na+. Oscillations corresponded to a cyclic activation of Ca2+-dependent K+ currents (IKCa probably correlated with variations in intracellular Ca2+ concentration. Addition of external Na+ (8 mM immediately abolished the outward current oscillations, suggesting that the absence of the cation is necessary not only for their induction but also for their maintenance. Oscillations were completely blocked by nisoldipine. Ruthenium red and ryanodine reduced the number of outward current cycles in each episode, whereas quercetin prolonged the hyperpolarization 2- to 15-fold. Neither low molecular weight heparin nor the absence of a Na+ gradient across the membrane had any influence on oscillations. The evidence suggests that Ca2+ entry through a pathway sensitive to Ca2+ channel blockers is elicited by membrane depolarization in Na+-free medium and is essential to initiate oscillations, which are also dependent on the cyclic release of Ca2+ from intracellular Ca2+-sensitive stores; Ca2+ ATPase acts by reducing intracellular Ca2+, thus allowing slow deactivation of IKCa. Evidence is presented that neither a Na+/Ca2+ antiporter nor Ca2+ release from IP3-sensitive Ca2+ stores participate directly in the mechanism of oscillation
Chaotic synchronization via linear controller
Institute of Scientific and Technical Information of China (English)
Chen Feng-Xiang; Zhang Wei-Dong
2007-01-01
A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascade-connected system is presented. Based on the method developed in the paper, two simple and linear feedback controllers, as examples, are derived for the synchronization of Liu chaotic system and Duffing oscillator, respectively.This method is quite flexible in constructing a control law. Its effectiveness is also illustrated by the simulation results.
Wireless current sensing by near field induction from a spin transfer torque nano-oscillator
Energy Technology Data Exchange (ETDEWEB)
Ramaswamy, B. [Fischell Department of Bioengineering, University of Maryland, College Park, Maryland 20742 (United States); Algarin, J. M.; Waks, E., E-mail: edowaks@umd.edu [Institute for Research in Electronics and Applied Physics (IREAP), University of Maryland, College Park, Maryland 20742 (United States); Weinberg, I. N. [Weinberg Medical Physics LLC, Bethesda, Maryland 20817 (United States); Chen, Y.-J.; Krivorotov, I. N. [Department of Physics and Astronomy, University of California, Irvine, California 92697 (United States); Katine, J. A. [HGST Research Center, San Jose, California 95135 (United States); Shapiro, B. [Fischell Department of Bioengineering, University of Maryland, College Park, Maryland 20742 (United States); Institute for Systems Research (ISR), University of Maryland, College Park, Maryland 20742 (United States)
2016-06-13
We demonstrate that spin transfer torque nano-oscillators (STNO) can act as wireless sensors for local current. The STNO acts as a transducer that converts weak direct currents into microwave field oscillations that we detect using an inductive coil. We detect direct currents in the range of 300–700 μA and report them wirelessly to a receiving induction coil at distances exceeding 6.5 mm. This current sensor could find application in chemical and biological sensing and industrial inspection.
Superpersistent currents and whispering gallery modes in relativistic quantum chaotic systems.
Xu, Hongya; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2015-03-11
Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems.
Modelling of low-current self-generated oscillations in a hollow cathode discharge
Donko, Z
1999-01-01
Low-current self-generated oscillations in a rectangular hollow cathode discharge in helium gas were investigated experimentally and by means of a two-dimensional self-consistent hybrid model. The model combines Monte Carlo simulation of the motion of fast electrons and a fluid description of slow electrons and positive ions. The low-frequency (<=20 kHz) oscillations were found to arise as an effect of the interaction of the gas discharge and the external electric circuit - consisting of a stable voltage source, a series resistor and a capacitor formed by the discharge electrodes. Good agreement was found between the experimentally observed and calculated oscillation frequency and current wave forms. Beside these characteristics the modelling also made it possible to calculate the time dependence of numerous other discharge characteristics (e.g. electron multiplication, ion density, potential distribution) and provided detailed insight into the mechanism of oscillations. The advantage of the present model ...
Intermittent chaotic chimeras for coupled rotators.
Olmi, Simona; Martens, Erik A; Thutupalli, Shashi; Torcini, Alessandro
2015-09-01
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 jumps erratically between laminar and turbulent phases. These states have finite lifetimes diverging as a power law with N and m. Lyapunov analyses reveal chaotic properties in quantitative agreement with theoretical predictions for globally coupled dissipative systems.
Micromagnetic modeling of critical current oscillations in magnetic Josephson junctions
Golovchanskiy, I. A.; Bol'ginov, V. V.; Stolyarov, V. S.; Abramov, N. N.; Ben Hamida, A.; Emelyanova, O. V.; Stolyarov, B. S.; Kupriyanov, M. Yu.; Golubov, A. A.; Ryazanov, V. V.
2016-12-01
In this work we propose and explore an effective numerical approach for investigation of critical current dependence on applied magnetic field for magnetic Josephson junctions with in-plane magnetization orientation. This approach is based on micromagnetic simulation of the magnetization reversal process in the ferromagnetic layer with introduced internal magnetic stiffness and subsequent reconstruction of the critical current value using total flux or reconstructed actual phase difference distribution. The approach is flexible and shows good agreement with experimental data obtained on Josephson junctions with ferromagnetic barriers. Based on this approach we have obtained a critical current dependence on applied magnetic field for rectangular magnetic Josephson junctions with high size aspect ratio. We have shown that the rectangular magnetic Josephson junctions can be considered for application as an effective Josephson magnetic memory element with the value of critical current defined by the orientation of magnetic moment at zero magnetic field. An impact of shape magnetic anisotropy on critical current is revealed and discussed. Finally, we have considered a curling magnetic state in the ferromagnetic layer and demonstrated its impact on critical current.
Fujii, Kanji; Fujii, Kanji; Shimomura, Takashi
2004-01-01
As a possible approach to the neutrino oscillation on the basis of quantum field theory, the expectation values of the flavor-neutrino currents are investigated by employing the finite-time transition matrix in the interaction representation. Such expectation values give us in the simplest form a possible way of treating the neutrino oscillation without recourse to any one flavor-neutrino states. The present paper is devoted to presenting the formulation and the main structures of the relevant expectation values.
FUJII, Kanji; Shimomura, Takashi
2004-01-01
As a possible approach to the neutrino oscillation on the basis of quantum field theory, the expectation values of the flavor-neutrino currents are investigated by employing the finite-time transition matrix in the interaction representation. Such expectation values give us in the simplest form a possible way of treating the neutrino oscillation without recourse to any one flavor-neutrino states. The present paper is devoted to presenting the formulation and the main structures of the relevan...
Titanium nitride coatings synthesized by IPD method with eliminated current oscillations
Directory of Open Access Journals (Sweden)
Chodun Rafał
2016-09-01
Full Text Available This paper presents the effects of elimination of current oscillations within the coaxial plasma accelerator during IPD deposition process on the morphology, phase structure and properties of synthesized TiN coatings. Current observations of waveforms have been made by use of an oscilloscope. As a test material for experiments, titanium nitride TiN coatings synthesized on silicon and high-speed steel substrates were used. The coatings morphology, phase composition and wear resistance properties were determined. The character of current waveforms in the plasma accelerator electric circuit plays a crucial role during the coatings synthesis process. Elimination of the current oscillations leads to obtaining an ultrafine grained structure of titanium nitride coatings and to disappearance of the tendency to structure columnarization. The coatings obtained during processes of a non-oscillating character are distinguished by better wear-resistance properties.
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, this p...
Optogalvanic effect and laser-induced current oscillations in hollow-cathode lamps
Eldakli, Mohsan S. A.; Ivković, Saša S.; Obradović, Bratislav M.
2017-03-01
This paper presents a study of two commercial hollow-cathode lamps (HCLs) with the intention of demonstrating different phenomena in gas discharges. The optogalvanic effect in both HCLs is produced by a laser diode radiated at the wavelength that corresponds to neon transition 1s2–2p2 at 659.89 nm. The voltage–current characteristics of the lamps are explained using a classical theory of hollow-cathode discharge, while the optogalvanic signal is treated as a small perturbation of the discharge current. For certain values of voltage self-sustained current oscillations are observed in one of the HCLs. In the same HCL laser-induced optogalvanic dumped oscillations are detected. A phenomenological model that includes the effective circuit parameters of the discharge is used to explain the oscillation characteristics.
Random symmetry breaking and freezing in chaotic networks.
Peleg, Y; Kinzel, W; Kanter, I
2012-09-01
Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a nonchaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped oscillators is shown to present chaotic dynamics while the sign amplitude of each damped oscillator is randomly frozen. This phenomenon of random broken global symmetry of the network simultaneous with random freezing of each degree of freedom is accompanied by the existence of exponentially many randomly frozen chaotic attractors with the size of the network. Results are exemplified by a network of modified Duffing oscillators with infinite range pseudoinverse delayed interactions.
Identification of fractional chaotic system parameters
Energy Technology Data Exchange (ETDEWEB)
Al-Assaf, Yousef E-mail: yassaf@aus.ac.ae; El-Khazali, Reyad E-mail: khazali@ece.ac.ae; Ahmad, Wajdi E-mail: wajdi@sharjah.ac.ae
2004-11-01
In this work, a technique is introduced for parameter identification of fractional order chaotic systems. Features are extracted, from chaotic system outputs obtained for different system parameters, using discrete Fourier transform (DFT), power spectral density (PSD), and wavelets transform (WT). Artificial neural networks (ANN) are then trained on these features to predict the fractional chaotic system parameters. A fractional chaotic oscillator model is used through this work to demonstrate the developed technique. Numerical results show that recurrent Jordan-Elman neural networks with features obtained by the PSD estimate via Welch functions give adequate identification accuracy compared to other techniques.
DC-current induced magneto-oscillations in very high-mobility 2D electron gas
Yang, C. L.; Zhang, Chi; Du, R. R.; Pfeiffer, L. N.; West, K. W.
2007-03-01
We report on a systematic experimental study of DC-current induced magneto-oscillations [1] using Hall bar samples of very high-mobility (8-20 x 10^6 cm^2/Vs) GaAs/AlxGa1-xAs heterostructures. Previously we show that remarkable nonlinear resistance and 1/B oscillations can arise when a high bias current (Ix) is passed through a Hall bar (width w), and the effect can be explained by a Zener tunneling model in the presence of a tilting Hall field [1]. Data of resistance Rxx≡Vx/Ix, differential resistance rxx≡Vx/Ix, and rxx'≡rxx/Ix in higher mobility samples, which show higher order oscillations, have confirmed the validity of this model. Our temperature dependent date show that this effect can persist to kBT>φc, where φc is the cyclotron energy. [1] Yang et al, Phys. Rev. Lett. 89, 076801 (2002).
High-frequency current oscillations in graphene-boron nitride resonant tunnel diodes
Greenaway, Mark; Gaskell, Jenn; Eaves, Laurence; Novoselov, Kostya; Mishchenko, Artem; Geim, Andre; Fromhold, Mark
The successful realisation of multilayer graphene-hBN-graphene resonant tunnelling diodes (graphene- RTDs) with negative differential conductance (NDC) and MHz current oscillations offers the exciting possibility of exploiting them as high-frequency oscillators and mixers. In this paper, we examine their potential for generating higher frequencies by simulating the oscillations in the tunnel current and charge that arise when the device is biased in the NDC region and placed in a resonant circuit. Using the Bardeen transfer Hamiltonian method, we examine the effect on the device characteristics of the twist angle, θ, between the two graphene electrodes, the hBN barrier thickness and of the carrier density in the graphene electrodes, which can be adjusted by chemical doping or by an applied bias voltage. The simulations accurately reproduce our recently-reported measurements on these RTDs (Fig. 4,). The results of simulations show that frequencies of tens of GHz are achievable by optimising the device parameters. Leverhulme Trust, UK.
Projective synchronization of chaotic systems with bidirectional nonlinear coupling
Indian Academy of Sciences (India)
Mohammada Ali Khan; Swarup Poria
2013-09-01
This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.
Dynamical skyrmion state in a spin current nano-oscillator with perpendicular magnetic anisotropy.
Liu, R H; Lim, W L; Urazhdin, S
2015-04-03
We study the spectral characteristics of spin current nano-oscillators based on the Pt/[Co/Ni] magnetic multilayer with perpendicular magnetic anisotropy. By varying the applied magnetic field and current, both localized and propagating spin wave modes of the oscillation are achieved. At small fields, we observe an abrupt onset of the modulation sidebands. We use micromagnetic simulations to identify this state as a dynamical magnetic skyrmion stabilized in the active device region by spin current injection, whose current-induced dynamics is accompanied by the gyrotropic motion of the core due to the skew deflection. Our results demonstrate a practical route for controllable skyrmion manipulation by spin current in magnetic thin films.
Bondur, V. G.; Sabinin, K. D.; Grebenyuk, Yu. V.
2017-01-01
The analysis of inertial oscillations on the Gelendzhik shelf of the Black Sea is presented. Spectral characteristics of the current fields are studied based on the measurements taken by the acoustic Doppler current profiler. Strong variability of the inertial oscillation hodographs at variations in the background shear current and diverse forms of inertial oscillations measured at a fixed point at various values of the shear current are revealed. The relation between the passage of the multidirectional jets and the trains of inertial oscillations inside the jets in the studied region are established.
Institute of Scientific and Technical Information of China (English)
孙清文; 张金锋
2012-01-01
The traditional weak signal detection theory based on single Duffing chaotic oscillator system is described. In the traditional method based on chaos theory for detection of weak signals in strong noise environment, there prone to be instability in the phase change of system and the anti-noise should also be further enhanced. For solving the problems, the method of detecting the weak signal in strong noise environment based on double Duffing coupled improved oscillator system is proposed, and the weak sinusoidal signal detection in strong noise environment is finished the simulation by using this method. By simulation, the result is that based on the system of two-coupled improved chaotic oscillator, the weak signals in the strong noise environment can be better detected and the noise is better suppressed.%介绍传统的单Duffing混沌振子系统检测微弱信号的原理.传统混沌检测弱信号方法中,在强噪声环境下检测弱信号时系统易出现相位变化不稳定、抗噪性需进一步增强等问题.针对这些问题,本文提出基于双Duffing耦合改进型振子系统来对强噪声环境下的弱信号进行检测的方法,并用此方法对强噪声下的微弱正弦信号进行检测仿真.通过仿真得出双耦合改进型混沌振子系统能够更好地检测强噪声环境下的弱信号,对噪声有着更好的抑制作用.
Pacemaker neuron and network oscillations depend on a neuromodulator-regulated linear current
Directory of Open Access Journals (Sweden)
Shunbing Zhao
2010-05-01
Full Text Available Linear leak currents have been implicated in the regulation of neuronal excitability, generation of neuronal and network oscillations, and network state transitions. Yet, few studies have directly tested the dependence of network oscillations on leak currents or explored the role of leak currents on network activity. In the oscillatory pyloric network of decapod crustaceans neuromodulatory inputs are necessary for pacemaker activity. A large subset of neuromodulators is known to activate a single voltage-gated inward current IMI, which has been shown to regulate the rhythmic activity of the network and its pacemaker neurons. Using the dynamic clamp technique, we show that the crucial component of IMI for the generation of oscillatory activity is only a close-to-linear portion of the current-voltage relationship. The nature of this conductance is such that the presence or the absence of neuromodulators effectively regulates the amount of leak current and the input resistance in the pacemaker neurons. When deprived of neuromodulatory inputs, pyloric oscillations are disrupted; yet, a linear reduction of the total conductance in a single neuron within the pacemaker group recovers not only the pacemaker activity in that neuron, but also leads to a recovery of oscillations in the entire pyloric network. The recovered activity produces proper frequency and phasing that is similar to that induced by neuromodulators. These results show that the passive properties of pacemaker neurons can significantly affect their capacity to generate and regulate the oscillatory activity of an entire network, and that this feature is exploited by neuromodulatory inputs.
Novel Wien Bridge Oscillator Design Using Functional Block Structure with Current Conveyors
Directory of Open Access Journals (Sweden)
Pavel Brandstetter
2012-01-01
Full Text Available The purpose of this paper is to generally present possibilities of the current conveyor use in the well-known active electronic circuits. Current conveyors are able to substitute all known active elements. This claim is supported by the fact, that four basic functional block structures can be realized by use of current conveyors - voltage-controlled voltage source, voltage-controlled current source, current-controlled current source and current-controlled voltage source. The paper presents particular example of use of functional block structure with current conveyors in Wien bridge oscillator, where it successfully substitutes operational amplifier on the place of active element. Both theoretical formulae and design description are given. Finally, OrCAD PSpice simulation results are presented.
Robust ion current oscillations under a steady electric field: An ion channel analog
Yan, Yu; Wang, Yunshan; Senapati, Satyajyoti; Schiffbauer, Jarrod; Yossifon, Gilad; Chang, Hsueh-Chia
2016-08-01
We demonstrate a nonlinear, nonequilibrium field-driven ion flux phenomenon, which unlike Teorell's nonlinear multiple field theory, requires only the application of one field: robust autonomous current-mass flux oscillations across a porous monolith coupled to a capillary with a long air bubble, which mimics a hydrophobic protein in an ion channel. The oscillations are driven by the hysteretic wetting dynamics of the meniscus when electro-osmotic flow and pressure driven backflow, due to bubble expansion, compete to approach zero mass flux within the monolith. Delayed rupture of the film around the advancing bubble cuts off the electric field and switches the monolith mass flow from the former to the latter. The meniscus then recedes and repairs the rupture to sustain an oscillation for a range of applied fields. This generic mechanism shares many analogs with current oscillations in cell membrane ion channel. At sufficiently high voltage, the system undergoes a state transition characterized by appearance of the ubiquitous 1 /f power spectrum.
Formulation of statistical mechanics for chaotic systems
Indian Academy of Sciences (India)
Vishnu M Bannur; Ramesh Babu Thayyullathil
2009-02-01
We formulate the statistical mechanics of chaotic system with few degrees of freedom and investigated the quartic oscillator system using microcanonical and canonical ensembles. Results of statistical mechanics are numerically verified by considering the dynamical evolution of quartic oscillator system with two degrees of freedom.
InP Gunn Diodes with Current Limiting Contact for High Efficiency Gunn Oscillators
Kim, Mi-Ra; Rhee, Jin-Koo; Lee, Chang-Woo; Chae, Yeon-Sik; Choi, Jae-Hyun; Kim, Wan-Joo
We fabricated and examined current limiting effect for InP Gunn diodes with stable depletion layer mode operation of diodes for high efficiency Gunn oscillators. Current limiting at the cathode was achieved by a shallow Schottky barrier at the interface. We discussed fabrication procedure, the results for negative differential resistance and rf tests for InP Gunn diodes. It was shown that the fabricated Gunn diodes have the output power of 10.22dBm at a frequency of 90.13GHz. Its input voltage and corresponding current were 8.55V and 252mA, respectively.
Goodman, Michael L
2014-01-01
A magnetohydrodynamic model that includes a complete electrical conductivity tensor is used to estimate conditions for photospherically driven, linear, non-plane Alfvenic oscillations extending from the photosphere to the lower corona to drive a chromospheric heating rate due to Pedersen current dissipation that is comparable to the net chromospheric net radiative loss of $\\sim 10^7$ ergs-cm$^{-2}$-sec$^{-1}$. The heating rates due to electron current dissipation in the photosphere and corona are also computed. The wave amplitudes are computed self-consistently as functions of an inhomogeneous background (BG) atmosphere. The effects of the conductivity tensor are resolved numerically using a resolution of 3.33 m. The oscillations drive a chromospheric heating flux $F_{Ch} \\sim 10^7 - 10^8$ ergs-cm$^{-2}$-sec$^{-1}$ at frequencies $\
Antiferromagnetic THz-frequency Josephson-like Oscillator Driven by Spin Current
Khymyn, Roman; Lisenkov, Ivan; Tiberkevich, Vasyl; Ivanov, Boris A.; Slavin, Andrei
2017-01-01
The development of compact and tunable room temperature sources of coherent THz-frequency signals would open a way for numerous new applications. The existing approaches to THz-frequency generation based on superconductor Josephson junctions (JJ), free electron lasers, and quantum cascades require cryogenic temperatures or/and complex setups, preventing the miniaturization and wide use of these devices. We demonstrate theoretically that a bi-layer of a heavy metal (Pt) and a bi-axial antiferromagnetic (AFM) dielectric (NiO) can be a source of a coherent THz signal. A spin-current flowing from a DC-current-driven Pt layer and polarized along the hard AFM anisotropy axis excites a non-uniform in time precession of magnetizations sublattices in the AFM, due to the presence of a weak easy-plane AFM anisotropy. The frequency of the AFM oscillations varies in the range of 0.1–2.0 THz with the driving current in the Pt layer from 108 A/cm2 to 109 A/cm2. The THz-frequency signal from the AFM with the amplitude exceeding 1 V/cm is picked up by the inverse spin-Hall effect in Pt. The operation of a room-temperature AFM THz-frequency oscillator is similar to that of a cryogenic JJ oscillator, with the energy of the easy-plane magnetic anisotropy playing the role of the Josephson energy. PMID:28262731
Antiferromagnetic THz-frequency Josephson-like Oscillator Driven by Spin Current
Khymyn, Roman; Lisenkov, Ivan; Tiberkevich, Vasyl; Ivanov, Boris A.; Slavin, Andrei
2017-03-01
The development of compact and tunable room temperature sources of coherent THz-frequency signals would open a way for numerous new applications. The existing approaches to THz-frequency generation based on superconductor Josephson junctions (JJ), free electron lasers, and quantum cascades require cryogenic temperatures or/and complex setups, preventing the miniaturization and wide use of these devices. We demonstrate theoretically that a bi-layer of a heavy metal (Pt) and a bi-axial antiferromagnetic (AFM) dielectric (NiO) can be a source of a coherent THz signal. A spin-current flowing from a DC-current-driven Pt layer and polarized along the hard AFM anisotropy axis excites a non-uniform in time precession of magnetizations sublattices in the AFM, due to the presence of a weak easy-plane AFM anisotropy. The frequency of the AFM oscillations varies in the range of 0.1–2.0 THz with the driving current in the Pt layer from 108 A/cm2 to 109 A/cm2. The THz-frequency signal from the AFM with the amplitude exceeding 1 V/cm is picked up by the inverse spin-Hall effect in Pt. The operation of a room-temperature AFM THz-frequency oscillator is similar to that of a cryogenic JJ oscillator, with the energy of the easy-plane magnetic anisotropy playing the role of the Josephson energy.
High-power Čerenkov microwave oscillators utilizing High-Current nanosecond Electron beams
Korovin, S. D.; Polevin, S. D.; Rostov, V. V.
1996-12-01
A short review is given of results obtained at the Institute of High-Current Electronics of the Siberian Branch of the Russian Academy of Sciences on generating high-power microwave radiation. Most of the research was devoted to a study of stimulated Čerenkov radiation from relativistic electron beams. It is shown that the efficiency of a relativistic 3-cm backward wave tube with a nonuniform coupling resistance can reach 35%. High-frequency radiation was discovered in the emission spectrum of the Čerenkov oscillators and it was shown that the nature of the radiation was associated with the stimulated scattering of low-frequency radiation by the relativistic electrons. Radiation with a power of 500 MW was obtained in the 8-mm wavelength range using a two-beam Čerenkov oscillator. High-current pulse-periodic nanosecond accelerators with a charging device utilizing a Tesla transformer were used in the experiments. The possibility was demonstrated of generating high-power microwave radiation with a pulse-repetition frequency of up to 100 Hz. An average power of ˜500 W was achieved from the relativistic oscillators. A relativistic backward wave tube with a high-current electron beam was used to make a prototype nanosecond radar device. Some of the results presented were obtained jointly with the Russian Academy of Sciences Institute of Applied Physics. Questions concerning multiwave Čerenkov interaction are not considered in this paper.
Spintronic Oscillator Based on Spin-Current Feedback Using the Spin Hall Effect
Bhuktare, Swapnil; Singh, Hanuman; Bose, Arnab; Tulapurkar, Ashwin. A.
2017-01-01
We propose a radio-frequency nano-oscillator based on feedback of spin current into a magnetic tunnel junction (MTJ) with an in-plane magnetized pinned layer and an out-of-plane magnetized free layer. The MTJ is connected to a "feedback" strip of a material like tungsten with a giant spin Hall effect. On passing a dc current through the MTJ, the thermal fluctuations of its free layer produce an oscillatory voltage across itself owing to the magnetoresistance effect. This oscillatory voltage drives an oscillatory current into the tungsten strip which converts this charge current into spin current via the spin Hall effect and feeds it back to the MTJ. We show that this feedback can amplify the fluctuations further and drive the free layer into periodic precessional states. We also propose a way of implementing spin-current feedback by using a nanomagnet coupled to the free layer of the MTJ by dipolar magnetic field.
Chaotic region of elastically restrained single-walled carbon nanotube
Hu, Weipeng; Song, Mingzhe; Deng, Zichen; Zou, Hailin; Wei, Bingqing
2017-02-01
The occurrence of chaos in the transverse oscillation of the carbon nanotube in all of the precise micro-nano mechanical systems has a strong impact on the stability and the precision of the micro-nano systems, the conditions of which are related with the boundary restraints of the carbon nanotube. To generalize some transverse oscillation problems of the carbon nanotube studied in current references, the elastic restraints at both ends of the single-walled carbon nanotube are considered by means of rotational and translational springs to investigate the effects of the boundary restraints on the chaotic properties of the carbon nanotube in this paper. Based on the generalized multi-symplectic theory, both the generalized multi-symplectic formulations for the governing equation describing the transverse oscillation of the single-walled carbon nanotube subjected to the transverse load and the constraint equations resulting from the elastic restraints are presented firstly. Then, the structure-preserving scheme with discrete constraint equations is constructed to simulate the transverse oscillation process of the carbon nanotube. Finally, the chaotic region of the carbon nanotube is captured, and the oscillations of the two extreme cases (including simply supported and cantilever) are investigated in the numerical investigations. From the numerical results, it can be concluded that the relative bending stiffness coefficient and the absolute bending stiffness coefficients at both ends of the carbon nanotube are two important factors that affect the chaotic region of the carbon nanotube, which provides guidance on the design and manufacture of precise micro-nano mechanical systems. In addition, the different routes to the chaos of the carbon nanotube in two extreme cases are revealed.
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
Altmann, Eduardo G; Tél, Tamás
2015-01-01
We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that (i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an information dimension smaller than that of the phase space,(ii) such exploding cases can be described by an operator formalism similar to the one applied to chaotic systems with absorption (decaying intensities), but (iii) the invariant quantities characterizing explosion and absorption are typically not directly related to each other, e.g., the decay rate and fractal dimensions of absorbing maps typically differ from the ones computed in the corresponding inverse (exploding) maps. We illustrate our general results through numerical simulation in the cardioid billiard mimicking a lasing optical cavity, and through analytical calculations in the baker map.
Chaotic Synchronzation System and Electrocardiogram
Institute of Scientific and Technical Information of China (English)
LiuqingPei; XinlaiDai; 等
1997-01-01
A mathematical model of chaotic synchronization of the heart-blood flow coupling dynamics is propsed,which is based on a seven dimension nonlinear dynamical system constructed by three subsystems of the sinoatrial node natural pacemaker,the cardiac relaxation oscillator and the dynamics of blood-fluid in heart chambers.The existence and robustness of the self-chaotic synchronization of the system are demonstrated by both methods of theoretical analysis and numerical simulation.The spectrum of Lyapunov exponent,the Lyapunov dimension and the Kolmogorov entropy are estimated when the system was undergoing the state of self-chaotic synchronization evolution.The time waveform of the dynamical variable,which represents the membrane potential of the cardiac integrative cell,shows a shape which is similar to that of the normal electrocardiogram(ECG) of humans,thus implying that the model possesses physiological significance functionally.
Self-sustained spin-polarized current oscillations in multiquantum well structures
Energy Technology Data Exchange (ETDEWEB)
Escobedo, Ramon [Departamento de Matematica Aplicada y Ciencias de la Computacion, Universidad de Cantabria, 39005 Santander (Spain); Carretero, Manuel; Bonilla, Luis L [G. Millan Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganes (Spain); Platero, Gloria [Instituto de Ciencia de Materiales, CSIC, 28049 Cantoblanco (Spain)], E-mail: escobedo@unican.es, E-mail: manuel.carretero@uc3m.es, E-mail: bonilla@ing.uc3m.es, E-mail: gplatero@icmm.csic.es
2009-01-15
Nonlinear transport through diluted magnetic semiconductor nanostructures is investigated. We have considered a II-VI multiquantum well nanostructure whose wells are selectively doped with Mn. The response to a dc voltage bias may be either a stationary or an oscillatory current. We have studied the transition from stationary to time-dependent current as a function of the doping density and the number of quantum wells. Analysis and numerical solution of a nonlinear spin transport model shows that the current in a structure without magnetic impurities is stationary, whereas current oscillations may appear if at least one well contains magnetic impurities. For long structures having two wells with magnetic impurities, a detailed analysis of nucleation of charge dipole domains shows that self-sustained current oscillations are caused by repeated triggering of dipole domains at the magnetic wells and motion towards the collector. Depending on the location of the magnetic wells and the voltage, dipole domains may be triggered at both wells or at only one. In the latter case, the well closer to the collector may inhibit domain motion between the first and the second well inside the structure. Our study could allow design of oscillatory spin-polarized current injectors.
Target Detection and Ranging through Lossy Media using Chaotic Radar
Directory of Open Access Journals (Sweden)
Bingjie Wang
2015-04-01
Full Text Available A chaotic radar system has been developed for through-wall detection and ranging of targets. The chaotic signal generated by an improved Colpitts oscillator is designed as a probe signal. Ranging to target is achieved by the cross-correlation between the time-delayed reflected return signal and the replica of the transmitted chaotic signal. In this paper, we explore the performance of the chaotic radar system for target detection and ranging through lossy media. Experimental results show that the designed chaotic radar has the advantages of high range resolution, unambiguous correlation profile, and can be used for through wall target detection and sensing.
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.
Automatic synthesis of 2D‐n‐scrolls chaotic systems by behavioral modeling
Directory of Open Access Journals (Sweden)
J. M. Muñoz‐Pacheco
2009-04-01
Full Text Available This paper introduces the guidelines to synthesize 2D chaotic systems by means of high‐level descriptions. The aim of thisinvestigation is to synthesize 2D‐n‐scrolls chaotic systems based on saturated functions with multisegments. The newmethodology of circuit synthesis is performed by three hierarchical levels. First, the 2D chaotic oscillator is numericallysimulated at the electronic system level by applying state variables and piecewise‐linear approximation. Second, the excursionlevels of the chaotic signals are scaled to control the breaking points and slopes of the saturated functions within practicalvalues. Additionally, the frequency scaling of 2D‐n‐scrolls chaotic attractors is performed. Finally, current and voltage saturatedfunctions are synthesized using Verilog‐A models for the operational amplifiers and in this manner a 2D chaotic system issynthesized using operational amplifiers to generate 2D‐n‐scrolls attractors. Numerical results are confirmed by H‐SPICEsimulations to show the usefulness of the proposed synthesis approach.
Spread Spectrum Communication with Chaotic Frequency Modulation
Volkovskii, Alexander R.; Tsimring, Lev S.; Rulkov, Nikolai F.; Langmore, Ian; Young, Stephen C.
We describe two different approaches to employ chaotic signals in spread-spectrum (SS) communication systems with phase and frequency modulation. In the first one a chaotic signal is used as a carrier. We demonstrate that using a feedback loop controller, the local chaotic oscillator in the receiver can be synchronized to the transmitter. The information can be transmitted using phase or frequency modulation of the chaotic carrier signal. In the second system the chaotic signal is used for frequency modulation of a voltage controlled oscillator (VCO) to provide a SS signal similar to frequency hopping systems. We show that in a certain parameter range the receiver VCO can be synchronized to the transmitter VCO using a relatively simple phase lock loop (PLL) circuit. The same PLL is used for synchronization of the chaotic oscillators. The information signal can be transmitted using a binary phase shift key (BPSK) or frequency shift key (BFSK) modulation of the frequency modulated carrier signal. Using an experimental circuit operating at radio frequency band and a computer modeling we study the bit error rate (BER) performance in a noisy channel as well as multiuser capability of the system.
2003-01-01
[figure removed for brevity, see original site] Released 4 June 2003Chaotic terrain on Mars is thought to form when there is a sudden removal of subsurface water or ice, causing the surface material to slump and break into blocks. The chaotic terrain in this THEMIS visible image is confined to a crater just south of Elysium Planitia. It is common to see chaotic terrain in the vicinity of the catastrophic outflow channels on Mars, but the terrain in this image is on the opposite side of the planet from these channels, making it somewhat of an oddity.Image information: VIS instrument. Latitude -5.9, Longitude 108.1 East (251.9 West). 19 meter/pixel resolution.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
Mapping entrained brain oscillations during transcranial alternating current stimulation (tACS).
Witkowski, Matthias; Garcia-Cossio, Eliana; Chander, Bankim S; Braun, Christoph; Birbaumer, Niels; Robinson, Stephen E; Soekadar, Surjo R
2016-10-15
Transcranial alternating current stimulation (tACS), a non-invasive and well-tolerated form of electric brain stimulation, can influence perception, memory, as well as motor and cognitive function. While the exact underlying neurophysiological mechanisms are unknown, the effects of tACS are mainly attributed to frequency-specific entrainment of endogenous brain oscillations in brain areas close to the stimulation electrodes, and modulation of spike timing dependent plasticity reflected in gamma band oscillatory responses. tACS-related electromagnetic stimulator artifacts, however, impede investigation of these neurophysiological mechanisms. Here we introduce a novel approach combining amplitude-modulated tACS during whole-head magnetoencephalography (MEG) allowing for artifact-free source reconstruction and precise mapping of entrained brain oscillations underneath the stimulator electrodes. Using this approach, we show that reliable reconstruction of neuromagnetic low- and high-frequency oscillations including high gamma band activity in stimulated cortical areas is feasible opening a new window to unveil the mechanisms underlying the effects of stimulation protocols that entrain brain oscillatory activity.
Energy Technology Data Exchange (ETDEWEB)
Sivaprasad, K. [Department of Metallurgical and Materials Engineering, Indian Institute of Technology Madras, Chennai (India); Ganesh Sundara Raman, S. [Department of Metallurgical and Materials Engineering, Indian Institute of Technology Madras, Chennai (India)]. E-mail: ganesh@iitm.ac.in; Mastanaiah, P. [Defence Research and Development Laboratory, Hyderabad (India); Madhusudhan Reddy, G. [Defence Metallurgical Research Laboratory, Hyderabad (India)
2006-07-25
The aim of the present work is to study the effect of magnetic arc oscillation and current pulsing on the microstructure and high temperature tensile strength of alloy 718 tungsten inert gas weldments. The magnetic arc oscillation technique resulted in refined Laves phase with lesser interconnectivity. The full benefits of current pulsing in breaking the dendrites could not be realized in the present study due to relatively higher heat input used in the welding process. In the direct aged condition weldments prepared using magnetic arc oscillation technique exhibited higher tensile strength due to the presence of refined and lesser-interconnected Laves particles. In the solution treated and aged condition, magnetic arc oscillated weldments exhibited lower tensile strength compared with the weldments made without arc oscillation due to the presence of large amounts of finer {delta} needles.
Synchronization of chaotic systems with different order.
Femat, Ricardo; Solís-Perales, Gualberto
2002-03-01
The chaotic synchronization of third-order systems and second-order driven oscillator is studied in this paper. Such a problem is related to synchronization of strictly different chaotic systems. We show that dynamical evolution of second-order driven oscillators can be synchronized with the canonical projection of a third-order chaotic system. In this sense, it is said that synchronization is achieved in reduced order. Duffing equation is chosen as slave system whereas Chua oscillator is defined as master system. The synchronization scheme has nonlinear feedback structure. The reduced-order synchronization is attained in a practical sense, i.e., the difference e=x(3)-x(1)(') is close to zero for all time t> or =t(0)> or =0, where t(0) denotes the time of the control activation.
Oren, Iris; Mann, Edward O; Paulsen, Ole; Hájos, Norbert
2006-09-27
Gamma-frequency oscillations are prominent during active network states in the hippocampus. An intrahippocampal gamma generator has been identified in the CA3 region. To better understand the synaptic mechanisms involved in gamma oscillogenesis, we recorded action potentials and synaptic currents in distinct types of anatomically identified CA3 neurons during carbachol-induced (20-25 microM) gamma oscillations in rat hippocampal slices. We wanted to compare and contrast the relationship between excitatory and inhibitory postsynaptic currents in pyramidal cells and perisomatic-targeting interneurons, cell types implicated in gamma oscillogenesis, as well as in other interneuron subtypes, and to relate synaptic currents to the firing properties of the cells. We found that phasic synaptic input differed between cell classes. Most strikingly, the dominant phasic input to pyramidal neurons was inhibitory, whereas phase-coupled perisomatic-targeting interneurons often received a strong phasic excitatory input. Differences in synaptic input could account for some of the differences in firing rate, action potential phase precision, and mean action potential phase angle, both between individual cells and between cell types. There was a strong positive correlation between the ratio of phasic synaptic excitation to inhibition and firing rate over all neurons and between the phase precision of excitation and action potentials in interneurons. Moreover, mean action potential phase angle correlated with the phase of the peak of the net-estimated synaptic reversal potential in all phase-coupled neurons. The data support a recurrent mechanism of gamma oscillations, whereby spike timing is controlled primarily by inhibition in pyramidal cells and by excitation in interneurons.
Directory of Open Access Journals (Sweden)
David Salamon, Mirva Eriksson, Mats Nygren and Zhijian Shen
2012-01-01
Full Text Available The spark plasma sintering (SPS process is known for its rapid densification of metals and ceramics. The mechanism behind this rapid densification has been discussed during the last few decades and is yet uncertain. During our SPS experiments we noticed oscillations in the applied pressure, related to a change in electric current. In this study, we investigated the effect of pulsed electrical current on the applied mechanical pressure and related changes in temperature. We eliminated the effect of sample shrinkage in the SPS setup and used a transparent quartz die allowing direct observation of the sample. We found that the use of pulsed direct electric current in our apparatus induces pressure oscillations with the amplitude depending on the current density. While sintering Ti samples we observed temperature oscillations resulting from pressure oscillations, which we attribute to magnetic forces generated within the SPS apparatus. The described current–pressure–temperature relations might increase understanding of the SPS process.
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.
Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz
1995-01-01
Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.
Oscillations of low-current electrical discharges between parallel-plane electrodes. III. Models
Phelps, A. V.; Petrović, Z. Lj.; Jelenković, B. M.
1993-04-01
Simple models are developed to describe the results of measurements of the oscillatory and negative differential resistance properties of low- to moderate-current discharges in parallel-plane geometry. The time-dependent model assumes that the ion transit time is fixed and is short compared to the times of interest, that electrons are produced at the cathode only by ions, and that space-charge distortion of the electric field is small but not negligible. Illustrative numerical solutions are given for large voltage and current changes and analytic solutions for the time dependence of current and voltage are obtained in the small-signal limit. The small-signal results include the frequency and damping constants for decaying oscillations following a voltage change or following the injection of photoelectrons. The conditions for underdamped, overdamped, and self-sustained or growing oscillations are obtained. A previously developed steady-state, nonequilibrium model for low-pressure hydrogen discharges that includes the effects of space-charge distortion of the electric field on the yield of electrons at the cathode is used to obtain the negative differential resistance. Analytic expressions for the differential resistance and capacitance are developed using the steady-state, local-equilibrium model for electron and ion motion and a first-order perturbation treatment of space-charge electric fields. These models generally show good agreement with data from dc and pulsed discharge experiments presented in the accompanying papers.
Multiple resonances of a moving, oscillating surface disturbance on a shear current
Li, Yan
2016-01-01
We consider waves radiated by a disturbance of oscillating strength moving at constant velocity along the free surface of a shear flow which, when undisturbed, has uniform horizontal vorticity of magnitude $S$. When no current is present the problem is a classical one and much studied, and in deep water a resonance is known to occur when $\\tau=|\\boldsymbol{V}|\\omega_0/g$ equals the critical value $1/4$ ($\\boldsymbol{V}$: velocity of disturbance, $\\omega_0$: oscillation frequency, $g$: gravitational acceleration). We show that the presence of the sub-surface shear current can change this picture radically. Not only does the resonant value of $\\tau$ depend strongly on the angle between $\\boldsymbol{V}$ and the current's direction and the "shear-Froude number" $\\mathrm{Frs}=|\\boldsymbol{V}|S/g$; when $\\mathrm{Frs}>1/3$, multiple resonant values --- as many as $4$ --- can occur for some directions of motion. At sufficiently large values of $\\mathrm{Frs}$, the smallest resonance frequency tends to zero, representi...
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
Enhancing chaotic behavior at room temperature in GaAs/(Al,Ga)As superlattices
Ruiz-Garcia, M.; Essen, J.; Carretero, M.; Bonilla, L. L.; Birnir, B.
2017-02-01
Previous theoretical and experimental work has put forward 50-period semiconductor superlattices as fast, true random number generators at room temperature. Their randomness stems from feedback between nonlinear electronic dynamics and stochastic processes that are intrinsic to quantum transitions. This paper theoretically demonstrates that shorter superlattices with higher potential barriers contain fully chaotic dynamics over several intervals of the applied bias voltage compared to the 50-period device which presented a much weaker chaotic behavior. The chaos arises from deterministic dynamics, hence it persists even in the absence of additional stochastic processes. Moreover, the frequency of the chaotic current oscillations is higher for shorter superlattices. These features should allow for faster and more robust generation of true random numbers.
Projective synchronization in fractional order chaotic systems and its control
Li, Chunguang
2006-01-01
The chaotic dynamics of fractional (non-integer) order systems have begun to attract much attention in recent years. In this paper, we study the projective synchronization in two coupled fractional order chaotic oscillators. It is shown that projective synchronization can also exist in coupled fractional order chaotic systems. A simple feedback control method for controlling the scaling factor onto a desired value is also presented.
Fast-Scale and Slow-Scale Subharmonic Oscillation of Valley Current-Mode Controlled Buck Converter
Institute of Scientific and Technical Information of China (English)
ZHOU Guo-Hua; XU Jian-Ping; BAO Bo-Cheng; ZHANG Fei; LIU Xue-Shan
2010-01-01
@@ A valley current-mode (VCM) controlled buck converter with current source load (CSI) has complex phenomena of fast-scale and slow-scale subharmonic oscillations.The piecewise smooth switching model of the VCM controlled buck converter with CSI is established.It is found that attractive regions of fast-scale and slow-scale subharmonic oscillations exist in the bifurcation diagram,and two tori exist in the corresponding Poincaré mapping.The research results by time-domain simulation indicate that U-type subharmonic oscillation (SO) constituted by SO and frequency-reduced subharmonic oscillation (FSO) exists in inductor current,and sine-type SO constituted by fast scale and low scaie exists in output voltage respectively.Experimental results are given to verify the analysis and simulation results.
The DPSK Signal Noncoherent Demodulation Receiver Based on the Duffing Oscillators Array
Fu, Yongqing; Li, Yanan; Zhang, Lin; Li, Xingyuan
2016-12-01
Chaotic communication requires the knowledge of corresponding phase relationship between the primary phase of Duffing oscillator’s internal driving force and the primary phase of the undetected signal. Currently, there is no method of noncoherent demodulation for DPSK (Differential Phase Shift Keying) signal and mobile communication signal by Duffing oscillator. To solve this problem, this study presents a noncoherent demodulation method based on the Duffing oscillators array and Duffing oscillator optimization. We first present the model of Duffing oscillator and its sensitivity to undetected signal primary phase. Then the zone partition is proposed to identify the Duffing oscillator’s phase trajectory, and subsequently, the mathematical model and implementation method of the Duffing oscillators array are outlined. Thirdly, the Duffing oscillator optimization and its adaptive strobe technique are proposed, also their application to DPSK signal noncoherent demodulation are discussed. Finally, the design of new concept DPSK chaotic digital receiver based on the Duffing oscillators array is presented, together with its simulation results obtained by using SystemView simulation platform. The simulation results suggest that the new concept receiver based on the Duffing oscillator optimization of Duffing oscillators array owns better SNR (signal-to-noise ratio) threshold property than typical existing receivers (chaotic or nonchaotic) in the AWGN (additive white Gaussian noise) channel and multipath Rayleigh fading channel. In addition, the new concept receiver may detect mobile communication signal.
Duan, Wenye; Wang, Wei; Zhang, Chao; Jin, Kuijuan; Ma, Zhongshui
2016-10-01
The proximity properties of edge currents in the vicinity of the interface between the graphene and superconductor in the presence of magnetic field are investigated. It is shown that the edge states introduced by Andreev reflection at the graphene-superconductor (G/S) interface give rise to the charge neutral states in all Landau levels. We note that in a topological insulator-superconductor (TI/S) hybrid structure, only N = 0 Landau level can support this type of charge neutral states. The different interface states of a G/S hybrid and a TI/S hybrid is due to that graphene consists of two distinct sublattices. The armchair edge consists of two inequivalent atoms. This gives rise to unique electronic properties of edge states when connected to a superconductor. A direct consequence of zero charge states in all Landau levels is that the current density approaches zero at interface. The proximity effect leads to quantum magnetic oscillation of the current density in the superconductor region. The interface current density can also be tuned with a finite interface potential. For sharp δ-type interface potential, the derivative of the wavefunction is discontinuous. As a result, we found that there is current density discontinuity at the interface. The step of the current discontinuity is proportional to the strength of the interface potential.
Energy Technology Data Exchange (ETDEWEB)
Leitner, Tina; Buss, Oliver; Mosel, Ulrich [Institut fuer Theoretische Physik, Universitaet Giessen (Germany); Alvarez-Ruso, Luis [Departamento de Fisica Teorica and IFIC, Universidad de Valencia - CSIC (Spain)
2008-07-01
Neutrino oscillation results depend on the neutrino energy - a quantity which can not be measured directly but has to be reconstructed from the hadronic debris coming out of the neutrino-nucleus reaction inside the detector. A reliable reconstruction of the neutrino kinematics and the initial scattering process has to account for in-medium modifications and, in particular, for final state interactions inside the target nucleus. They can, e.g. through intranuclear rescattering, change particle multiplicities and also redistribute their energy. Those effects can be simulated with our fully coupled channel GiBUU transport model where the neutrino first interacts with a bound nucleon producing secondary particles which are then transported out of the nucleus. We use a relativistic formalism that incorporates recent form factor parametrizations, and apply, besides Fermi motion, full in-medium kinematics, mean-field potentials and in-medium spectral functions. In this talk, we compare the reconstructed quantities obtained within our framework to the ones obtained by the current experiments, which, as e.g. MiniBooNE, mostly rely on simple two-body kinematics. We then discuss how these uncertainties influence not only the cross section measurements but also the oscillation results.
Critical Current Oscillations in the Intrinsic Hybrid Vortex State of SmFeAs(O,F)
Moll, Philip J. W.; Balicas, Luis; Zhu, Xiyu; Wen, Hai-Hu; Zhigadlo, Nikolai D.; Karpinski, Janusz; Batlogg, Bertram
2014-10-01
In layered superconductors the order parameter may be modulated within the unit cell, leading to nontrivial modifications of the vortex core if the interlayer coherence length ξc(T ) is comparable to the interlayer spacing. In the iron pnictide SmFeAs(O,F) (Tc≈50 K ) this occurs below a crossover temperature T⋆≈41 K , which separates two regimes of vortices: anisotropic Abrikosov-like at high and Josephson-like at low temperatures. Yet in the transition region around T⋆ , hybrid vortices between these two characteristics appear. Only in this region around T⋆ and for magnetic fields well aligned with the FeAs layers, we observe oscillations of the c -axis critical current jc(H ) periodic in 1 /√{H } due to a delicate balance of intervortex forces and interaction with the layered potential. jc(H ) shows pronounced maxima when a hexagonal vortex lattice is commensurate with the underlying crystal structure. The narrow temperature window in which oscillations are observed suggests a significant suppression of the order parameter between the superconducting layers in SmFeAs(O,F), despite its low coherence length anisotropy (γξ≈3 - 5 ).
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.
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.
Alternating Current Zeeman and Stark Interference Effect in Ramsey Separated Oscillating Fields
Institute of Scientific and Technical Information of China (English)
CHEN Jing-Biao; WANG Feng-Zhi; YANG Dong-Hai; WANG Yi-Qiu
2001-01-01
Analytic expressions have been derived of the alternating current (ac) Zeeman and ac Stark effect in an atomic beam magnetic resonance method using Ramsey separated oscillating fields. An interesting feature which will affect the normal Ramsey pattern is that an interference fringe is superimposed on the dispersion lineshapes of the normal ac Zeeman or ac Stark effect. We point out that this new character of ac Zeeman (ac Stark) effect generally exists in all kinds of Ramsey method, for example, in the optical Ramsey atomic interferometer and atomic beam frequency standard. An important implication is that, particularly in an atomic beam frequency standard using Ramsey method, this effect has an influence on the evaluation of the second-order Doppler frequency shift.PACS: 32. 60. ＋i, 06. 20. Fn, 32. 30. Dx
DEFF Research Database (Denmark)
Nielsen, Dennis; Knott, Arnold; Andersen, Michael A. E.
2013-01-01
A hysteretic self-oscillating bandpass current mode control (BPCM) scheme for Class D audio amplifiers driving capacitive transducers are presented. The scheme provides excellent stability margins and low distortion over a wide range of operating conditions. Small-signal behavior of the amplifier...... the rules of electrostatics have been known as very interesting alternatives to the traditional inefficient electrodynamic transducers. When driving capacitive transducers from a Class D audio amplifier the high impedance nature of the load represents a key challenge. The BPCM control scheme ensures a flat...... is analysis through transfer function based linear control methodology. Measurements are performed on a single-ended ± 300 V half-bridge amplifier driving a capacitive load of 100 nF. Total Harmonic Distortion plus noise (THD+N) below 0.1 % are reported. Transducers representing a capacitive load and obeying...
Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; D'Incerti, Ludovico; Jovicich, Jorge
2015-03-01
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 (D2), 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.
Chaos in nonlinear oscillations controlling and synchronization
Lakshamanan, M
1996-01-01
This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.
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.
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 ...
Pattern formations in chaotic spatio-temporal systems
Indian Academy of Sciences (India)
Ying Zhang; Shihong Wang; Jinhua Xiao; Hilda A Cerdeira; S Chen; Gang Hu
2005-06-01
Pattern formations in chaotic spatio-temporal systems modelled by coupled chaotic oscillators are investigated. We focus on various symmetry breakings and different kinds of chaos synchronization–desynchronization transitions, which lead to certain types of spontaneous spatial orderings and the emergence of some typical ordered patterns, such as rotating wave patterns with splay phase ordering (orientational symmetry breaking) and partially synchronous standing wave patterns with in-phase ordering (translational symmetry breaking). General pictures of the global behaviors of pattern formations and transitions in coupled chaotic oscillators are provided.
Íñiguez-de-la-Torre, A.; Mateos, J.; González, T.
2010-03-01
Under certain conditions, plasma instabilities associated with streaming motion of carriers taking place in n+nn+ diodes can lead to current oscillations. The origin of the phenomenon, known as optical phonon transit time resonance, is characterized by a frequency related to the transit time between consecutive optical phonon emissions by electrons along the active region of the diode. By means of Monte Carlo simulations, the possibility to obtaining current oscillations in GaN n+nn+ diodes is analyzed. The optimum conditions for the onset of such mechanism are investigated: applied bias, temperature, doping, and length of the active n region. Simulations show that current oscillations at frequencies in the terahertz range can be obtained at very low temperatures. Moreover, by choosing the appropriate applied voltage and length of the n region, some degree of tunability can be achieved for frequencies close to the plasma frequency of the n region of the n+nn+ diode.
Li, Chunhe; Wang, Erkang; Wang, Jin
2012-05-21
We developed a potential flux landscape theory to investigate the dynamics and the global stability of a chemical Lorenz chaotic strange attractor under intrinsic fluctuations. Landscape was uncovered to have a butterfly shape. For chaotic systems, both landscape and probabilistic flux are crucial to the dynamics of chaotic oscillations. Landscape attracts the system down to the chaotic attractor, while flux drives the coherent motions along the chaotic attractors. Barrier heights from the landscape topography provide a quantitative measure for the robustness of chaotic attractor. We also found that the entropy production rate and phase coherence increase as the molecular numbers increase. Power spectrum analysis of autocorrelation function provides another way to quantify the global stability of chaotic attractor. We further found that limit cycle requires more flux and energy to sustain than the chaotic strange attractor. Finally, by detailed analysis we found that the curl probabilistic flux may provide the origin of the chaotic attractor.
Measurement of Neutrino Oscillation Parameters Using Anti-fiducial Charged Current Events in MINOS
Energy Technology Data Exchange (ETDEWEB)
Strait, Matthew Levy [Minnesota U.
2010-09-01
Abstract The Main Injector Neutrino Oscillation Search (MINOS) obse rves the disappearance of muon neutrinos as they propagate in the long baseline Neutri nos at the Main Injector (NuMI) beam. MINOS consists of two detectors. The near detector sam ples the initial composition of the beam. The far detector, 735 km away, looks for an energy-d ependent deficit in the neutrino spectrum. This energy-dependent deficit is interpreted as q uantum mechanical oscillations be- tween neutrino flavors. A measurement is made of the effective two-neutrino mixing parameters ∆ m 2 ≈ ∆ m 2 23 and sin 2 2 θ ≈ sin 2 2 θ 23 . The primary MINOS analysis uses charged current events in the fiducial volume of the far detector. This analysis uses the roughly equal-sized sample of events that fails the fiducial cut, consisting of interact ions outside the fiducial region of the detector and in the surrounding rock. These events provide a n independent and complementary measurement, albeit weaker due to incomplete reconstructi on of the events. This analysis reports on an exposure of 7 . 25 × 10 20 protons-on-target. Due to poor energy resolution, the meas urement of sin 2 2 θ is much weaker than established results, but the measuremen t of sin 2 2 θ > 0 . 56 at 90% confidence is consistent with the accepted value. The measur ement of ∆ m 2 is much stronger. Assuming sin 2 2 θ = 1 , ∆ m 2 = (2 . 20 ± 0 . 18[stat] ± 0 . 14[syst]) × 10 − 3 eV 2 .
Measurement of Neutrino Oscillation Parameters Using Anti-fiducial Charged Current Events in MINOS
Energy Technology Data Exchange (ETDEWEB)
Strait, Matthew Levy [Univ. of Minnesota, Minneapolis, MN (United States)
2010-09-01
Abstract The Main Injector Neutrino Oscillation Search (MINOS) obse rves the disappearance of muon neutrinos as they propagate in the long baseline Neutri nos at the Main Injector (NuMI) beam. MINOS consists of two detectors. The near detector sam ples the initial composition of the beam. The far detector, 735 km away, looks for an energy-d ependent deficit in the neutrino spectrum. This energy-dependent deficit is interpreted as q uantum mechanical oscillations be- tween neutrino flavors. A measurement is made of the effective two-neutrino mixing parameters Δ m 2 ≈ Δ m ^{2} 23 and sin ^{2} 2 θ ≈ sin ^{2} 2 θ _{23} . The primary MINOS analysis uses charged current events in the fiducial volume of the far detector. This analysis uses the roughly equal-sized sample of events that fails the fiducial cut, consisting of interact ions outside the fiducial region of the detector and in the surrounding rock. These events provide a n independent and complementary measurement, albeit weaker due to incomplete reconstructi on of the events. This analysis reports on an exposure of 7 . 25 × 10 ^{20} protons-on-target. Due to poor energy resolution, the meas urement of sin ^{2} 2 θ is much weaker than established results, but the measuremen t of sin ^{2} 2 θ > 0 . 56 at 90% confidence is consistent with the accepted value. The measur ement of Δ m 2 is much stronger. Assuming sin 2 ^{2} θ = 1 , Δ m ^{2} = (2 . 20 ± 0 . 18[stat] ± 0 . 14[syst]) × 10 - ^{-3} eV ^{2} .
Ardavan, A; Ardavan, H; Fopma, J; Halliday, D; Hayes, W
2004-01-01
We describe the experimental implementation of a superluminal ({\\it i.e.} faster than light {\\it in vacuo}) polarization current distribution that both oscillates and undergoes centripetal acceleration. Theoretical treatments lead one to expect that the radiation emitted from each volume element of such a polarization current will comprise a \\v{C}erenkov-like envelope with two sheets that meet along a cusp. The emission from the experimental machine is in good agreement with these expectations, the combined effect of the volume elements leading to tightly-defined beams of a well-defined geometry, determined by the source speed and trajectory. In addition, over a restricted range of angles, we detect the presence of cusps in the emitted radiation. These are due to the detection over a short time period (in the laboratory frame) of radiation emitted over a considerably longer period of source time. Consequently, the intensity of the radiation at these angles was observed to decline more slowly with increasing d...
Chaotic motifs in gene regulatory networks.
Zhang, Zhaoyang; Ye, Weiming; Qian, Yu; Zheng, Zhigang; Huang, Xuhui; Hu, Gang
2012-01-01
Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs. On the other hand, the topic of motifs has attracted great attention in studying biological networks, and network motifs are suggested to be elementary building blocks that carry out some key functions in the network. In this paper, chaotic motifs (subnetworks with chaos) in GRNs are systematically investigated. The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities. Conditions required for chaotic GRNs are found to be very strict, which make chaotic GRNs extremely rare. (ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos, and serve as the intrinsic source of chaos of random few-node GRNs. Several optimal motifs causing chaos with atypically high probability are figured out. (iii) Moreover, we discovered that a number of special oscillators can never produce chaos. These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms. (iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs.
Institute of Scientific and Technical Information of China (English)
ShiEnhui; ZhouLizhen; ZhouYoucheng
2003-01-01
It is proved that there is no chaotic group actions on any topological space with free arc.In this paper the chaotic actions of the group like G×F,where F is a finite group,are studied.In particular,under a suitable assumption ,if F is a cyclic group,then the topological space which admits a chaotic action of Z×F must admit a chatotic homeomorphism.A topological space which admits a chaotic group action but admits no chaotic horneomorphism is constructed.
Ziskind-Conhaim, Lea; Wu, Linying; Wiesner, Eric P
2008-10-01
Neurochemically induced membrane voltage oscillations and firing episodes in spinal excitatory interneurons expressing the HB9 protein (Hb9 INs) are synchronous with locomotor-like rhythmic motor outputs, suggesting that they contribute to the excitatory drive of motoneurons during locomotion. Similar to central pattern generator neurons in other systems, Hb9 INs are interconnected via electrical coupling, and their rhythmic activity does not depend on fast glutamatergic synaptic transmission. The primary objective of this study was to determine the contribution of fast excitatory and inhibitory synaptic transmission and subthreshold voltage-dependent currents to the induced membrane oscillations in Hb9 INs in the postnatal mouse spinal cord. The non-N-methyl-D-aspartate receptor antagonist 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) reduced the amplitude of voltage oscillations but did not alter their frequency. CNQX suppressed rhythmic motor activity. Blocking glycine and GABAA receptor-mediated inhibitory synapses as well as cholinergic transmission did not change the properties of CNQX-resistant membrane oscillations. However, disinhibition triggered new episodes of slow motor bursting that were not correlated with induced locomotor-like rhythms in Hb9 INs. Our observations indicated that fast excitatory and inhibitory synaptic inputs did not control the frequency of induced rhythmic activity in Hb9 INs. We next examined the contribution of persistent sodium current (INaP) to subthreshold membrane oscillations in the absence of primary glutamatergic, GABAergic and glycinergic synaptic drive to Hb9 INs. Low concentrations of riluzole that blocked the slow-inactivating component of sodium current gradually suppressed the amplitude and reduced the frequency of voltage oscillations. Our finding that INaP regulates locomotor-related rhythmic activity in Hb9 INs independently of primary synaptic transmission supports the concept that these neurons constitute an
Weak Signal Detection Based on Phase Locked Loop and Chaotic Oscillator%基于锁相环和浞沌振子的微弱信号检测
Institute of Scientific and Technical Information of China (English)
张瑜; 贺秋瑞
2012-01-01
In order to detect accurately the amplitude and frequency of a nV-level sine signal,a hybrid detection system of weak signal based on phase locked loop and chaotic oscillator was built.First,by locking the measured signal which is input to phase locked loop,the signal frequency detection is completed.Then,taking the phase locked loop output signal whose frequency is known as the internal motive power signal of the chaos system,the amplitude of the input measured signal to the chaos system can be detected by Duffing oscillator.Simulation results show that: the hybrid system can detect the frequency and the amplitude of a nv-level weak signal at the same time; the lowest SNR of the signal is -22.23dB,and the hybrid system is easy to operate,which needs small amount of work and is easy to realize.%为精确检测纳伏级微弱正弦信号的频率和幅值,构建了基于锁相环和Duffing振子的微弱信号混合检测系统.首先通过锁定输入锁相环的待测信号,完成信号频率的检测;然后利用锁相环输出的已知频率信号作为混沌系统的内置策动力信号,将输入到混沌系统的待测信号用Duffing振子进行幅值检测.仿真结果表明,混合系统可同时完成纳伏级微弱正弦信号的频率和幅值的检测,检测信号的最低信噪比为-22.23dB,且操作简单,工作量小,易于实现.
An adaptive strategy for controlling chaotic system
Institute of Scientific and Technical Information of China (English)
曹一家; 张红先
2003-01-01
This paper presents an adaptive strategy for controlling chaotic systems. By employing the phase space reconstruction technique in nonlinear dynamical systems theory, the proposed strategy transforms the nonlinear system into canonical form, and employs a nonlinear observer to estimate the uncertainties and disturbances of the nonlinear system, and then establishes a state-error-like feedback law. The developed control scheme allows chaos control in spite of modeling errors and parametric variations. The effectiveness of the proposed approach has been demonstrated through its applications to two well-known chaotic systems : Duffing oscillator and Rǒssler chaos.
An adaptive strategy for controlling chaotic system.
Cao, Yi-Jia; Hang, Hong-Xian
2003-01-01
This paper presents an adaptive strategy for controlling chaotic systems. By employing the phase space reconstruction technique in nonlinear dynamical systems theory, the proposed strategy transforms the nonlinear system into canonical form, and employs a nonlinear observer to estimate the uncertainties and disturbances of the nonlinear system, and then establishes a state-error-like feedback law. The developed control scheme allows chaos control in spite of modeling errors and parametric variations. The effectiveness of the proposed approach has been demonstrated through its applications to two well-known chaotic systems: Duffing oscillator and Rössler chaos.
An adaptive strategy for controlling chaotic system
Institute of Scientific and Technical Information of China (English)
曹一家; 张红先
2003-01-01
This paper presents an adaptive strategy for controlling chaotic systems. By employing the phase space reconstruction technique in nonlinear dynamical systems theory, the proposed strategy transforms the nonlinear system into canonical form, and employs a nonlinear observer to estimate the uncertainties and disturbances of the nonlinear system, and then establishes a state-error-like feedback law. The developed control scheme allows chaos control in spite of modeling errors and parametric variations. The effectiveness of the proposed approach has been demonstrated through its applications to two well-known chaotic systems: Duffing oscillator and Rossler chaos.
Hramov, Alexander E; Morozov, Mikhail; Mushtakov, Alexander
2008-01-01
In this Letter we research the space charge limiting current value at which the oscillating virtual cathode is formed in the relativistic electron beam as a function of the external magnetic field guiding the beam electrons. It is shown that the space charge limiting (critical) current decreases with growth of the external magnetic field, and that there is an optimal induction value of the magnetic field at which the critical current for the onset of virtual cathode oscillations in the electron beam is minimum. For the strong external magnetic field the space charge limiting current corresponds to the analytical relation derived under the assumption that the motion of the electron beam is one-dimensional [High Power Microwave Sources. Artech House Microwave Library, 1987. Chapter~13]. Such behavior is explained by the characteristic features of the dynamics of electron space charge in the longitudinal and radial directions in the drift space at the different external magnetic fields.
Unmasking Chaotic Attributes in Time Series of Living Cell Populations
Laurent, Michel; Deschatrette, Jean; Wolfrom, Claire M.
2010-01-01
Background Long-range oscillations of the mammalian cell proliferation rate are commonly observed both in vivo and in vitro. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes related to proliferation rate, including metabolic activity, telomere homeostasis, gene expression, and tumor growth. Methodology/Principal Findings Using a simple, original, nonlinear method based on return maps, we previously found a geometrical deterministic structure coordinating such fluctuations in populations of various cell types. However, nonlinearity and determinism are only necessary conditions for chaos; they do not by themselves constitute a proof of chaotic dynamics. Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators. All four systems also display this geometrical structure, coordinating the oscillations of one or two variables of the oscillator. No such structure could be observed in periodic or stochastic fluctuations. Conclusion/Significance Theoretical models predict various cell population dynamics, from stable through periodically oscillating to a chaotic regime. Periodic and stochastic fluctuations were first described long ago in various mammalian cells, but by contrast, chaotic regulation had not previously been evidenced. The findings with our nonlinear geometrical approach are entirely consistent with the notion that fluctuations of cell populations can be chaotically controlled. PMID:20179755
Unmasking chaotic attributes in time series of living cell populations.
Directory of Open Access Journals (Sweden)
Michel Laurent
Full Text Available BACKGROUND: Long-range oscillations of the mammalian cell proliferation rate are commonly observed both in vivo and in vitro. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes related to proliferation rate, including metabolic activity, telomere homeostasis, gene expression, and tumor growth. METHODOLOGY/PRINCIPAL FINDINGS: Using a simple, original, nonlinear method based on return maps, we previously found a geometrical deterministic structure coordinating such fluctuations in populations of various cell types. However, nonlinearity and determinism are only necessary conditions for chaos; they do not by themselves constitute a proof of chaotic dynamics. Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators. All four systems also display this geometrical structure, coordinating the oscillations of one or two variables of the oscillator. No such structure could be observed in periodic or stochastic fluctuations. CONCLUSION/SIGNIFICANCE: Theoretical models predict various cell population dynamics, from stable through periodically oscillating to a chaotic regime. Periodic and stochastic fluctuations were first described long ago in various mammalian cells, but by contrast, chaotic regulation had not previously been evidenced. The findings with our nonlinear geometrical approach are entirely consistent with the notion that fluctuations of cell populations can be chaotically controlled.
Super Persistent Chaotic Transients And Catastrophic Bifurcation From Riddled To Fractal Basins
Andrade, V A
2002-01-01
This dissertation treats two related problems in chaotic dynamics: (1) super persistent chaotic transients in physical systems, and (2) catastrophic bifurcation from riddled to fractal basins. For the first problem, we investigate super persistent chaotic transient by studying the effect of noise on phase synchronization of coupled chaotic oscillators. A super persistent chaotic transient is typically induced by an unstable-unstable pair bifurcation in which two unstable periodic orbits of the same period coalesce and disappear as a system parameter is changed through a critical value. So far examples illustrating this type of transient chaos utilize discrete-time maps. We present a class of continuous-time dynamical systems that exhibit super persistent chaotic transients in parameter regimes of positive measure. In particular, we examine the effect of noise on phase synchronization of coupled chaotic oscillators. It is found that additive white noise can induce phase slips in integer multi...
Coexistence of anticipated and layered chaotic synchronization in time-delay systems.
Wang, H J; Huang, H B; Qi, G X
2005-09-01
We study the dynamic stabilities of unidirectionally coupled linear arrays of chaotic oscillators with time-delay feedbacks in star configuration, and find that if all oscillators in the network are identical, then the oscillators in the linear arrays can anticipate the driving oscillators, and simultaneously the oscillators in the linear arrays with the same position with respect to the central one are in synchronous chaotic state. Compared with the anticipated synchronization, the layered synchronization is first generated and last destroyed as the coupling constant is increased. This coexistence of anticipated and layered chaotic synchronization is destroyed by long time feedback. If the driving and driven oscillators are different, then only layered chaotic synchronization is possible.
Energy Technology Data Exchange (ETDEWEB)
Chen, Shujun; Zhang, Senfu; Zhu, Qiyuan; Liu, Xianyin; Jin, Chendong; Wang, Jianbo; Liu, Qingfang, E-mail: liuqf@lzu.edu.cn [Key Laboratory for Magnetism and Magnetic Materials of Ministry of Education, Lanzhou University, Lanzhou 730000 (China)
2015-05-07
By micromagnetic simulation, we investigated the dynamic of magnetic vortex driven by spin-polarized current in Permalloy nanodisks in the presence of interfacial/superficial Dzyaloshinskii-Moriya interactions (DMI). It is found that spin-polarized current can drive the vortex precession. In the presence of DMI, the oscillation frequency of the vortex is about 3 times higher than that of without DMI for the same nanodisk. Moreover, the linewidth is more narrow than that of without DMI when the radius of nanodisk is 50 nm. In addition, the vortex can support a higher current density than that of without DMI. Introduction of DMI in this system can provide a new way to design magnetic vortex oscillator.
On nonlinear control design for autonomous chaotic systems of integer and fractional orders
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M. E-mail: wajdi@sharjah.ac.ae; Harb, Ahmad M. E-mail: aharb@just.edu.jo
2003-11-01
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.
Lai, Wenxi; Cao, Yunshan; Ma, Zhongshui
2012-05-01
A general master equation is derived to describe an electromechanical single-dot transistor in the Coulomb blockade regime. In the equation, Fermi distribution functions in the two leads are taken into account, which allows one to study the system as a function of bias voltage and temperature of the leads. Furthermore, we treat the coherent interaction mechanism between electron tunneling events and the dynamics of excited vibrational modes. Stationary solutions of the equation are numerically calculated. We show that current through the oscillating island at low temperature appears to have step-like characteristics as a function of the bias voltage and the steps depend on the mean phonon number of the oscillator. At higher temperatures the current steps would disappear and this event is accompanied by the emergence of thermal noise of the charge transfer. When the system is mainly in the ground state, the zero frequency Fano factor of current manifests sub-Poissonian noise and when the system is partially driven into its excited states it exhibits super-Poissonian noise. The difference in the current noise would almost be removed for the situation in which the dissipation rate of the oscillator is much larger than the bare tunneling rates of electrons.
Sivakov, A. G.; Pokhila, A. S.; Glukhov, A. M.; Kuplevakhsky, S. V.; Omelyanchouk, A. N.
2014-05-01
We report the results of experimental and theoretical studies of critical current oscillations in thin doubly-connected Sn films in an external perpendicular magnetic field. The experiments were performed on samples that consisted of two wide electrodes joined together by two narrow channels. The length of the channels l satisfied the condition l ≫ ξ (ξ is the Ginzburg-Landau coherence length). At temperatures close to the critical temperature Tc, the dependence of the critical current Ic on average external magnetic flux Φ¯e has the form of a piecewise linear function, periodic with respect to the flux quantum Φ0. The amplitude of the Ic oscillation at a given temperature is proportional to the factor ξ/l. Moreover, the dependence Ic=Ic(Φ ¯e) is found to be multivalued, hence indicating the presence of metastable states. Based on the Ginzburg-Landau approximation, a theory was constructed that explains the above features of the oscillation phenomenon taking a perfectly symmetric system as an example. Further, the experiments displayed the effects related to the critical currents imbalance between the superconducting channels, i.e., shift of the maxima of the dependence Ic=Ic(Φ ¯e) accompanied by an asymmetry with respect to the transport current direction.
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.
Wu, Ping; Sun, Jun; Song, Zhimin; Teng, Yan
2017-01-01
Explosive emission cathodes (EECs) are widely used in high power microwave generators. This paper researches the influence of the emission threshold and the current increase rate of annular EECs on the microwave starting time of a relativistic backward wave oscillator (RBWO) when the current amplitude is not affected. The results show that a moderate delay in explosive emission, as long as it's not too long and the current increase rate keeps fast enough, won't bring about a corresponding delay in the starting time of microwave, but inversely, may suppress the mode competition and thus expedite the starting process slightly. The current increase rate, however, has more prominent influence on the starting time of the RBWO. A slower current increase rate will delay the time when the beam current reaches the starting current and lead to a longer starting time.
Directory of Open Access Journals (Sweden)
J. Bajer
2011-04-01
Full Text Available The paper deals with a pair of current-mode sine-wave oscillator circuits. Both these circuits are implemented using positive second-generation current conveyors (CCII+. The principle of the first oscillator is based on a conventional Wien-bridge network. However, this implementation suffers from the use of a floating capacitor, which can be unacceptable in the case of on-chip integration. This drawback is solved in the second variant via a slight modification of the Wien-bridge network, which then allows the use of all capacitors grounded. The modified circuit version was manufactured by means of the socalled diamond transistors, which play the role of CCII+ active building blocks. The circuit behavior was analyzed theoretically, with particular emphasis on the identification of real effects and their elimination, and subsequently verified experimentally. The experimental results are included in the paper.
Kiss, István Z.; Munjal, Neil; Martin, R. Scott
2009-01-01
We investigate the oscillatory electro-oxidation of formic acid on platinum in a microchip-based dual-electrode cell with microfluidic flow control. The main dynamical features of current oscillations on single Pt electrode that had been observed in macro-cells are reproduced in the microfabricated electrochemical cell. In dual-electrode configuration nearly in-phase synchronized current oscillations occur when the reference/counter electrodes are placed far away from the microelectrodes. The synchronization disappears with close reference/counter electrode placements. We show that the cause for synchronization is weak albeit important, bidirectional electrical coupling between the electrodes; therefore the unidirectional mass transfer interactions are negligible. The experimental design enables the investigation of the dynamical behavior in micro-electrode arrays with well-defined control of flow of the electrolyte in a manner where the size and spacing of the electrodes can be easily varied. PMID:20160883
Kiss, István Z; Munjal, Neil; Martin, R Scott
2009-12-30
We investigate the oscillatory electro-oxidation of formic acid on platinum in a microchip-based dual-electrode cell with microfluidic flow control. The main dynamical features of current oscillations on single Pt electrode that had been observed in macro-cells are reproduced in the microfabricated electrochemical cell. In dual-electrode configuration nearly in-phase synchronized current oscillations occur when the reference/counter electrodes are placed far away from the microelectrodes. The synchronization disappears with close reference/counter electrode placements. We show that the cause for synchronization is weak albeit important, bidirectional electrical coupling between the electrodes; therefore the unidirectional mass transfer interactions are negligible. The experimental design enables the investigation of the dynamical behavior in micro-electrode arrays with well-defined control of flow of the electrolyte in a manner where the size and spacing of the electrodes can be easily varied.
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...
Spread spectrum communication system with chaotic frequency modulation
Volkovskii, A. R.; Tsimring, L. Sh.; Rulkov, N. F.; Langmore, I.
2005-09-01
A new spread spectrum communication system utilizing chaotic frequency modulation of sinusoidal signals is discussed. A single phase lock loop (PLL) system in the receiver is used both to synchronize the local chaotic oscillator and to recover the information signal. We study the dynamics of the synchronization process, stability of the PLL system, and evaluate the bit-error-rate performance of this chaos-based communication system.
Periodization of Duffing oscillators suspended on elastic structure: Mechanical explanation
Energy Technology Data Exchange (ETDEWEB)
Czolczynski, K. [Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz (Poland)]. E-mail: dzanta@ck-sg.p.lodz.pl; Kapitaniak, T. [Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz (Poland); Perlikowski, P. [Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz (Poland); Stefanski, A. [Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz (Poland)
2007-05-15
We consider the dynamics of chaotic oscillators suspended on the elastic structure. We show that for the given conditions of the structure, initially uncorrelated chaotic oscillators can synchronize both in chaotic and periodic regimes. The phenomena of the periodization, i.e., the behavior of nonlinear oscillators become periodic as a result of interaction with elastic structure, have been observed. We formulate the criterion for periodization of double well-potential Duffing oscillator evolution in terms of the forces and displacements in the spring elements. We argue that the observed phenomena are generic in the parameter space and independent of the number of oscillators and their location on the elastic structure.
Directory of Open Access Journals (Sweden)
Yimy eAmarillo
2015-05-01
Full Text Available Thalamocortical neurons are involved in the generation and maintenance of brain rhythms associated with global functional states. The repetitive burst firing of TC neurons at delta frequencies (1-4 Hz has been linked to the oscillations recorded during deep sleep and during episodes of absence seizures. To get insight into the biophysical properties that are the basis for intrinsic delta oscillations in these neurons, we performed a bifurcation analysis of a minimal conductance-based thalamocortical neuron model including only the IT channel and the sodium and potassium leak channels. This analysis unveils the dynamics of repetitive burst firing of TC neurons, and describes how the interplay between the amplifying variable mT and the recovering variable hT of the calcium channel IT is sufficient to generate low threshold oscillations in the delta band. We also explored the role of the hyperpolarization activated cationic current Ih in this reduced model and determine that, albeit not required, Ih amplifies and stabilizes the oscillation.
Amarillo, Yimy; Mato, Germán; Nadal, Marcela S
2015-01-01
Thalamocortical neurons are involved in the generation and maintenance of brain rhythms associated with global functional states. The repetitive burst firing of TC neurons at delta frequencies (1-4 Hz) has been linked to the oscillations recorded during deep sleep and during episodes of absence seizures. To get insight into the biophysical properties that are the basis for intrinsic delta oscillations in these neurons, we performed a bifurcation analysis of a minimal conductance-based thalamocortical neuron model including only the IT channel and the sodium and potassium leak channels. This analysis unveils the dynamics of repetitive burst firing of TC neurons, and describes how the interplay between the amplifying variable mT and the recovering variable hT of the calcium channel IT is sufficient to generate low threshold oscillations in the delta band. We also explored the role of the hyperpolarization activated cationic current Ih in this reduced model and determine that, albeit not required, Ih amplifies and stabilizes the oscillation.
Chaotic phenomena in Josephson circuits coupled quantum cellular neural networks
Institute of Scientific and Technical Information of China (English)
Wang Sen; Cai Li; Li Qin; Wu Gang
2007-01-01
In this paper the nonlinear dynamical behaviour of a quantum cellular neural network (QCNN) by coupling Josephson circuits was investigated and it was shown that the QCNN using only two of them can cause the onset of chaotic oscillation. The theoretical analysis and simulation for the two Josephson-circuits-coupled QCNN have been done by using the amplitude and phase as state variables. The complex chaotic behaviours can be observed and then proved by calculating Lyapunov exponents. The study provides valuable information about QCNNs for future application in high-parallel signal processing and novel chaotic generators.
Quantum chaotic attractor in a dissipative system
Liu, W V; Schieve, William C.
1997-01-01
A dissipative quantum system is treated here by coupling it with a heat bath of harmonic oscillators. Through quantum Langevin equations and Ehrenfest's theorem, we establish explicitly the quantum Duffing equations with a double-well potential chosen. A quantum noise term appears the only driving force in dynamics. Numerical studies show that the chaotic attractor exists in this system while chaos is certainly forbidden in the classical counterpart.
Frequency-Locking in Coupled Chaotic Systems
Institute of Scientific and Technical Information of China (English)
HU Bam-Bi; LIU Zong-Hua; ZHENG Zhi-Gang
2001-01-01
A novel approach is presented for measuring the phase synchronization (frequency-locking) of coupled N nonidentical oscillators, which can characterize frequency-locking for chaotic systems without well-defined phase by measuring the mean frequency. Numerical simulations confirm the existence of frequency-locking. The relations between the mean frequency and the coupling strength and the frequency mismatch are given. For the coupled hyperchaotic systems, the frequency-locking can be better characterized by more than one mean frequency curves.
Deciphering Secure Chaotic Communication
Mathiazhagen, C
1999-01-01
A simple technique for decoding an unknown modulated chaotic time-series is presented. We point out that, by fitting a polynomial model to the modulated chaotic signal, the error in the fit gives sufficient information to decode the modulating signal. For analog implementation, a lowpass filter can be used for fitting. This method is simple and easy to implement in hardware.
Rising Above Chaotic Likelihoods
Du, Hailiang
2014-01-01
Berliner (Likelihood and Bayesian prediction for chaotic systems, J. Am. Stat. Assoc. 1991) identified a number of difficulties in using the likelihood function within the Bayesian paradigm for state estimation and parameter estimation of chaotic systems. Even when the equations of the system are given, he demonstrated "chaotic likelihood functions" of initial conditions and parameter values in the 1-D Logistic Map. Chaotic likelihood functions, while ultimately smooth, have such complicated small scale structure as to cast doubt on the possibility of identifying high likelihood estimates in practice. In this paper, the challenge of chaotic likelihoods is overcome by embedding the observations in a higher dimensional sequence-space, which is shown to allow good state estimation with finite computational power. An Importance Sampling approach is introduced, where Pseudo-orbit Data Assimilation is employed in the sequence-space in order first to identify relevant pseudo-orbits and then relevant trajectories. Es...
Current driven spin–orbit torque oscillator: ferromagnetic and antiferromagnetic coupling
Johansen, Øyvind; Linder, Jacob
2016-01-01
We consider theoretically the impact of Rashba spin–orbit coupling on spin torque oscillators (STOs) in synthetic ferromagnets and antiferromagnets that have either a bulk multilayer or a thin film structure. The synthetic magnets consist of a fixed polarizing layer and two free magnetic layers that interact through the Ruderman-Kittel-Kasuya-Yosida interaction. We determine analytically which collinear states along the easy axis that are stable, and establish numerically the phase diagram for when the system is in the STO mode and when collinear configurations are stable, respectively. It is found that the Rashba spin–orbit coupling can induce anti-damping in the vicinity of the collinear states, which assists the spin transfer torque in generating self-sustained oscillations, and that it can substantially increase the STO part of the phase diagram. Moreover, we find that the STO phase can extend deep into the antiferromagnetic regime in the presence of spin–orbit torques. PMID:27653357
Prediction of femtosecond oscillations in the transient current of a quantum dot in the Kondo regime
Goker, A.
2010-10-11
We invoke the time-dependent noncrossing approximation in order to study the effects of the density of states of gold contacts on the instantaneous conductance of a single electron transistor which is abruptly moved into the Kondo regime by means of a gate voltage. For an asymmetrically coupled system, we observe that the instantaneous conductance in the Kondo time scale exhibits beating with distinct frequencies, which are proportional to the separation between the Fermi level and the sharp features in the density of states of gold. Increasing the ambient temperature or bias quenches the amplitude of the oscillations. We attribute the oscillations to interference between the emerging Kondo resonance and van-Hove singularities in the density of state. In addition, we propose an experimental realization of this model.
Pagitsas, M; Sazou, D
2003-01-01
Analysis of the passive-active oscillatory region of the Fe-0.75 M H sub 2 SO sub 4 system, perturbed by adding small amounts of halide species, allow the distinction between pitting and general corrosion. Complex periodic and aperiodic current oscillations characterize pitting corrosion whereas monoperiodic oscillations of a relaxation type indicate general corrosion. A point defect model (PDM) is considered for the microscopic description of the growth and breakdown of the iron oxide film. The physicochemical processes leading to different types of corrosion can be clarified in terms of the PDM. Occupation of an anion vacancy by a halide ion results in the localized attack of the passive oxide and pitting corrosion. On the other hand, the formation of surface soluble iron complexes is related to the uniform dissolution of the passive oxide and general corrosion.
New developments in classical chaotic scattering.
Seoane, Jesús M; Sanjuán, Miguel A F
2013-01-01
Classical chaotic scattering is a topic of fundamental interest in nonlinear physics due to the numerous existing applications in fields such as celestial mechanics, atomic and nuclear physics and fluid mechanics, among others. Many new advances in chaotic scattering have been achieved in the last few decades. This work provides a current overview of the field, where our attention has been mainly focused on the most important contributions related to the theoretical framework of chaotic scattering, the fractal dimension, the basins boundaries and new applications, among others. Numerical techniques and algorithms, as well as analytical tools used for its analysis, are also included. We also show some of the experimental setups that have been implemented to study diverse manifestations of chaotic scattering. Furthermore, new theoretical aspects such as the study of this phenomenon in time-dependent systems, different transitions and bifurcations to chaotic scattering and a classification of boundaries in different types according to symbolic dynamics are also shown. Finally, some recent progress on chaotic scattering in higher dimensions is also described.
Chaotic neurodynamics for autonomous agents.
Harter, Derek; Kozma, Robert
2005-05-01
Mesoscopic level neurodynamics study the collective dynamical behavior of neural populations. Such models are becoming increasingly important in understanding large-scale brain processes. Brains exhibit aperiodic oscillations with a much more rich dynamical behavior than fixed-point and limit-cycle approximation allow. Here we present a discretized model inspired by Freeman's K-set mesoscopic level population model. We show that this version is capable of replicating the important principles of aperiodic/chaotic neurodynamics while being fast enough for use in real-time autonomous agent applications. This simplification of the K model provides many advantages not only in terms of efficiency but in simplicity and its ability to be analyzed in terms of its dynamical properties. We study the discrete version using a multilayer, highly recurrent model of the neural architecture of perceptual brain areas. We use this architecture to develop example action selection mechanisms in an autonomous agent.
HARMONIC COMPONENT EXTRACTION FROM A CHAOTIC SIGNAL BASED ON EMPIRICAL MODE DECOMPOSITION METHOD
Institute of Scientific and Technical Information of China (English)
LI Hong-guang; MENG Guang
2006-01-01
A novel approach of signal extraction of a harmonic component from a chaotic signal generated by a Duffing oscillator was proposed. Based on empirical mode decomposition (EMD) and concept that any signal is composed of a series of the simple intrinsic modes, the harmonic components were extracted from the chaotic signals. Simulation results show the approach is satisfactory.
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.
Simple Autonomous Chaotic Circuits
Piper, Jessica; Sprott, J.
2010-03-01
Over the last several decades, numerous electronic circuits exhibiting chaos have been proposed. Non-autonomous circuits with as few as two components have been developed. However, the operation of such circuits relies on the non-ideal behavior of the devices used, and therefore the circuit equations can be quite complex. In this paper, we present two simple autonomous chaotic circuits using only opamps and linear passive components. The circuits each use one opamp as a comparator, to provide a signum nonlinearity. The chaotic behavior is robust, and independent of nonlinearities in the passive components. Moreover, the circuit equations are among the algebraically simplest chaotic systems yet constructed.
Chaos control of parametric driven Duffing oscillators
Energy Technology Data Exchange (ETDEWEB)
Jin, Leisheng; Mei, Jie; Li, Lijie, E-mail: L.Li@swansea.ac.uk [College of Engineering, Swansea University, Swansea SA2 8PP (United Kingdom)
2014-03-31
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Chaos control of parametric driven Duffing oscillators
Jin, Leisheng; Mei, Jie; Li, Lijie
2014-03-01
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Morin, France; Haufler, Darrell; Skinner, Frances K; Lacaille, Jean-Claude
2010-06-01
CA1 inhibitory interneurons at the stratum lacunosum-moleculare and radiatum junction (LM/RAD-INs) display subthreshold membrane potential oscillations (MPOs) involving voltage-dependent Na(+) and A-type K(+) currents. LM/RAD-INs also express other voltage-gated K(+) currents, although their properties and role in MPOs remain unclear. Here, we characterized these voltage-gated K(+) currents and investigated their role in MPOs. Using outside-out patch recordings from LM/RAD-IN somata, we distinguished four voltage-gated K(+) currents based on their pharmacology and activation/inactivation properties: a fast delayed rectifier current (I(Kfast)), a slow delayed rectifier current (I(Kslow)), a rapidly inactivating A-type current (I(A)), and a slowly inactivating current (I(D)). Their relative contribution to the total K(+) current was I(A) > I(Kfast) > I(Kslow) = I(D). The presence of I(D) and the relative contributions of K(+) currents in LM/RAD-INs are different from those of other CA1 interneurons, suggesting the presence of differential complement of K(+) currents in subgroups of interneurons. We next determined whether these K(+) currents were sufficient for MPO generation using a single-compartment model of LM/RAD-INs. The model captured the subthreshold voltage dependence of MPOs. Moreover, all K(+) currents were active at subthreshold potentials but I(D), I(A), and the persistent sodium current (I(NaP)) were most active near threshold. Using impedance analysis, we found that I(A) and I(NaP) contribute to MPO generation by modulating peak spectral frequency during MPOs and governing the voltage range over which MPOs occur. Our findings uncover a differential expression of a complement of K(+) channels that underlies intrinsic rhythmic activity in inhibitory interneurons.
Doeltgen, Sebastian H; McAllister, Suzanne M; Ridding, Michael C
2012-09-01
The objective of this study was to assess whether the simultaneous application of slow-oscillation transcranial direct current stimulation enhances the neuroplastic response to transcranial magnetic theta burst stimulation. Motor evoked potential amplitude was assessed at baseline and at regular intervals up to 60 min following continuous theta burst stimulation, slow-oscillation transcranial direct current stimulation, and the simultaneous application of these paradigms. In addition, the electroencephalographic power spectra of slow and fast delta, and theta frequency bands recorded over the motor cortex were analyzed prior to and up to 5 min following each intervention. There was longer-lasting motor evoked potential suppression following the simultaneous application of continuous theta burst stimulation and slow-oscillation transcranial direct current stimulation compared with when continuous theta burst stimulation was applied alone. Slow-oscillation transcranial direct current stimulation applied alone did not modulate the motor evoked potential amplitude. No significant changes in spectral power were observed following slow-oscillation transcranial direct current stimulation. Simultaneous application of continuous theta burst stimulation and slow-oscillation transcranial direct current stimulation may provide an approach to prolong the induction of neuroplastic changes in motor cortical circuits by repetitive transcranial magnetic brain stimulation.
Shot noise of charge current in a quantum dot responded by rotating and oscillating magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Zhao, Hong-Kang, E-mail: zhaohonk@yahoo.com; Zou, Wei-Ke [School of Physics, Beijing Institute of Technology, Beijing 100081 (China); Chen, Qiao [Department of Maths and Physics, Hunan Institute of Engineering, Xiangtan 411104 (China)
2014-09-07
We have investigated the shot noise and Fano factor of the dynamic spin-polarized quantum dot under the perturbations of a rotating magnetic field (RMF), and an oscillating magnetic field (OMF) by employing the non-equilibrium Green's function approach. The shot noise is enhanced from sub-Poissonian to super-Poissonian due to the application of RMF and OMF, and it is controlled sensitively by the tilt angle θ of RMF. The magnitude of shot noise increases as the photon energy ℏω of OMF increases, and its valley eventually is reversed to peaks as the photon energy is large enough. Double-peak structure of Fano factor is exhibited as the frequency of OMF increases to cover a large regime. The Zeeman energy μ{sub 0}B{sub 0} acts as an effective gate bias to exhibit resonant behavior, and novel peak emerges associated with the applied OMF.
Nuclear mass dependence of chaotic dynamics in Ginocchio model
Yoshinaga, N; Shigehara, T; Yoshinaga, Naotaka; Yoshida, Nobuaki; Shigehara, Takaomi
1995-01-01
The chaotic dynamics in nuclear collective motion is studied in the framework of a schematic shell model which has only monopole and quadrupole degrees of freedom. The model is shown to reproduce the experimentally observed global trend toward less chaotic motion in heavier nuclei. The relation between current approach and the earlier studies with bosonic models is discussed.
Passive control of chaotic system with multiple strange attractors
Institute of Scientific and Technical Information of China (English)
Song Yun-Zhong; Zhao Guang-Zhou; Qi Dong-Lian
2006-01-01
In this paper we present a new simple controller for a chaotic system, that is, the Newton-Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form.Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one,and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.
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.
Chaotic signal processing: information aspects
Andreyev, Y V; Efremova, E V; Anagnostopoulos, A N
2003-01-01
One of the features of chaotic signals that make them different of other types of signals is their special information properties. In this paper, we investigate the effect of these properties on the procedures of chaotic signal processing. On examples of cleaning chaotic signals off noise, chaotic synchronization and separation of chaotic signals we demonstrate the existence of basic limits imposed by information theory on chaotic signal processing, independent of concrete algorithms. Relations of these limits with the Second law, Shannon theorems and Landauer principle are discussed.
Enhancing chaoticity of spatiotemporal chaos.
Li, Xiaowen; Zhang, Heqiao; Xue, Yu; Hu, Gang
2005-01-01
In some practical situations strong chaos is needed. This introduces the task of chaos control with enhancing chaoticity rather than suppressing chaoticity. In this paper a simple method of linear amplifications incorporating modulo operations is suggested to make spatiotemporal systems, which may be originally chaotic or nonchaotic, strongly chaotic. Specifically, this control can eliminate periodic windows, increase the values and the number of positive Lyapunov exponents, make the probability distributions of the output chaotic sequences more homogeneous, and reduce the correlations of chaotic outputs for different times and different space units. The applicability of the method to practical tasks, in particular to random number generators and secure communications, is briefly discussed.
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...
A direct numerical method for quantifying regular and chaotic orbits
Energy Technology Data Exchange (ETDEWEB)
Awrejcewicz, J. E-mail: awrejcew@ck-sg.p.lodz.pl; Dzyubak, L.; Grebogi, C
2004-02-01
Both a theoretical argument and a numerical algorithm to identify periodic and chaotic orbits are presented and discussed. Reliability of the approach is verified using the Duffing oscillator through the standard computation of Lyapunov exponents. Advantages of the proposed approach are given.
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...
Wakita, Hitoshi; Tamura, Kozo; Ozawa, Tatsuhiko; Bando, Yoshimasa; Kawamoto, Tadashi; Mori, Takehiko
2010-12-01
In an organic conductor β″-[bis(ethylenedithio)tetrathiafulvalene]3(HSO4)2, characteristic voltage oscillation is observed in the negative differential resistance region of the nonlinear conductivity below the metal-insulator transition at 125 K. The observed frequency f is 4-25 kHz and increases linearly with the collective current Jco. The oscillation appears in the two crystal directions of the conducting layer in agreement with the two-dimensional nonstripe charge order, where the anisotropy of the Jco/f slope is about two. The voltage oscillation disappears when the contact distance is larger than 0.02 cm, and at the same time the current-voltage characteristics loses a sharp negative resistance region. Since this critical length corresponds to the characteristic domain size of the charge order, the observed oscillation is interpreted by coherent transport of charge order which can move in different two directions.
Tsunegi, Sumito; Lebrun, Romain; Grimaldi, Eva; Jenkins, Alex S.; Kubota, Hitoshi; Yakushiji, Kay; Bortolotti, Paolo; Grollier, Julie; Fukushima, Akio; Yuasa, Shinji; Cros, Vincent
2016-10-01
The rich physics of spin transfer nano-oscillators (STNO) has provoked a huge interest to create a new generation of multi-functional microwave spintronic devices [1]. It has been often emphasized that their nonlinear behavior gives a unique opportunity to tune their radiofrequency (rf) properties but at the cost of large phase noise, not compatible with practical applications. To tackle this issue as well as to open the opportunities to new developments for non-boolean computations [1], one strategy is to use electrical synchronization of STOs through the rf current. Thereby, it is crucial to understand how the synchronization forces transmitted through the electric current. In this talk, we will first present the results of an experimental study showing the self-synchronization of STNO by re-injecting its rf current after a certain delay time [2]. In the second part, we demonstrate that the synchronization of two vortex-STNOs connected in parallel can be tuned either by an artificial delay or by the spin transfer torques [3]. The synchronization of spin-torque oscillators, combined with the drastic improvement of the rf-features (linewidth decreases by a factor of 2 and power increases by a factor of 4) in the synchronized state, marks an important milestone towards a new generation of rf-devices based on STNO. The authors acknowledge the financial support from ANR agency (SPINNOVA: ANR-11-NANO-0016) and EU grant (MOSAIC: ICT-FP7-317950). [1] N. Locatelli, V. Cros, and J. Grollier, Nat Mater 13, 11 (2014). [2] S. Tsunegi et al., arXiv:1509.05583 (2015) [3] R. Lebrun et al., arXiv:1601.01247 (2016)
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
Zhang, Junshi; Chen, Hualing; Li, Dichen
2017-09-01
Subject to a high voltage, leakage current and induced electrical energy dissipation inevitably occur during the actuation of dielectric elastomers (DEs). In this article, a theoretical model is developed to investigate the dissipative performance of DEs in dynamic actuation. Effects of three different actuation conditions, including DE materials’ viscoelasticity intensity, amplitude of applied voltage, and mechanical tensile force, are considered. Numerical calculations are employed to detect the dynamic dissipative performance of DEs including leakage current, electrical power density, and electrical energy density in certain vibrational periods. Leakage current and induced electrical energy dissipation are enhanced with the enlargement of amplitude of applied voltage and mechanical force, and are suppressed as the intensity of DEs’ viscoelastic creep increases. The electrical energy for dissipation and actuation is also analyzed and compared.
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.
Indian Academy of Sciences (India)
A M Jayannavar
2002-02-01
We present a simple model of transmission across a metallic mesoscopic ring. In one of its arm an electron interacts with a single magnetic impurity via an exchange coupling. We show that entanglement between electron and spin impurity states leads to reduction of Aharonov–Bohm oscillations in the transmission coefﬁcient. The spin-conductance is asymmetric in the ﬂux reversal as opposed to the two-probe electrical conductance which is symmetric. In the same model, in contradiction to the naive expectation of a current magniﬁcation effect, we observe enhancement as well as suppression of this effect depending on the system parameters. The limitations of this model to the general notion of dephasing or decoherence in quantum systems are pointed out.
A Self-Oscillating Control Scheme for a Boost Converter Providing a Controlled Output Current
DEFF Research Database (Denmark)
Knott, Arnold; Pfaffinger, Gerhard R.; Andersen, Michael A. E.
2011-01-01
Most switched mode power supplies provide a regulated voltage at their output. However, there are applications requiring a controlled current. Among others are battery chargers, test equipment for converters driven by solar cells, and LED drivers. This paper describes a dc–dc power converter real...
Mapping entrained brain oscillations during transcranial alternating current stimulation (tACS)
Witkowski, M.; Garcia Cossio, E.; Chander, B.S.; Braun, C.; Birbaumer, N.; Robinson, S.E.; Soekadar, S.R.
2016-01-01
Transcranial alternating current stimulation (tACS), a non-invasive and well-tolerated form of electric brain stimulation, can influence perception, memory, as well as motor and cognitive function. While the exact underlying neurophysiological mechanisms are unknown, the effects of tACS are mainly
Implications of the first neutral current data from SNO for Solar Neutrino Oscillation
Bandyopadhyay, A; Goswami, S; Roy, D P; Bandyopadhyay, Abhijit; Choubey, Sandhya; Goswami, Srubabati
2002-01-01
We perform model independent and model dependent analyses of solar neutrino data including the neutral current event rate from SNO. The inclusion of the first SNO NC data in the model independent analysis determines the allowed ranges of $^{8}{B}$ flux normalisation and the $\
Nonlinear damped oscillators on Riemannian manifolds: Numerical simulation
Fiori, Simone
2017-06-01
Nonlinear oscillators are ubiquitous in sciences, being able to model the behavior of complex nonlinear phenomena, as well as in engineering, being able to generate repeating (i.e., periodic) or non-repeating (i.e., chaotic) reference signals. The state of the classical oscillators known from the literature evolves in the space Rn , typically with n = 1 (e.g., the famous van der Pol vacuum-tube model), n = 2 (e.g., the FitzHugh-Nagumo model of spiking neurons) or n = 3 (e.g., the Lorenz simplified model of turbulence). The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices.
Chaotic LIDAR for Naval Applications
2014-09-30
LIDAR for Naval Applications: FY12 Progress Report (7/1/2014- 9/30/2014) This document provides a progress report on the project "Chaotic LIDAR for...digital receiver to form a chaotic LIDAR (CLIDAR) ranging system. The design of the chaotic fiber ring laser and the fiber amplifiers are guided by...Wideband Amplifier Chain High Power Blue-Green Ranging Fig 1. The chaotic LIDAR (CLIDAR) transmitter approach. Several stages are used to
Directory of Open Access Journals (Sweden)
Shane eLee
2013-12-01
Full Text Available Gamma frequency rhythms have been implicated in numerous studies for their role in healthy and abnormal brain function. The frequency band has been described to encompass as broad a range as 30–150 Hz. Crucial to understanding the role of gamma in brain function is an identification of the underlying neural mechanisms, which is particularly difficult in the absence of invasive recordings in macroscopic human signals such as those from magnetoencephalography (MEG and electroencephalography (EEG. Here, we studied features of current dipole (CD signals from two distinct mechanisms of gamma generation, using a computational model of a laminar cortical circuit designed specifically to simulate CDs in a biophysically principled manner (Jones et al., 2007; Jones et al., 2009. We simulated spiking pyramidal interneuronal gamma (PING whose period is regulated by the decay time constant of GABAA-mediated synaptic inhibition and also subthreshold gamma driven by gamma-periodic exogenous excitatory synaptic drive. Our model predicts distinguishable CD features created by spiking PING compared to subthreshold driven gamma that can help to disambiguate mechanisms of gamma oscillations in human signals. We found that gamma rhythms in neocortical layer 5 can obscure a simultaneous, independent gamma in layer 2/3. Further, we arrived at a novel interpretation of the origin of high gamma frequency rhythms (100–150 Hz, showing that they emerged from a specific temporal feature of CDs associated with single cycles of PING activity and did not reflect a separate rhythmic process. Last we show that the emergence of observable subthreshold gamma required highly coherent exogenous drive. Our results are the first to demonstrate features of gamma oscillations in human current source signals that distinguish cellular and circuit level mechanisms of these rhythms and may help guide understanding of their functional role.
Directory of Open Access Journals (Sweden)
Olivia Morgan Lapenta
2013-06-01
Full Text Available Motor system neural networks are activated during movement imagery, observation and execution, with a neural signature characterized by suppression of the Mu rhythm. In order to investigate the origin of this neurophysiological marker, we tested whether transcranial direct current stimulation (tDCS modifies Mu rhythm oscillations during tasks involving observation and imagery of biological and non-biological movements. We applied tDCS (anodal, cathodal and sham in 21 male participants (mean age 23.8+3.06, over the left M1 with a current of 2mA for 20 minutes. Following this, we recorded the EEG at C3, C4 and Cz and surrounding C3 and C4 electrodes. Analyses of C3 and C4 showed significant effects for biological vs. non-biological movement (p=0.005, and differential hemisphere effects according to the type of stimulation (p=0.04 and type of movement (p=0.02. Analyses of surrounding electrodes revealed significant interaction effects considering type of stimulation and imagery or observation of biological or non-biological movement (p=0.03. The main findings of this study were (i Mu desynchronization during biological movement of the hand region in the contralateral hemisphere after sham tDCS; (ii polarity-dependent modulation effects of tDCS on the Mu rhythm, i.e. anodal tDCS led to Mu synchronization while cathodal tDCS led to Mu desynchronization during movement observation and imagery (iii specific focal and opposite inter-hemispheric effects, i.e. contrary effects for the surrounding electrodes during imagery condition and also for inter-hemispheric electrodes (C3 vs. C4. These findings provide insights into the cortical oscillations during movement observation and imagery. Furthermore it shows that tDCS can be highly focal when guided by a behavioral task.
Gitterman, Moshe
2010-01-01
Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multip
Charge and spin current oscillations in a tunnel junction induced by magnetic field pulses
Dartora, C. A.; Nobrega, K. Z.; Cabrera, G. G.
2016-08-01
Usually, charge and spin transport properties in tunnel junctions are studied in the DC bias regime and/or in the adiabatic regime of time-varying magnetic fields. In this letter, the temporal dynamics of charge and spin currents in a tunnel junction induced by pulsed magnetic fields is considered. At low bias voltages, energy and momentum of the conduction electrons are nearly conserved in the tunneling process, leading to the description of the junction as a spin-1/2 fermionic system coupled to time-varying magnetic fields. Under the influence of pulsed magnetic fields, charge and spin current can flow across the tunnel junction, displaying oscillatory behavior, even in the absence of DC bias voltage. A type of spin capacitance function, in close analogy to electric capacitance, is predicted.
Plasma Charge Current for Controlling and Monitoring Electron Beam Welding with Beam Oscillation
Directory of Open Access Journals (Sweden)
Valeriy Shchavlev
2012-12-01
Full Text Available Electron beam welding (EBW shows certain problems with the control of focus regime. The electron beam focus can be controlled in electron-beam welding based on the parameters of a secondary signal. In this case, the parameters like secondary emissions and focus coil current have extreme relationships. There are two values of focus coil current which provide equal value signal parameters. Therefore, adaptive systems of electron beam focus control use low-frequency scanning of focus, which substantially limits the operation speed of these systems and has a negative effect on weld joint quality. The purpose of this study is to develop a method for operational control of the electron beam focus during welding in the deep penetration mode. The method uses the plasma charge current signal as an additional informational parameter. This parameter allows identification of the electron beam focus regime in electron-beam welding without application of additional low-frequency scanning of focus. It can be used for working out operational electron beam control methods focusing exactly on the welding. In addition, use of this parameter allows one to observe the shape of the keyhole during the welding process.
Plasma charge current for controlling and monitoring electron beam welding with beam oscillation.
Trushnikov, Dmitriy; Belenkiy, Vladimir; Shchavlev, Valeriy; Piskunov, Anatoliy; Abdullin, Aleksandr; Mladenov, Georgy
2012-12-14
Electron beam welding (EBW) shows certain problems with the control of focus regime. The electron beam focus can be controlled in electron-beam welding based on the parameters of a secondary signal. In this case, the parameters like secondary emissions and focus coil current have extreme relationships. There are two values of focus coil current which provide equal value signal parameters. Therefore, adaptive systems of electron beam focus control use low-frequency scanning of focus, which substantially limits the operation speed of these systems and has a negative effect on weld joint quality. The purpose of this study is to develop a method for operational control of the electron beam focus during welding in the deep penetration mode. The method uses the plasma charge current signal as an additional informational parameter. This parameter allows identification of the electron beam focus regime in electron-beam welding without application of additional low-frequency scanning of focus. It can be used for working out operational electron beam control methods focusing exactly on the welding. In addition, use of this parameter allows one to observe the shape of the keyhole during the welding process.
Resurgence of oscillation in coupled oscillators under delayed cyclic interaction
Bera, Bidesh K.; Majhi, Soumen; Ghosh, Dibakar
2017-07-01
This paper investigates the emergence of amplitude death and revival of oscillations from the suppression states in a system of coupled dynamical units interacting through delayed cyclic mode. In order to resurrect the oscillation from amplitude death state, we introduce asymmetry and feedback parameter in the cyclic coupling forms as a result of which the death region shrinks due to higher asymmetry and lower feedback parameter values for coupled oscillatory systems. Some analytical conditions are derived for amplitude death and revival of oscillations in two coupled limit cycle oscillators and corresponding numerical simulations confirm the obtained theoretical results. We also report that the death state and revival of oscillations from quenched state are possible in the network of identical coupled oscillators. The proposed mechanism has also been examined using chaotic Lorenz oscillator.
IMPULSIVE CONTROL OF CHAOTIC ATTRACTORS IN NONLINEAR CHAOTIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
马军海; 任彪; 陈予恕
2004-01-01
Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.
Directory of Open Access Journals (Sweden)
Gonzalo Martín-Vázquez
Full Text Available Fluctuations in successive waves of oscillatory local field potentials (LFPs reflect the ongoing processing of neuron populations. However, their amplitude, polarity and synaptic origin are uncertain due to the blending of electric fields produced by multiple converging inputs, and the lack of a baseline in standard AC-coupled recordings. Consequently, the estimation of underlying currents by laminar analysis yields spurious sequences of inward and outward currents. We devised a combined analytical/experimental approach that is suitable to study laminated structures. The approach was essayed on an experimental oscillatory LFP as the Schaffer-CA1 gamma input in anesthetized rats, and it was verified by parallel processing of model LFPs obtained through a realistic CA1 aggregate of compartmental units. This approach requires laminar LFP recordings and the isolation of the oscillatory input from other converging pathways, which was achieved through an independent component analysis. It also allows the spatial and temporal components of pathway-specific LFPs to be separated. While reconstructed Schaffer-specific LFPs still show spurious inward/outward current sequences, these were clearly stratified into distinct subcellular domains. These spatial bands guided the localized delivery of neurotransmitter blockers in experiments. As expected, only Glutamate but not GABA blockers abolished Schaffer LFPs when applied to the active but not passive subcellular domains of pyramidal cells. The known chemical nature of the oscillatory LFP allowed an empirical offset of the temporal component of Schaffer LFPs, such that following reconstruction they yield only sinks or sources at the appropriate sites. In terms of number and polarity, some waves increased and others decreased proportional to the concomitant inputs in native multisynaptic LFPs. Interestingly, the processing also retrieved the initiation time for each wave, which can be used to discriminate
DEFF Research Database (Denmark)
Ostrikov, K.; Tsakadze, E.L.; Tsakadze, Z.L.;
2005-01-01
plasma parameters by the optical and Langmuir probes are presented. It is shown that the spatial profiles of the electron density, the effective electron temperature and plasma potential feature a great deal of the radial and axial uniformity compared with conventional sources of inductively coupled......A new source of low-frequency (0.46 MHz) inductively coupled plasmas sustained by the internal planar "unidirectional" RF current driven through a specially designed internal antenna configuration has been developed. The experimental results of the investigation of the optical and global argon...... applications and surface engineering. (c) 2005 Elsevier B.V. All rights reserved....
Karagueuzian, H S; Katzung, B G
1982-06-01
1. We studied the effects of a toxic concentration of ouabain on transmembrane electrical activity and on mechanical behaviour of right ventricular papillary muscles from ferrets in a single sucrose-gap using current clamp and voltage clamp.2. Ouabain (1.4-1.8 muM) induced oscillatory after-potentials and after-concentrations in current-clamp experiments. Voltage clamp showed that the oscillatory after-potential was caused by a transient inward current, similar to that in Purkinje fibres.3. The transient current had a sigmoidal dependence on the preceding (activating) voltage step V1, with a treshold around -13 mV and a plateau between +10 and 20 mV. There was a decline in current amplitude for more positive clamps. When activated by a fixed V1 voltage step, and measured at different repolarization levels V2, the transient current manifested an inverse dependence on V2 between -50 and -10 mV. No outward transient current could be detected. Total replacement of Na in the bathing medium by Tris or by sucrose abolished the transient current.4. Ouabain caused an increase of phasic (twitch) tension responses to voltage steps at all potentials without shifting the curve relating these variables on the voltage axis. The drug evoked an even greater increase in the tonic tension responses.5. After prolonged exposure, oscillatory mechanical responses were frequently recorded during positive voltage steps. Unlike the after-contraction, these mechanical fluctuations were not consistently damped and were not accompanied by detectable synchronous current fluctuations. Catecholamines and dibutyryl cyclic AMP markedly reduced the amplitude of the tonic contraction and the mechanical oscillations but increased their frequency. Caffeine had no effect on the tonic contraction amplitude but abolished the fluctuations.6. These results support the proposal that Ca is transiently released from the overloaded sarcoplasmic reticulum in ouabain-intoxicated muscle and may evoke oscillatory
Energy Technology Data Exchange (ETDEWEB)
Celso Grebogi
2000-02-29
This is the final report on a research project that explored (a) controlling complex dynamical systems; (b) using controlled chaotic signals for communication (c) methods of controlling chaos via targeting; (d) deterministic modeling; and miscellaneous work on the interface between chaotic and stable periodic behavior as system parameters vary, bifurcations of non-smooth systems that describe impact oscillators; phenomena that occur in quasiperiodically forced systems, and the fractal and topological properties of chaotic inveriant sets, in particular those arising in fluid flow.
Chandramouli, V. V. M. S.; Martens, M.; De Melo, W.; Tresser, C. P.
2009-01-01
The period doubling renormalization operator was introduced by Feigenbaum and by Coullet and Tresser in the 1970s to study the asymptotic small-scale geometry of the attractor of one-dimensional systems that are at the transition from simple to chaotic dynamics. This geometry turns out not to depend
Kamarajan, Chella; Rangaswamy, Madhavi; Manz, Niklas; Chorlian, David B; Pandey, Ashwini K; Roopesh, Bangalore N; Porjesz, Bernice
2012-05-01
Recent studies have linked alcoholism with a dysfunctional neural reward system. Although several electrophysiological studies have explored reward processing in healthy individuals, such studies in alcohol-dependent individuals are quite rare. The present study examines theta oscillations during reward processing in abstinent alcoholics. The electroencephalogram (EEG) was recorded in 38 abstinent alcoholics and 38 healthy controls as they performed a single outcome gambling task, which involved outcomes of either loss or gain of an amount (10 or 50¢) that was bet. Event-related theta band (3.0-7.0 Hz) power following each outcome stimulus was computed using the S-transform method. Theta power at the time window of the outcome-related negativity (ORN) and positivity (ORP) (200-500 ms) was compared across groups and outcome conditions. Additionally, behavioral data of impulsivity and task performance were analyzed. The alcoholic group showed significantly decreased theta power during reward processing compared to controls. Current source density (CSD) maps of alcoholics revealed weaker and diffuse source activity for all conditions and weaker bilateral prefrontal sources during the Loss 50 condition when compared with controls who manifested stronger and focused midline sources. Furthermore, alcoholics exhibited increased impulsivity and risk-taking on the behavioral measures. A strong association between reduced anterior theta power and impulsive task-performance was observed. It is suggested that decreased power and weaker and diffuse CSD in alcoholics may be due to dysfunctional neural reward circuitry. The relationship among alcoholism, theta oscillations, reward processing, and impulsivity could offer clues to understand brain circuitries that mediate reward processing and inhibitory control.
The Semiclassical Regime of the Chaotic Quantum-Classical Transition
Greenbaum, B D; Shizume, K; Sundaram, B; Greenbaum, Benjamin D.; Habib, Salman; Shizume, Kosuke; Sundaram, Bala
2004-01-01
An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Previous numerical work has shown that in this regime, the results from a quantum master equation are very close to those obtained from a classical Fokker-Planck equation. We provide an explanation of these results by demonstrating that environmental noise plays the dual roles of suppressing the development of fine structure in classical phase space and damping nonlocal contributions to the semiclassical Wigner function. A numerical investigation of the chaotic Duffing oscillator supports these conclusions.
Energy Technology Data Exchange (ETDEWEB)
Yang, Yuchen [State Key Lab for Materials Processing and Die & Mold Technology, School of Materials Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074 (China); Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720 (United States); Zhou, Xue [Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720 (United States); Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150000 (China); Liu, Jason X. [Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720 (United States); Department of Physics, University of California, Berkeley, Berkeley, California 94720 (United States); Anders, André, E-mail: aanders@lbl.gov [Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720 (United States)
2016-01-18
We present evidence for breathing modes in magnetron sputtering plasmas: periodic axial variations of plasma parameters with characteristic frequencies between 10 and 100 kHz. A set of azimuthally distributed probes shows synchronous oscillations of the floating potential. They appear most clearly when considering the intermediate current regime in which the direction of azimuthal spoke motion changes. Breathing oscillations were found to be superimposed on azimuthal spoke motion. Depending on pressure and current, one can also find a regime of chaotic fluctuations and one of stable discharges, the latter at high current. A pressure-current phase diagram for the different situations is proposed.
Xavier, J C; Strunz, W T; Beims, M W
2015-08-01
We consider the energy flow between a classical one-dimensional harmonic oscillator and a set of N two-dimensional chaotic oscillators, which represents the finite environment. Using linear response theory we obtain an analytical effective equation for the system harmonic oscillator, which includes a frequency dependent dissipation, a shift, and memory effects. The damping rate is expressed in terms of the environment mean Lyapunov exponent. A good agreement is shown by comparing theoretical and numerical results, even for environments with mixed (regular and chaotic) motion. Resonance between system and environment frequencies is shown to be more efficient to generate dissipation than larger mean Lyapunov exponents or a larger number of bath chaotic oscillators.
On chaotic conductivity in the magnetotail
Holland, Daniel L.; Chen, James
1992-01-01
The concept of chaotic conductivity and the acceleration of particles due to a constant dawn dusk electric field are studied in a magnetotail-like magnetic field. A test particle simulation is used including the full nonlinear dynamics. It is found that the acceleration process can be understood without invoking chaos and that the cross tail current is determined by the particle dynamics and distributions. It is concluded that in general there is no simple relationship between the electric field and the current.
Mikelskis, Helmut
1980-01-01
Discusses oscillations and waves as a new topic for primary and secondary science curricula because of the many developments in the fields of optics and electronics. Outlines current problems in physics instruction under the headings of social aspects, disadvantaged pupils, and developing countries. (GS)
The characteristics of nonlinear chaotic dynamics in quantum cellular neural networks
Institute of Scientific and Technical Information of China (English)
Wang Sen; Cai Li; Kang Qiang; Wu Gang; Li Qin
2008-01-01
With the polarization of quantum-dot cell and quantum phase serving as state variables, this paper does both theoretical analysis and simulation for the complex nonlinear dynamical behaviour of a three-cell-coupled Quantum Cel- lular Neural Network (QCNN), including equilibrium points, bifurcation and chaotic behaviour. Different phenomena, such as quasi-periodic, chaotic and hyper-chaotic states as well as bifurcations are revealed. The system's bifurcation and chaotic behaviour under the influence of the different coupling parameters are analysed. And it finds that the unbalanced ceils coupled QCNN is easy to cause chaotic oscillation and the system response enters into chaotic state from quasi-periodic state by quasi-period bifurcation; however, the balanced cells coupled QCNN also can be chaotic when coupling parameters is in some region. Additionally, both the unbalanced and balanced cells coupled QCNNs can possess hyper-chaotic behaviour. It provides valuable information about QCNNs for future application in high-parallel signal processing and novel ultra-small chaotic generators.
Norman, Sharon E; Butera, Robert J; Canavier, Carmen C
2016-09-01
Oscillatory neurons integrate their synaptic inputs in fundamentally different ways than normally quiescent neurons. We show that the oscillation period of invertebrate endogenous pacemaker neurons wanders, producing random fluctuations in the interspike intervals (ISI) on a time scale of seconds to minutes, which decorrelates pairs of neurons in hybrid circuits constructed using the dynamic clamp. The autocorrelation of the ISI sequence remained high for many ISIs, but the autocorrelation of the ΔISI series had on average a single nonzero value, which was negative at a lag of one interval. We reproduced these results using a simple integrate and fire (IF) model with a stochastic population of channels carrying an adaptation current with a stochastic component that was integrated with a slow time scale, suggesting that a similar population of channels underlies the observed wander in the period. Using autoregressive integrated moving average (ARIMA) models, we found that a single integrator and a single moving average with a negative coefficient could simulate both the experimental data and the IF model. Feeding white noise into an integrator with a slow time constant is sufficient to produce the autocorrelation structure of the ISI series. Moreover, the moving average clearly accounted for the autocorrelation structure of the ΔISI series and is biophysically implemented in the IF model using slow stochastic adaptation. The observed autocorrelation structure may be a neural signature of slow stochastic adaptation, and wander generated in this manner may be a general mechanism for limiting episodes of synchronized activity in the nervous system.
Frontiers of chaotic advection
Aref, Hassan; Budišić, Marko; Cartwright, Julyan H E; Clercx, Herman J H; Feudel, Ulrike; Golestanian, Ramin; Gouillart, Emmanuelle; Guer, Yves Le; van Heijst, GertJan F; Krasnopolskaya, Tatyana S; MacKay, Robert S; Meleshko, Vyacheslav V; Metcalfe, Guy; Mezić, Igor; de Moura, Alessandro P S; Omari, Kamal El; Piro, Oreste; Speetjens, Michel F M; Sturman, Rob; Thiffeault, Jean-Luc; Tuval, Idan
2014-01-01
We review the present position of and survey future perspectives in the physics of chaotic advection; the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, micro-fluidics, biological flows, and large-scale dispersion of pollutants in oceanographic and atmospheric flows.
Charged Particle Motion in Temporal Chaotic and Spatiotemporal Chaotic Fields
Institute of Scientific and Technical Information of China (English)
张海云; 贺凯芬
2002-01-01
We investigate charged particle motion in temporal chaotic and spatiotemporal chaotic fields. In its steady wave frame a few key modes of the solution of the driven/damped nonlinear wave equation are used as the field. It is found that in the spatiotemporal chaotic field the particle drifts relative to the steady wave, in contrast to that in the temporal chaotic field where the particle motion is localized in a trough of the wave field. The result is of significance for understanding stochastic acceleration of particles.
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.
Cryptography with chaotic mixing
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Luiz P.L. de [Programa Interdisciplinar de Pos-Graduacao em Computacao Aplicada - PIPCA, Universidade do Vale do Rio dos Sinos - UNISINOS, Av. Unisinos 950, 93022-000 Sao Leopoldo, RS (Brazil)], E-mail: lpluna@unisinos.br; Sobottka, Marcelo [Centro de Modelamiento Matematico, Universidad de Chile, Blanco Encalada 2120, 7o piso Casilla 170/3, Correo 3, Santiago (Chile)], E-mail: sobottka@dim.uchile.cl
2008-02-15
We propose a cryptosystem based on one-dimensional chaotic maps of the form H{sub p}(x)=r{sub p}{sup -1}0G0r{sub p}(x) defined in the interval [0, 10{sup p}) for a positive integer parameter p, where G(x)=10x(mod10) and r{sub p}(x)={sup p}{radical}(x), which is a topological conjugacy between G and the shift map {sigma} on the space {sigma} of the sequences with 10 symbols. There are three advantages in comparison with the recently proposed cryptosystem based on chaotic logistic maps F{sub {mu}}(x)={mu}x(1-x) with 3 < {mu} {<=} 4: (a) H{sub 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{sub p}'s domain and (c) for each p, the security of the cryptosystem is manageable against brute force attacks.
Directory of Open Access Journals (Sweden)
Surjo R Soekadar
2014-03-01
Full Text Available Objective: Transcranial direct current stimulation (tDCS improves motor learning and can influence emotional processing or attention. However, it remained unclear whether learned electroencephalography (EEG-based brain-machine interface (BMI control during tDCS is feasible and how application of transcranial electric currents during BMI control would interfere with feature-extraction of physiological brain signals. Here we tested this combination and evaluated stimulation-dependent artifacts across different EEG frequencies and stability of motor imagery-based BMI control. Approach: Ten healthy volunteers were invited to two BMI-sessions, each comprising two 60-trial blocks. During the trials, modulation of mu-rhythms (8-15Hz associated with motor imagery recorded over C4 was translated into online cursor movements on a computer screen. During block 2, either sham (session A or anodal tDCS (session B was applied at 1mA with the stimulation electrode placed 1cm anterior of C4. Main results: tDCS was associated with a significant signal power increase in the lower frequencies most evident in the signal spectrum of the EEG channel closest to the stimulation electrode. Stimulation-dependent signal power increase exhibited a decay of 12dB per decade, leaving frequencies above 9Hz unaffected. Analysis of BMI control performance did not indicate a difference between blocks and tDCS conditions. Conclusion: Application of tDCS during learned EEG-based self-regulation of brain oscillations above 9Hz is feasible and safe, and might improve applicability of BMI systems in patient populations.
Forced synchronization of quasiperiodic oscillations
Stankevich, N. V.; Kurths, J.; Kuznetsov, A. P.
2015-01-01
A model of a generator of quasiperiodic oscillations forced by a periodic pulse sequence is studied. We analyze synchronization when the autonomous generator demonstrates periodic, quasiperiodic, respective weakly chaotic oscillations. For the forced quasiperiodic oscillations a picture of synchronization, consisting of small-scale and large-scale structures was uncovered. It even includes the existence of stable the three-frequency tori. For the regime of weak chaos a partial destruction of this features and of the regime of three-frequency tori are found.
Chaotic Control of Network Traffic
Institute of Scientific and Technical Information of China (English)
YANG Tan; CUI Yi-Dong; JIN Yue-Hui; CHENG Shi-Duan
2009-01-01
A method of chaotic control on network traffic is presented.By this method,the chaotic network traffic can be controlled to a pre-assigned equilibrium point according to chaotic prediction and the largest Lyapunov exponent of the traffic on congested link is reduced,thereby the probability of traffic burst and network congestion can be reduced.Numerical examples show that this method is effective.
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.
Touma, Jihad; Wisdom, Jack
1993-01-01
The discovery (by Laskar, 1989, 1990) that the evolution of the solar system is chaotic, made in a numerical integration of the averaged secular approximation of the equations of motions for the planets, was confirmed by Sussman and Wisdom (1992) by direct numerical integration of the whole solar system. This paper presents results of direct integrations of the rotation of Mars in the chaotically evolved planetary system, made using the same model as that used by Sussman and Wisdom. The numerical integration shows that the obliquity of Mars undergoes large chaotic variations, which occur as the system evolves in the chaotic zone associated with a secular spin-orbit resonance.
Directory of Open Access Journals (Sweden)
Abhirup Lahiri
2011-01-01
Full Text Available This paper reports two new circuit topologies using second-generation current conveyors (CCIIs for realizing variable frequency sinusoidal oscillators with minimum passive components. The proposed topologies in this paper provide new realizations of resistance-controlled and capacitor-controlled variable frequency oscillators (VFOs using only four passive components. The first topology employs three CCIIs, while the second topology employs two CCIIs. The second topology provides an advantageous feature of frequency tuning through two grounded elements. Application of the proposed circuits as a wide-frequency range digitally controlled sinusoid generator is exhibited wherein the digital frequency control has been enabled by replacing both the capacitors by two identical variable binary capacitor banks tunable by means of the same binary code. SPICE simulations of the CMOS implementation of the oscillators using 0.35 μm TSMC CMOS technology parameters and bipolar implementation of the oscillators using process parameters for NR200N-2X (NPN and PR200N-2X (PNP of bipolar arrays ALA400-CBIC-R have validated their workability. One of the oscillators (with CMOS implementation is exemplified as a digitally controlled sinusoid generator with frequency generation from 25 kHz to 6.36 MHz, achieved by switching capacitors and with power consumption of 7 mW in the entire operating frequency range.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The quantum mechanical behavior of classically chaotic systems,usually referred to as quantum chaos,is of interest,since the classical limit is still poorly understood for soft chaos~([1,2]).Here the spatio-temporal evolution of axially symmetric harmonic oscillator coherent states under the action of perturbed Harniltonian with octupole deformation is studied for a classically soft chaotic systems.The initial coherent state
Erickson, K R; Ronnekleiv, O K; Kelly, M J
1993-05-01
Guinea pig magnocellular neurosecretory cells (MNCs) of the supraoptic nucleus (SON) were studied using the in vitro slice preparation. Intracellular recordings were made with biocytin-filled electrodes, permitting immunocytochemical identification of the recorded cells as arginine vasopressin- (AVP) versus oxytocin- (OT) containing. Only AVP cells displaying a depolarizing potential (DP) fired phasically. The DP was associated with a transient inward current measured in voltage clamp, which exhibited a number of properties of the T-type calcium current: activation threshold of -64 mV, time course of up to 250 ms, blockade by nickel and augmentation by barium chloride. This current has not been reported previously in SON neurons. The T-type current (IT) was always associated with a damped oscillation of the membrane following the offset from hyperpolarizing steps. In all cells tested, an apamin-sensitive afterhyperpolarization (AHP) was observed, similar to the calcium-dependent potassium current (IK, Ca) described in rat SON and other CNS regions. Therefore, as with other CNS regions displaying damped oscillations, guinea pig SON cells possess both an IT and an IK, Ca. We have previously described an Ih activating at hyperpolarized potentials in these cells, which depolarizes the membrane to a range in which the IT and IK, Ca can interactively support oscillations. In summary, the IT and associated depolarizing potential appears to be a requisite feature for phasic firing in AVP cells of guinea pig SON.
Detection of harmonic signals from chaotic interference by empirical mode decomposition
Energy Technology Data Exchange (ETDEWEB)
Li, H.G. [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail: hgli@sjtu.edu.cn; Meng, G. [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail: gmeng@sjtu.edu.cn
2006-11-15
An empirical mode decomposition (EMD) approach to the harmonic signal extraction from chaotic interference is proposed. Based on the EMD and the concept that any signal is composed of a series of simple intrinsic modes, the chaotic interference signal is decomposed to a series of intrinsic mode functions (IMFs), among which one IMF is the recovered harmonic signal. In this study, harmonic signals are contaminated with a chaotic interference signal which is generated by a Duffing oscillator, and the simulation results show that the harmonic signals can be effectively recovered from the contaminated signals by the EMD approach.
Chaotic Josephson effects in two-coupled Bose-Einstein condensates
Fang, Jianshu; Hai, Wenhua; Chong, Guishu; Xie, Qiongtao
2005-04-01
We discuss the chaotic Josephson effects in two weakly coupled Bose-Einstein condensates (BECs). The boson Josephson junction (BJJ) dynamics in BECs is governed by the two-mode Gross-Pitaevskii equation. We obtained a perturbed chaotic solution of the BJJ equation by using the direct perturbation technique. Theoretical analysis reveals that the stable oscillating orbits are embedded in the Melnikov chaotic attractors. The corresponding numerical results show that the Poincaré sections in the equivalent phase space (φ,φ˙) sensitively depends on the system parameter and initial conditions. Therefore, we can control the transitions between chaos and order by adjusting these parameters and conditions.
Synchronization and Stabilization of Chaotic Dynamics in a Quasi-1D Bose-Einstein Condensate
Directory of Open Access Journals (Sweden)
B. A. Idowu
2013-01-01
Full Text Available A nonlinear control is proposed for the exponential stabilization and synchronization of chaotic behaviour in a model of Bose-Einstein condensate (BEC. The active control technique is designed based on Lyapunov stability theory and Routh-Hurwitz criteria. The control design approach in both cases guarantees the stability of the controlled states. Whereas the synchronization of two identical BEC in their chaotic states can be realized using the scheme; a suitable controller is also capable of driving the otherwise chaotic oscillation to a stable state which could be expected in practice. The effectiveness of this technique is theoretically and numerically demonstrated.
Synchronization and anti-synchronization of chaotic systems: A differential and algebraic approach
Energy Technology Data Exchange (ETDEWEB)
Martinez-Guerra, Rafael [Departamento de Control Automatico, Cinvestav-IPN A. P. 14-740, Av. IPN 2508, 07360 Mexico, D.F. (Mexico)], E-mail: rguerra@ctrl.cinvestav.mx; Pasaye, Jose Juan Rincon [Departamento de Control Automatico, Cinvestav-IPN A. P. 14-740, Av. IPN 2508, 07360 Mexico, D.F. (Mexico)], E-mail: jrincon@ctrl.cinvestav.mx
2009-10-30
Chaotic systems synchronization and anti-synchronization problems are tackled by means of differential and algebraic techniques for nonlinear systems. An algebraic observer is proposed for systems satisfying an algebraic observability condition. This observer can be used as a slave system whose states are synchronized with the master (chaotic) system. This approach has the advantages of being independent of the chaotic nature of the master system, it uses a reduced set of measurable signal from the master system and it also solves the anti-synchronization problem as a straightforward extension of the synchronization one. A Colpitts oscillator is given to illustrate the effectiveness of the suggested approach.
Hopf Bifurcation Analysis and Chaos Control of a Chaotic System without ilnikov Orbits
Directory of Open Access Journals (Sweden)
Na Li
2015-01-01
Full Text Available This paper mainly investigates the dynamical behaviors of a chaotic system without ilnikov orbits by the normal form theory. Both the stability of the equilibria and the existence of local Hopf bifurcation are proved in view of analyzing the associated characteristic equation. Meanwhile, the direction and the period of bifurcating periodic solutions are determined. Regarding the delay as a parameter, we discuss the effect of time delay on the dynamics of chaotic system with delayed feedback control. Finally, numerical simulations indicate that chaotic oscillation is converted into a steady state when the delay passes through a certain critical value.
Restoration of oscillation in network of oscillators in presence of direct and indirect interactions
Majhi, Soumen; Bera, Bidesh K.; Bhowmick, Sourav K.; Ghosh, Dibakar
2016-10-01
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.
Xu, Kesheng; Maidana, Jean P.; Caviedes, Mauricio; Quero, Daniel; Aguirre, Pablo; Orio, Patricio
2017-01-01
In this article, we describe and analyze the chaotic behavior of a conductance-based neuronal bursting model. This is a model with a reduced number of variables, yet it retains biophysical plausibility. Inspired by the activity of cold thermoreceptors, the model contains a persistent Sodium current, a Calcium-activated Potassium current and a hyperpolarization-activated current (Ih) that drive a slow subthreshold oscillation. Driven by this oscillation, a fast subsystem (fast Sodium and Potassium currents) fires action potentials in a periodic fashion. Depending on the parameters, this model can generate a variety of firing patterns that includes bursting, regular tonic and polymodal firing. Here we show that the transitions between different firing patterns are often accompanied by a range of chaotic firing, as suggested by an irregular, non-periodic firing pattern. To confirm this, we measure the maximum Lyapunov exponent of the voltage trajectories, and the Lyapunov exponent and Lempel-Ziv's complexity of the ISI time series. The four-variable slow system (without spiking) also generates chaotic behavior, and bifurcation analysis shows that this is often originated by period doubling cascades. Either with or without spikes, chaos is no longer generated when the Ih is removed from the system. As the model is biologically plausible with biophysically meaningful parameters, we propose it as a useful tool to understand chaotic dynamics in neurons. PMID:28344550
Loss of lag synchronization in coupled chaotic systems
Sosnovtseva, O. V.; Balanov, A. G.; Vadivasova, T. E.; Astakhov, V. V.; Mosekilde, Erik
1999-01-01
Lag synchronization denotes a particular form of synchronization in which the amplitudes of two interacting, nonidentical chaotic oscillators are correlated but there is a characteristic time delay between them. We study transitions to and between different forms of synchronization for the attractors defined as "in-phase" and "out-of-phase" and investigate the processes by which lag synchronization is lost in two coupled Rossler systems. With a small frequency mismatch between the two systems...
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 rapidly can transform into robustly determined multicellular coherence. PMID:9861041
An exponential polynomial observer for synchronization of chaotic systems
Mata-Machuca, J. L.; Martínez-Guerra, R.; Aguilar-López, R.
2010-12-01
In this paper, we consider the synchronization problem via nonlinear observer design. A new exponential polynomial observer for a class of nonlinear oscillators is proposed, which is robust against output noises. A sufficient condition for synchronization is derived analytically with the help of Lyapunov stability theory. The proposed technique has been applied to synchronize chaotic systems (Rikitake and Rössler systems) by means of numerical simulation.
Gills, Zelda; Roy, Rajarshi
1995-01-01
Irregular fluctuations in intensity have long plagued the operation of a wide variety of solid-state lasers. We are exploring the possibility of exploiting rather than avoiding a laser's chaotic output. As an important step in that direction, we have applied a novel control technique to stabilize a solid state laser. By making small periodic changes in only one input parameter of the laser, we are able to stabilize complex periodic waveforms and steady state behavior in the laser output. We demonstrate the application of this approach in a diode pumped Nd:/YAG laser system.
Binzel, R. P.; Green, J. R.; Opal, C. B.
1986-01-01
Thomas et al. (1984) analyzed 14 Voyager 2 images of Saturn's satellite Hyperion and interpreted them to be consistent with a coherent (nonchaotic) rotation period of 13.1 days. This interpretation was criticized by Peale and Wisdom (1984), who argued that the low sampling frequency of Voyager data does not allow chaotic or nonchaotic rotation to be distinguished. New observations obtained with a higher sampling frequency are reported here which conclusively show that the 13.1 day period found by Thomas et al. was not due to coherent rotation.
DEFF Research Database (Denmark)
Schäfer, Mirko; Greiner, Martin
Chaotic strings are coupled Tchebyscheff maps on a ring-network. With a well-specified empirical prescription they are able to explain the coupling constants of the standard model of elementary particle physics. This empirical relationship is tested further by introducing a tunable disorder to ch...... of the standard model of elementary particle physics. For the electromagnetic sector it is found that already a small disorder pushes the associated energy scale of the running coupling constant far away from the result without disorder....
Chaotic mixer improves microarray hybridization.
McQuain, Mark K; Seale, Kevin; Peek, Joel; Fisher, Timothy S; Levy, Shawn; Stremler, Mark A; Haselton, Frederick R
2004-02-15
Hybridization is an important aspect of microarray experimental design which influences array signal levels and the repeatability of data within an array and across different arrays. Current methods typically require 24h and use target inefficiently. In these studies, we compare hybridization signals obtained in conventional static hybridization, which depends on diffusional target delivery, with signals obtained in a dynamic hybridization chamber, which employs a fluid mixer based on chaotic advection theory to deliver targets across a conventional glass slide array. Microarrays were printed with a pattern of 102 identical probe spots containing a 65-mer oligonucleotide capture probe. Hybridization of a 725-bp fluorescently labeled target was used to measure average target hybridization levels, local signal-to-noise ratios, and array hybridization uniformity. Dynamic hybridization for 1h with 1 or 10ng of target DNA increased hybridization signal intensities approximately threefold over a 24-h static hybridization. Similarly, a 10- or 60-min dynamic hybridization of 10ng of target DNA increased hybridization signal intensities fourfold over a 24h static hybridization. In time course studies, static hybridization reached a maximum within 8 to 12h using either 1 or 10ng of target. In time course studies using the dynamic hybridization chamber, hybridization using 1ng of target increased to a maximum at 4h and that using 10ng of target did not vary over the time points tested. In comparison to static hybridization, dynamic hybridization reduced the signal-to-noise ratios threefold and reduced spot-to-spot variation twofold. Therefore, we conclude that dynamic hybridization based on a chaotic mixer design improves both the speed of hybridization and the maximum level of hybridization while increasing signal-to-noise ratios and reducing spot-to-spot variation.
Blowout bifurcation of chaotic saddles
Directory of Open Access Journals (Sweden)
Tomasz Kapitaniak
1999-01-01
Full Text Available Chaotic saddles are nonattracting dynamical invariant sets that can lead to a variety of physical phenomena. We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant manifold of coupled systems and discuss dynamical phenomena associated with this bifurcation.
Energy Technology Data Exchange (ETDEWEB)
Beaumont, A.; Leroy, J.; Crunteanu, A., E-mail: aurelian.crunteanu@xlim.fr [XLIM Research Institute UMR 7252, CNRS/University of Limoges, 123 avenue Albert Thomas, 87060 Limoges (France); Orlianges, J.-C. [SPCTS UMR 7513, CNRS/University of Limoges, 12 rue Atlantis, 87068 Limoges (France)
2014-04-21
Electrically activated metal-insulator transition (MIT) in vanadium dioxide (VO{sub 2}) is widely studied from both fundamental and practical points of view. It can give valuable insights on the currently controversial phase transition mechanism in this material and, at the same time, allows the development of original MIT-based electronic devices. Electrically triggered insulator-metal transitions are demonstrated in novel out-of-plane, metal-oxide-metal type devices integrating a VO{sub 2} thin film, upon applying moderate threshold voltages. It is shown that the current-voltage characteristics of such devices present clear negative differential resistance effects supporting the onset of continuous, current-driven phase oscillations across the vanadium dioxide material. The frequencies of these self-sustained oscillations are ranging from 90 to 300 kHz and they may be tuned by adjusting the injected current. A phenomenological model of the device and its command circuit is developed, and allows to extract the analytical expressions of the oscillation frequencies and to simulate the electrical oscillatory phenomena developed across the VO{sub 2} material. Such out-of-plane devices may further contribute to the general understanding of the driving mechanism in metal-insulator transition materials and devices, a prerequisite to promising applications in high speed/high frequency networks of oscillatory or resistive memories circuits.
Beaumont, A.; Leroy, J.; Orlianges, J.-C.; Crunteanu, A.
2014-04-01
Electrically activated metal-insulator transition (MIT) in vanadium dioxide (VO2) is widely studied from both fundamental and practical points of view. It can give valuable insights on the currently controversial phase transition mechanism in this material and, at the same time, allows the development of original MIT-based electronic devices. Electrically triggered insulator-metal transitions are demonstrated in novel out-of-plane, metal-oxide-metal type devices integrating a VO2 thin film, upon applying moderate threshold voltages. It is shown that the current-voltage characteristics of such devices present clear negative differential resistance effects supporting the onset of continuous, current-driven phase oscillations across the vanadium dioxide material. The frequencies of these self-sustained oscillations are ranging from 90 to 300 kHz and they may be tuned by adjusting the injected current. A phenomenological model of the device and its command circuit is developed, and allows to extract the analytical expressions of the oscillation frequencies and to simulate the electrical oscillatory phenomena developed across the VO2 material. Such out-of-plane devices may further contribute to the general understanding of the driving mechanism in metal-insulator transition materials and devices, a prerequisite to promising applications in high speed/high frequency networks of oscillatory or resistive memories circuits.
Connelly, M. J.
2014-05-01
The slow light effect in SOAs has many applications in microwave photonics such as phase shifting and filtering. Models are needed to predict slow light in SOAs and its dependence on the bias current, optical power and modulation index. In this paper we predict the slow light characteristics of a tensile-strained SOA by using a detailed time-domain model. The model includes full band-structure based calculations of the material gain, bimolecular recombination and spontaneous emission, a carrier density rate equation and travelling wave equations for the input signal and amplified spontaneous emission. The slow light effect is caused by coherent population oscillations, whereby beating between the spectral components of an amplitude modulated lightwave causes carrier density oscillations at the beat frequency, leading to changes in the group velocity. The resulting beat signal at the SOA output after photodetection, is phase shifted relative to the SOA input beat signal. The phase shift can be adjusted by controlling the optical power and bias current. However the beat signal gain is low at low frequencies, leading to a poor beat signal output signal-to-noise ratio. If the optical input and SOA drive current are simultaneously modulated, this leads to forced population oscillations that greatly enhance the low frequency beat signal gain. The model is used to determine the improvement in gain and phase response and its dependency on the optical power, bias current and modulation index. Model predictions show good agreement with experimental trends reported in the literature.
The chaotic rotation of Hyperion
Wisdom, J.; Peale, S. J.; Mignard, F.
1984-01-01
Under the assumption that the satellite is rotating about a principal axis that is normal to its orbit plane, a plot of spin rate-versus-orientation for Hyperion at the pericenter of its orbit has revealed a large, chaotic zone surrounding Hyperion's synchronous spin-orbit state. The chaotic zone is so large that it surrounds the 1/2 and 2 states, and libration in the 3/2 state is not possible. Rotation in the chaotic zone is also attitude-unstable. As tidal dissipation drives Hyperion's spin toward a nearly synchronous value, Hyperion necessarily enters the large chaotic zone, becoming attitude-unstable and tumbling. It is therefore predicted that Hyperion will be found to be tumbling chaotically.
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.
Synchronization of spectral components and its regularities in chaotic dynamical systems.
Hramov, Alexander E; Koronovskii, Alexey A; Kurovskaya, Mariya K; Moskalenko, Olga I
2005-05-01
The chaotic synchronization regime in coupled dynamical systems is considered. It has been shown that the onset of a synchronous regime is based on the appearance of a phase relation between the interacting chaotic oscillator frequency components of Fourier spectra. The criterion of synchronization of spectral components as well as the measure of synchronization has been discussed. The universal power law has been described. The main results are illustrated by coupled Rössler systems, Van der Pol and Van der Pol-Duffing oscillators.
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.
Synchronizing the information content of a chaotic map and flow via symbolic dynamics.
Corron, Ned J; Pethel, Shawn D; Myneni, Krishna
2002-09-01
In this paper we report an extension to the concept of generalized synchronization for coupling different types of chaotic systems, including maps and flows. This broader viewpoint takes disparate systems to be synchronized if their information content is equivalent. We use symbolic dynamics to quantize the information produced by each system and compare the symbol sequences to establish synchronization. A general architecture is presented for drive-response coupling that detects symbols produced by a chaotic drive oscillator and encodes them in a response system using the methods of chaos control. We include experimental results demonstrating synchronization of information content in an electronic oscillator circuit driven by a logistic map.
Periodic and Chaotic Flapping of Insectile Wings
Huang, Yangyang
2015-01-01
Insects use flight muscles attached at the base of the wings to produce impressive wing flapping frequencies. The maximum power output of these flight muscles is insufficient to maintain such wing oscillations unless there is good elastic storage of energy in the insect flight system. Here, we explore the intrinsic self-oscillatory behavior of an insectile wing model, consisting of two rigid wings connected at their base by an elastic torsional spring. We study the wings behavior as a function of the total energy and spring stiffness. Three types of behavior are identified: end-over-end rotation, chaotic motion, and periodic flapping. Interestingly, the region of periodic flapping decreases as energy increases but is favored as stiffness increases. These findings are consistent with the fact that insect wings and flight muscles are stiff. They further imply that, by adjusting their muscle stiffness to the desired energy level, insects can maintain periodic flapping mechanically for a range of operating condit...
Institute of Scientific and Technical Information of China (English)
JIN Zhi; SU Yong-bo; CHENG Wei; LIU Xin-Yu; XU An-Huai; QI Ming
2008-01-01
@@ A four-finger InGaAs/InP double heterojunction bipolar transistor is designed and fabricated successfully by using planarization technology. The emitter area of each finger is 1 × 15 μm2. The breakdown voltage is more than 7V, the maximum collector current could be more than 100mA. The current gain cutoff frequency is as high as 155 GHz and the maximum oscillation frequency reaches 253 GHz. The heterostructure bipolar transistor can offer more than 70mW class-A maximum output power at W band and the maximum power density can be as high as 1.2 W/mm.
Dynamics of Coupled Quantum-Classical Oscillators
Institute of Scientific and Technical Information of China (English)
HE Wei-Zhong; XU Liu-Su; ZOU Feng-Wu
2004-01-01
@@ The dynamics of systems consisting of coupled quantum-classical oscillators is numerically investigated. It is shown that, under certain conditions, the quantum oscillator exhibits chaos. When the mass of the classical oscillator increases, the chaos will be suppressed; if the energy of the system and/or the coupling strength between the two oscillators increases, chaotic behaviour of the system appears. This result will be helpful to understand the probability of the emergence of quantum chaos and may be applied to explain the spectra of complex atoms qualitatively.
A Novel Concatenated Chaotic Communication System
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A strategy for a novel concatenated chaotic communication system is presented. The transmitter system comprises chaotic turbo encoder and logistic CSK block in a serially concatenated form. Chaotic turbo code is capable of reducing bit error rate (BER) of the chaotic system in the AWGN channel. Through the chaotic turbo encoder, the coded sequence, which has quasi-chaotic properties, will be transmitted into the logistic CSK block. Having a very sensitive dependence on initial conditions of the map, the logistic CSK block can also be taken as the chaotic authentication method. The receiver, which has logistic demodulation block and chaotic decoder, is a linear asymptotic approximation to the inverse of the transmitter system. A chaotic iterative soft-decision decoding algorithm is also developed based on conventional maximum A posteriori decoding algorithm. At last, a two-step authentication method of this chaotic system is also presented.
Altmann, Eduardo G; Tél, Tamás
2013-01-01
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties of the closed system. In this paper we provide an unified treatment of leaking systems and we review applications to different physical problems, both in the classical and quantum pictures. Our treatment is based on the transient chaos theory of open systems, which is essential because real leaks have finite size and therefore estimations based on the closed system differ essentially from observations. The field of applications reviewed is very broad, ranging from planetary astronomy and hydrodynamical flows, to plasma physics and quantum fidelity. The theory is expanded and adapted to the case of partial leaks (partial absorption/transmission) with applications to room acoustics and optical microcavities in mind. Simulations in the lima .con family of billiards illustrate...
Chaotic systems with absorption
Altmann, Eduardo G; Tél, Tamás
2013-01-01
Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate $\\kappa$ in terms of the natural conditionally-invariant measure of the system; (ii) an increased multifractality when compared to the spectrum of dimensions $D_q$ obtained without taking absorption and return times into account; and (iii) a generalization of the Kantz-Grassberger formula that expresses $D_1$ in terms of $\\kappa$, the positive Lyapunov exponent, the average return time, and a new quantity, the reflection rate. Simulations in the cardioid billiard confirm these results.
Chaotic advection in blood flow.
Schelin, A B; Károlyi, Gy; de Moura, A P S; Booth, N A; Grebogi, C
2009-07-01
In this paper we argue that the effects of irregular chaotic motion of particles transported by blood can play a major role in the development of serious circulatory diseases. Vessel wall irregularities modify the flow field, changing in a nontrivial way the transport and activation of biochemically active particles. We argue that blood particle transport is often chaotic in realistic physiological conditions. We also argue that this chaotic behavior of the flow has crucial consequences for the dynamics of important processes in the blood, such as the activation of platelets which are involved in the thrombus formation.
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.)
Critical dimension for chaotic cosmology
Energy Technology Data Exchange (ETDEWEB)
Hosoya, Akio; Jensen, L.G.; Stein-Schabes, J.A.
1987-03-16
Using the ADM formalism for general relativity the approach to a space-time singularity of a general inhomogeneous universe, in an arbitrary number of dimensions, is studied. The question of whether chaotic behaviour is a generic feature of Einstein's equations, in an arbitrary number of dimensions, is explored. We find that models that contain ten or more spatial dimensions are non-chaotic and their approach toward the initial singularity is monotonic, whereas for those with dimensionality between four and nine their approach is chaotic. A clear geometrical picture is constructed whereby this result can be understood.
Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems.
Custódio, M S; Manchein, C; Beims, M W
2012-06-01
The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions (ICs) and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and four particles globally coupled on a discrete lattice, we show that in these models, the transition from integrable motion to weak chaos emerges via chaotic stripes as the nonlinear parameter is increased. The stripes represent intervals of initial conditions which generate chaotic trajectories and increase with the nonlinear parameter of the system. In the billiard case, the initial conditions are the injection angles. For higher-dimensional systems and small nonlinearities, the chaotic stripes are the initial condition inside which Arnold diffusion occurs.
Building a Chaotic Proved Neural Network
Bahi, Jacques M; Salomon, Michel
2011-01-01
Chaotic neural networks have received a great deal of attention these last years. In this paper we establish a precise correspondence between the so-called chaotic iterations and a particular class of artificial neural networks: global recurrent multi-layer perceptrons. We show formally that it is possible to make these iterations behave chaotically, as defined by Devaney, and thus we obtain the first neural networks proven chaotic. Several neural networks with different architectures are trained to exhibit a chaotical behavior.
A new multi-scroll chaotic system
Institute of Scientific and Technical Information of China (English)
Wang Fa-Qiang; Liu Chong-Xin
2006-01-01
This paper proposes a new simple autonomous chaotic system which can generate multi-scroll chaotic attractors.The characteristic of this new multi-scroll chaotic system is that the 4n + 2m +4-scroll chaotic attractors are generated easily with n and m varying under n ≤ m. Various number of scroll chaotic attractors are illustrated not on ly by computer simulation but also by the realization of an electronic circuit experiment on EWB (Electronics Workbench).
Directory of Open Access Journals (Sweden)
Marcos Alberto de Armas Teyra
2013-06-01
Full Text Available En las plantas de generación distribuidas accionadas por motores reciprocantes es necesario conocer las fluctuaciones de tensión, corriente y potencia para evaluar la calidad de la energía que entregan estos grupos electrógenos y como criterio de diagnóstico técnico. Las causas de estas fluctuaciones son diversas. La fundamental se debe a la presencia de oscilaciones forzadas producidas por el momento irregular de los motores primarios. Otras razones se encuentran en las excentricidades constructivas, el desbalance de corriente, los armónicos espaciales y de tiempo, la variación de la configuración del sistema, etc. En este trabajo fueron evaluadas satisfactoriamente las oscilaciones de una máquina conectada a la red mediante la instalación de un analizador de redes de 32 cortes por ciclo a la salida del generador de una de estas unidades. Se expone como caso de estudio las oscilaciones observadas en un generador de 425 kVA480 V accionado por un motor Diesel de seis cilindros y cuatro tiempos en la Provincia de Cienfuegos, Cuba. In distributed and standby power plants driven by reciprocating motors, is important to know the voltage, current and power oscillation as a delivery power quality and diagnostic criteria. There are several oscillation causes. The fundamental is due to the irregular torque of primary motors. Other causes are due to constructive eccentricities, current unbalance, time and spatial harmonics, changes in systems configuration, etc. In this paper the fundamental oscillations of a grid connected machine were evaluated with a power analyzer installed in one generating power plant. As a case there are shown the observed oscillations in 425 kVA generator driven by a four times, six cylinders Diesel motor in Cienfuegos Province of Cuba.
Directory of Open Access Journals (Sweden)
Marcos Alberto de Armas Teyra
2013-06-01
Full Text Available En las plantas de generación distribuidas accionadas por motores reciprocantes es necesario conocer las fluctuaciones de tensión, corriente y potencia para evaluar la calidad de la energía que entregan estos grupos electrógenos y como criterio de diagnóstico técnico. Las causas de estas fluctuaciones son diversas. La fundamental se debe a la presencia de oscilaciones forzadas producidas por el momento irregular de los motores primarios. Otras razones se encuentran en las excentricidades constructivas, el desbalance de corriente, los armónicos espaciales y de tiempo, la variación de la configuración del sistema, etc. En este trabajo fueron evaluadas satisfactoriamente las oscilaciones de una máquina conectada a la red mediante la instalación de un analizador de redes de 32 cortes por ciclo a la salida del generador de una de estas unidades. Se expone como caso de estudio las oscilaciones observadas en un generador de 425 kVA480 V accionado por un motor Diesel de seis cilindros y cuatro tiempos en la Provincia de Cienfuegos, Cuba.In distributed and standby power plants driven by reciprocating motors, is important to know the voltage, current and power oscillation as a delivery power quality and diagnostic criteria. There are several oscillation causes. The fundamental is due to the irregular torque of primary motors. Other causes are due to constructive eccentricities, current unbalance, time and spatial harmonics, changes in systems configuration, etc. In this paper the fundamental oscillations of a grid connected machine were evaluated with a power analyzer installed in one generating power plant. As a case there are shown the observed oscillations in 425 kVA generator driven by a four times, six cylinders Diesel motor in Cienfuegos Province of Cuba.
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...
Chaotic diagonal recurrent neural network
Institute of Scientific and Technical Information of China (English)
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 andlearning 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.
Institute of Scientific and Technical Information of China (English)
周国华; 许建平; 包伯成; 王金平; 金艳艳
2011-01-01
Peak current controlled buck converter with current source load shows the complex phenomenon of fast-scale and slow-scale subharmonic oscillations Its piecewise smooth switching model and discrete iterative map model are established in this paper According to its discrete iterative map model, the effects of circuit parameters on the nonlinear dynamic behaviors of buck converter are analyzed by numerical simulation.It is found that attractive regions of fast-scale and slowscale subharmonic oscillations and dual tori phenomena exist in the bifurcation diagram and Poincaré mapping,respectively.Time-domain simulation waveforms and phase portraits of buck converter are obtained by Runge-Kutta algorithm using the piecewise smooth switching model.The research results indicate that n-type subharmonic oscillation constituted by subharmonic oscillation and frequency-reduced subharmonic oscillation exists in the inductor current, and sine-type subharmonic oscillation constituted by fast scale and low scale exists in the output voltage, respectively.Analysis and simulation results are verified by experimental results.%电流源负载峰值电流控制buck变换器具有次谐波振荡快慢复杂现象.本文建立了它的分段光滑开关模型及离散迭代映射模型.根据离散迭代映射模型,通过数值仿真研究了电路参数对buck变换器的非线性动力学行为的影响,发现了具有快慢效应次谐波振荡吸引域的分岔图和呈现双环带状的庞加莱映射.根据分段光滑开关模型,采用龙格-库塔算法,仿真研究了buck变换器的时域波形和相轨图,研究结果表明:电感电流存在由次谐波振荡与降频次谐波振荡组成的n型次谐波振荡现象;输出电压存在快标与慢标结合的正弦次谐波振荡现象.实验结果验证了文中的分析结果及仿真结果.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale
Energy Technology Data Exchange (ETDEWEB)
Maslennikov, Oleg V.; Nekorkin, Vladimir I. [Institute of Applied Physics of RAS, Nizhny Novgorod (Russian Federation)
2016-07-15
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.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale.
Maslennikov, Oleg V; Nekorkin, Vladimir I
2016-07-01
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.
Generalized reduced-order synchronization of chaotic system based on fast slide mode
Institute of Scientific and Technical Information of China (English)
Gao Tie-Gang; Chen Zeng-Qiang; Yuan Zhu-Zhi
2005-01-01
A new kind of generalized reduced-order synchronization of different chaotic systems is proposed in this paper.It is shown that dynamical evolution of third-order oscillator can be synchronized with the canonical projection of a fourth-order chaotic system generated through nonsingular states transformation from a cell neural net chaotic system.In this sense, it is said that generalized synchronization is achieved in reduced-order. The synchronization discussed here expands the scope of reduced-order synchronization studied in relevant literatures. In this way, we can achieve generalized reduced-order synchronization between many famous chaotic systems such as the second-order D(u)ffing system and the third-order Lorenz system by designing a fast slide mode controller. Simulation results are provided to verify the operation of the designed synchronization.
Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Yau, H.-T. [Department of Electrical Engineering, Far-East College, Tainan 744, Taiwan (China)]. E-mail: pan1012@ms52.hinet.net; Chen, C.-L. [Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan (China)
2006-11-15
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.
The open-plus-closed loop (OPCL) method for chaotic systems with multiple strange attractors
Institute of Scientific and Technical Information of China (English)
Song Yun-Zhong
2007-01-01
Based on the open-plus-closed-loop (OPCL) control method a systematic and comprehensive controller is presented in this paper for a chaotic system, that is, the Newton-Leipnik equation with two strange attractors: the upper attractor(UA) and the lower attractor (LA). Results show that the final structure of the suggested controller for stabilization has a simple linear feedback form. To keep the integrity of the suggested approach, the globality proof of the basins of entrainment is also provided. In virtue of the OPCL technique, three different kinds of chaotic controls of the system are investigated, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one; and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the proposed means.
Energy Technology Data Exchange (ETDEWEB)
Proddutur, Archana; Yu, Jiandong; Elgammal, Fatima S. [Department of Neurology and Neurosciences, New Jersey Medical School, Rutgers, Newark, New Jersey 07103 (United States); Santhakumar, Vijayalakshmi, E-mail: santhavi@njms.rutgers.edu [Department of Neurology and Neurosciences, New Jersey Medical School, Rutgers, Newark, New Jersey 07103 (United States); Department of Pharmacology and Physiology, New Jersey Medical School, Rutgers, Newark, New Jersey 07103 (United States)
2013-12-15
Gamma frequency oscillations have been proposed to contribute to memory formation and retrieval. Fast-spiking basket cells (FS-BCs) are known to underlie development of gamma oscillations. Fast, high amplitude GABA synapses and gap junctions have been suggested to contribute to gamma oscillations in FS-BC networks. Recently, we identified that, apart from GABAergic synapses, FS-BCs in the hippocampal dentate gyrus have GABAergic currents mediated by extrasynaptic receptors. Our experimental studies demonstrated two specific changes in FS-BC GABA currents following experimental seizures [Yu et al., J. Neurophysiol. 109, 1746 (2013)]: increase in the magnitude of extrasynaptic (tonic) GABA currents and a depolarizing shift in GABA reversal potential (E{sub GABA}). Here, we use homogeneous networks of a biophysically based model of FS-BCs to examine how the presence of extrasynaptic GABA conductance (g{sub GABA-extra}) and experimentally identified, seizure-induced changes in g{sub GABA-extra} and E{sub GABA} influence network activity. Networks of FS-BCs interconnected by fast GABAergic synapses developed synchronous firing in the dentate gamma frequency range (40–100 Hz). Systematic investigation revealed that the biologically realistic range of 30 to 40 connections between FS-BCs resulted in greater coherence in the gamma frequency range when networks were activated by Poisson-distributed dendritic synaptic inputs rather than by homogeneous somatic current injections, which were balanced for FS-BC firing frequency in unconnected networks. Distance-dependent conduction delay enhanced coherence in networks with 30–40 FS-BC interconnections while inclusion of gap junctional conductance had a modest effect on coherence. In networks activated by somatic current injections resulting in heterogeneous FS-BC firing, increasing g{sub GABA-extra} reduced the frequency and coherence of FS-BC firing when E{sub GABA} was shunting (−74 mV), but failed to alter average
Proddutur, Archana; Yu, Jiandong; Elgammal, Fatima S.; Santhakumar, Vijayalakshmi
2013-12-01
Gamma frequency oscillations have been proposed to contribute to memory formation and retrieval. Fast-spiking basket cells (FS-BCs) are known to underlie development of gamma oscillations. Fast, high amplitude GABA synapses and gap junctions have been suggested to contribute to gamma oscillations in FS-BC networks. Recently, we identified that, apart from GABAergic synapses, FS-BCs in the hippocampal dentate gyrus have GABAergic currents mediated by extrasynaptic receptors. Our experimental studies demonstrated two specific changes in FS-BC GABA currents following experimental seizures [Yu et al., J. Neurophysiol. 109, 1746 (2013)]: increase in the magnitude of extrasynaptic (tonic) GABA currents and a depolarizing shift in GABA reversal potential (EGABA). Here, we use homogeneous networks of a biophysically based model of FS-BCs to examine how the presence of extrasynaptic GABA conductance (gGABA-extra) and experimentally identified, seizure-induced changes in gGABA-extra and EGABA influence network activity. Networks of FS-BCs interconnected by fast GABAergic synapses developed synchronous firing in the dentate gamma frequency range (40-100 Hz). Systematic investigation revealed that the biologically realistic range of 30 to 40 connections between FS-BCs resulted in greater coherence in the gamma frequency range when networks were activated by Poisson-distributed dendritic synaptic inputs rather than by homogeneous somatic current injections, which were balanced for FS-BC firing frequency in unconnected networks. Distance-dependent conduction delay enhanced coherence in networks with 30-40 FS-BC interconnections while inclusion of gap junctional conductance had a modest effect on coherence. In networks activated by somatic current injections resulting in heterogeneous FS-BC firing, increasing gGABA-extra reduced the frequency and coherence of FS-BC firing when EGABA was shunting (-74 mV), but failed to alter average FS-BC frequency when EGABA was depolarizing
2013-01-01
We present an introduction to the study of chaos in discrete and continuous dynamical systems using the CAS Maxima. These notes are intended to cover the standard topics and techniques: discrete and continuous logistic equation to model growth population, staircase plots, bifurcation diagrams and chaos transition, nonlinear continuous dynamics (Lorentz system and Duffing oscillator), Lyapunov exponents, Poincar\\'e sections, fractal dimension and strange attractors. The distinctive feature her...
Waves from an oscillating point source with a free surface in the presence of a shear current
Ellingsen, Simen Å
2016-01-01
We investigate analytically the linearized water wave radiation problem for an oscillating submerged point source in an inviscid shear flow with a free surface. A constant depth is taken into account and the shear flow increases linearly with depth. The surface velocity relative to the source is taken to be zero, so that Doppler effects are absent. We solve the linearized Euler equations to calculate the resulting wave field as well as its far-field asymptotics. For values of the Froude number $F^2=\\omega^2 D/g$ ($\\omega$: oscillation frequency, $D$ submergence depth) below a resonant value $F^2_\\text{res}$ the wave field splits cleanly into separate contributions from regular dispersive propagating waves and non-dispersive "critical waves" resulting from a critical layer-like street of flow structures directly downstream of the source. In the sub-resonant regime the regular waves behave like sheared ring waves while the critical layer wave forms a street of a constant width of order $D\\sqrt{S/\\omega}$ ($S$ i...
REVIEWS OF TOPICAL PROBLEMS: On the use of chaotic synchronization for secure communication
Koronovskii, Aleksei A.; Moskalenko, Olga I.; Hramov, Aleksandr E.
2009-12-01
Research on the secure communication applications of chaotic synchronization is reviewed. A number of secure communication methods and devices using different types of synchronous behavior are examined. For the purpose of comparing existing methods, quantitative characteristics of operating capacity of various schemes are introduced and estimated. An extremely noise-stable secure information transmission method, based on the phenomenon of generalized chaos synchronization, is proposed. All of the methods considered are systematically checked for efficiency for the first time by numerically simulating unidirectionally coupled chaotic Rössler systems selected for transmitting and receiving oscillators. The key advantages and disadvantages of secure information transmission schemes using synchronized chaotic oscillations are discussed. The experimental data gathered in this field are also reviewed.
NONLINEAR DYNAMICAL BIFURCATION AND CHAOTIC MOTION OF SHALLOW CONICAL LATTICE SHELL
Institute of Scientific and Technical Information of China (English)
WANG Xin-zhi; HAN Ming-jun; ZHAO Yan-ying; ZHAO Yong-gang
2006-01-01
The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.
Sliding mode control for synchronization of chaotic systems with structure or parameters mismatching
Institute of Scientific and Technical Information of China (English)
LI Xiao-run; ZHAO Liao-ying; ZHAO Guang-zhou
2005-01-01
This paper deals with the synchronization of chaotic systems with structure or parameters difference. Nonlinear differential geometry theory was applied to transform the chaotic discrepancy system into canonical form. A feedback control for synchronizing two chaotic systems is proposed based on sliding mode control design. To make this controller physically realizable,an extended state observer is used to estimate the error between the transmitter and receiver. Two illustrative examples were carried out: (1) The Chua oscillator was used to show that synchronization was achieved and the message signal was recovered in spite of parametric variations; (2) Two second-order driven oscillators were presented to show that the synchronization can be achieved and that the message can be recovered in spite of the strictly different model.
Control of long-period orbits and arbitrary trajectories in chaotic systems using dynamic limiting.
Corron, Ned J.; Pethel, Shawn D.
2002-03-01
We demonstrate experimental control of long-period orbits and arbitrary chaotic trajectories using a new chaos control technique called dynamic limiting. Based on limiter control, dynamic limiting uses a predetermined sequence of limiter levels applied to the chaotic system to stabilize natural states of the system. The limiter sequence is clocked by the natural return time of the chaotic system such that the oscillator sees a new limiter level for each peak return. We demonstrate control of period-8 and period-34 unstable periodic orbits in a low-frequency circuit and provide evidence that the control perturbations are minimal. We also demonstrate control of an arbitrary waveform by replaying a sequence captured from the uncontrolled oscillator, achieving a form of delayed self-synchronization. Finally, we discuss the use of dynamic limiting for high-frequency chaos communications. (c) 2002 American Institute of Physics.
Dobrovolskis, Anthony R.; Cuzzi, Jeffrey N. (Technical Monitor)
1995-01-01
The shape and spin of Neptune's outermost satellite Nereid are still unknown. Ground-based photometry indicates large brightness variations, but different observers report very different lightcurve amplitudes and periods. On the contrary, Voyager 2 images spanning 12 days show no evidence of variations greater than 0.1 mag. The latter suggest either that Nereid is nearly spherical, or that it is rotating slowly. We propose that tides have already despun Nereid's rotation to a period of a few weeks, during the time before the capture of Triton when Nereid was closer to Neptune. Since Nereid reached its present orbit, tides have further despun Nereid to a period on the order of a month. For Nereid's orbital eccentricity of 0.75, tidal evolution ceases when the spin period is still approximately 1/8 of the orbital period. Furthermore, the synchronous resonance becomes quite weak for such high eccentricities, along with other low-order spin orbit commensurabilities. In contrast, high-order resonances become very strong particularly the 6:1, 6.5:1, 7:1, 7.5:1, and 8:1 spin states. If Nereid departs by more than approximately 1% from a sphere, however, these resonances overlap, generating chaos. Our simulations show that Nereid is likely to be in chaotic rotation for any spin period longer than about 2 weeks.
Matsumoto, R.; Imamura, H.
2016-12-01
Spin-torque induced magnetization dynamics in a spin-torque oscillator with an in-plane (IP) magnetized free layer and an out-of-plane (OP) magnetized polarizer under IP shape-anisotropy field (Hk) and applied IP magnetic field (Ha) was theoretically studied based on the macrospin model. The rigorous analytical expression of the critical current density (Jc1) for the OP precession was obtained. The obtained expression successfully reproduces the experimentally obtained Ha-dependence of Jc1 reported in [D. Houssameddine et al., Nat. Mater. 6, 447 (2007)].
Directory of Open Access Journals (Sweden)
R. Matsumoto
2016-12-01
Full Text Available Spin-torque induced magnetization dynamics in a spin-torque oscillator with an in-plane (IP magnetized free layer and an out-of-plane (OP magnetized polarizer under IP shape-anisotropy field (Hk and applied IP magnetic field (Ha was theoretically studied based on the macrospin model. The rigorous analytical expression of the critical current density (Jc1 for the OP precession was obtained. The obtained expression successfully reproduces the experimentally obtained Ha-dependence of Jc1 reported in [D. Houssameddine et al., Nat. Mater. 6, 447 (2007].
Kishimoto, Fuminao; Matsuhisa, Masayuki; Kawamura, Shinichiro; Fujii, Satoshi; Tsubaki, Shuntaro; Maitani, Masato M.; Suzuki, Eiichi; Wada, Yuji
2016-10-01
Various microwave effects on chemical reactions have been observed, reported and compared to those carried out under conventional heating. These effects are classified into thermal effects, which arise from the temperature rise caused by microwaves, and non-thermal effects, which are attributed to interactions between substances and the oscillating electromagnetic fields of microwaves. However, there have been no direct or intrinsic demonstrations of the non-thermal effects based on physical insights. Here we demonstrate the microwave enhancement of oxidation current of water to generate dioxygen with using an α-Fe2O3 electrode induced by pulsed microwave irradiation under constantly applied potential. The rectangular waves of current density under pulsed microwave irradiation were observed, in other words the oxidation current of water was increased instantaneously at the moment of the introduction of microwaves, and stayed stably at the plateau under continuous microwave irradiation. The microwave enhancement was observed only for the α-Fe2O3 electrode with the specific surface electronic structure evaluated by electrochemical impedance spectroscopy. This discovery provides a firm evidence of the microwave special non-thermal effect on the electron transfer reactions caused by interaction of oscillating microwaves and irradiated samples.
Kishimoto, Fuminao; Matsuhisa, Masayuki; Kawamura, Shinichiro; Fujii, Satoshi; Tsubaki, Shuntaro; Maitani, Masato M.; Suzuki, Eiichi; Wada, Yuji
2016-01-01
Various microwave effects on chemical reactions have been observed, reported and compared to those carried out under conventional heating. These effects are classified into thermal effects, which arise from the temperature rise caused by microwaves, and non-thermal effects, which are attributed to interactions between substances and the oscillating electromagnetic fields of microwaves. However, there have been no direct or intrinsic demonstrations of the non-thermal effects based on physical insights. Here we demonstrate the microwave enhancement of oxidation current of water to generate dioxygen with using an α-Fe2O3 electrode induced by pulsed microwave irradiation under constantly applied potential. The rectangular waves of current density under pulsed microwave irradiation were observed, in other words the oxidation current of water was increased instantaneously at the moment of the introduction of microwaves, and stayed stably at the plateau under continuous microwave irradiation. The microwave enhancement was observed only for the α-Fe2O3 electrode with the specific surface electronic structure evaluated by electrochemical impedance spectroscopy. This discovery provides a firm evidence of the microwave special non-thermal effect on the electron transfer reactions caused by interaction of oscillating microwaves and irradiated samples. PMID:27739529
Energy Technology Data Exchange (ETDEWEB)
Horley, Paul P., E-mail: paul.horley@cimav.edu.mx [Centro de Investigación en Materiales Avanzados, S.C. (CIMAV), Chihuahua/Monterrey, 120 Avenida Miguel de Cervantes, 31109 Chihuahua (Mexico); Kushnir, Mykola Ya. [Yuri Fedkovych Chernivtsi National University, 2 Kotsyubynsky str., 58012 Chernivtsi (Ukraine); Morales-Meza, Mishel [Centro de Investigación en Materiales Avanzados, S.C. (CIMAV), Chihuahua/Monterrey, 120 Avenida Miguel de Cervantes, 31109 Chihuahua (Mexico); Sukhov, Alexander [Institut für Physik, Martin-Luther Universität Halle-Wittenberg, 06120 Halle (Saale) (Germany); Rusyn, Volodymyr [Yuri Fedkovych Chernivtsi National University, 2 Kotsyubynsky str., 58012 Chernivtsi (Ukraine)
2016-04-01
We report on complex magnetization dynamics in a forced spin valve oscillator subjected to a varying magnetic field and a constant spin-polarized current. The transition from periodic to chaotic magnetic motion was illustrated with bifurcation diagrams and Hausdorff dimension – the methods developed for dissipative self-organizing systems. It was shown that bifurcation cascades can be obtained either by tuning the injected spin-polarized current or by changing the magnitude of applied magnetic field. The order–chaos transition in magnetization dynamics can be also directly observed from the hysteresis curves. The resulting complex oscillations are useful for development of spin-valve devices operating in harmonic and chaotic modes.
Conservative Chaos Generators with CCII+ Based on Mathematical Model of Nonlinear Oscillator
Directory of Open Access Journals (Sweden)
J. Slezak
2008-09-01
Full Text Available In this detailed paper, several novel oscillator's configurations which consist only of five positive second generation current conveyors (CCII+ are presented and experimentally verified. Each network is able to generate the conservative chaotic attractors with the certain degree of the structural stability. It represents a class of the autonomous deterministic dynamical systems with two-segment piecewise linear (PWL vector fields suitable also for the theoretical analysis. Route to chaos can be traced and observed by a simple change of the external dc voltage. Advantages and other possible improvements are briefly discussed in the text.
Semiclassics of the Chaotic Quantum-Classical Transition
Greenbaum, B D; Shizume, K; Sundaram, B; Greenbaum, Benjamin D.; Habib, Salman; Shizume, Kosuke; Sundaram, Bala
2006-01-01
We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the dual role of noise in regularizing the semiclassical Wigner function and averaging over fine structures in classical phase space. The results are interpreted in the novel context of applying recent advances in the theory of measurement and open systems to the semiclassical quantum regime. We use these methods to show how a local semiclassical picture is stabilized and can then be approximated by a classical distribution at arbitrary times. The general results are demonstrated explicitly via numerical simulations of the chaotic Duffing oscillator.
Chaotic ferroresonance in a non-autonomous circuit
Institute of Scientific and Technical Information of China (English)
Hui Meng; Zhang Yan-Bin; Liu Chong-Xin
2008-01-01
Accurate description of magnetization curve has important effect on ferroresonance.In most of earlier ferroresonance studies the magnetization curve is modelled a8 a 3rd or 5th order polynomial.However,it is not comprehensive.This paper investigates the chaotic ferroresonance behaviour exhibited by a non-autonomous circuit which contains a nonlinear flux-controlled inductance.The ferromagnetic characteristic of this nonlinear inductance represented by a magnetization curve could be expressed a8 an nth order two-term polynomial.By varying the value of exponent n,the circuit can assunle a diverse range of steady-state regimes including fundamental and subharmonic ferroresonance,quasi-periodic oscillations,and chaos. A detailed analysis of some simulations demonstrates that the probability of chaos increases as the exponent of the magnetization curve rises.The effect of varying the magnitude of the source voltage on the chaotic behaviour of the circuit is also studied.
High-speed chaotic communication using an optical fibre ring as a key
Institute of Scientific and Technical Information of China (English)
Zou Lin; Feng Ye; Yang Yi-Biao; Wang An-Bang; Yang Ling-Zhen; Zhang Jian-Zhong
2011-01-01
A chaotic communication scheme with a fibre ring inserted in the optical feedback of the transmitter laser as an additional key is proposed under anticipating synchronization. The numerical results show that the key can enhance the communication security effectively. It is theoretically safe for the communication scheme to transmit messages with a frequency beyond the relaxation oscillation frequency.
Holes and chaotic pulses of traveling waves coupled to a long-wave mode
Herrero, H; Herrero, Henar; Riecke, Hermann
1997-01-01
Localized traveling-wave pulses and holes, i.e. localized regions of vanishing wave amplitude, are investigated in a real Ginzburg-Landau equation coupled to a long-wave mode. In certain parameter regimes the pulses exhibit a Hopf bifurcation which leads to a breathing motion. Subsequently the oscillations undergo period-doubling bifurcations and become chaotic.
Frequency of self-oscillations
Groszkowski, Janusz
2013-01-01
Frequency of Self-Oscillations covers the realm of electric oscillations that plays an important role both in the scientific and technical aspects. This book is composed of nine chapters, and begins with the introduction to the alternating currents and oscillation. The succeeding chapters deal with the free oscillations in linear isolated systems. These topics are followed by discussions on self-oscillations in linear systems. Other chapters describe the self-oscillations in non-linear systems, the influence of linear elements on frequency of oscillations, and the electro mechanical oscillato
Institute of Scientific and Technical Information of China (English)
Lu Jun-Guo
2006-01-01
This paper proposes a new, simple and yet applicable output feedback synchronization theorem for a large class of chaotic systems. We take a linear combination of drive system state variables as a scale-driving signal. It is proved that synchronization between the drive and the response systems can be obtained via a simple linear output error feedback control. The linear feedback gain is a function of a free parameter. The approach is illustrated using the Rossler hyperchaotic systems and Chua's chaotic oscillators.
Kato, Shoji
2016-01-01
This book presents the current state of research on disk oscillation theory, focusing on relativistic disks and tidally deformed disks. Since the launch of the Rossi X-ray Timing Explorer (RXTE) in 1996, many high-frequency quasiperiodic oscillations (HFQPOs) have been observed in X-ray binaries. Subsequently, similar quasi-periodic oscillations have been found in such relativistic objects as microquasars, ultra-luminous X-ray sources, and galactic nuclei. One of the most promising explanations of their origin is based on oscillations in relativistic disks, and a new field called discoseismology is currently developing. After reviewing observational aspects, the book presents the basic characteristics of disk oscillations, especially focusing on those in relativistic disks. Relativistic disks are essentially different from Newtonian disks in terms of several basic characteristics of their disk oscillations, including the radial distributions of epicyclic frequencies. In order to understand the basic processes...
Berson, Arganthaël; Poignand, Gaëlle; Blanc-Benon, Philippe; Comte-Bellot, Geneviève
2010-01-01
A new procedure for the instantaneous correction of the thermal inertia of cold wires operated by a constant-current anemometer is proposed for oscillating flows. The thermal inertia of cold wires depends both on the wire properties and on the instantaneous incident flow velocity. Its correction is challenging in oscillating flows because no relationship between flow velocity and heat transfer around the wire is available near flow reversal. The present correction procedure requires neither calibration data for velocity nor thermophysical or geometrical properties of the wires. The method relies on the splitting of the time lag of cold wires into two factors, which are obtained using a constant-voltage anemometer in the heated mode. The first factor, which is intrinsic to the wire, is deduced from time-constant measurements performed in a low-turbulence flow. The second factor, which depends on the instantaneous flow velocity, is acquired in situ. In oscillating flows, data acquisition can be synchronized with a reference signal so that the same wire is alternatively operated in the cold mode by a constant-current anemometer and in the heated mode by a constant-voltage anemometer. Validation experiments are conducted in an acoustic standing-wave resonator, for which the fluctuating temperature field along the resonator axis is known independently from acoustic pressure measurements, so that comparisons can be made with cold-wire measurements. It is shown that despite the fact that the wire experiences flow reversal, the new procedure recovers accurately the instantaneous temperature of the flow.
Single ICCII Sinusoidal Oscillators Employing Grounded Capacitors
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J. W. Horng
2011-09-01
Full Text Available Two inverting second-generation current conveyors (ICCII based sinusoidal oscillators are presented. The first sinusoidal oscillator is composed of one ICCII, two grounded capacitors and two resistors. The oscillation condition and oscillation frequency can be orthogonally controllable. The second sinusoidal oscillator is composed of one ICCII, two grounded capacitors and three resistors. The oscillation condition and oscillation frequency can be independently controllable through different resistors.
Directory of Open Access Journals (Sweden)
Csilla eBordas
2015-04-01
Full Text Available The pedunculopontine nucleus is known as a cholinergic nucleus of the reticular activating system, participating in regulation of sleep and wakefulness. Besides cholinergic neurons, it consists of GABAergic and glutamatergic neurons as well. According to classical and recent studies, more subgroups of neurons were defined. Groups based on the neurotransmitter released by a neuron are not homogenous, but can be further subdivided.The PPN neurons do not only provide cholinergic and non-cholinergic inputs to several subcortical brain areas but they are also targets of cholinergic and other different neuromodulatory actions. Although cholinergic neuromodulation has been already investigated in the nucleus, one of its characteristic targets, the M-type potassium current has not been described yet.Using slice electrophysiology, we provide evidence in the present work that cholinergic neurons possess M-current, whereas GABAergic neurons lack it. The M-current contributes to certain functional differences of cholinergic and GABAergic neurons, as spike frequency adaptation, action potential firing frequency or the amplitude difference of medium afterhyperpolarizations. Furthermore, we showed that high threshold membrane potential oscillation with high power, around 20 Hz frequency is a functional property of almost all cholinergic cells, whereas GABAergic neurons have only low amplitude oscillations. Blockade of the M-current abolished the oscillatory activity at 20 Hz, and largely diminished it at other frequencies.Taken together, the M-current seems to be characteristic for PPN cholinergic neurons. It provides a possibility for modulating gamma band activity of these cells, thus contributing to neuromodulatory regulation of the reticular activating system.
2006-01-01
[figure removed for brevity, see original site] Poster Version Large Magellanic Cloud This vibrant image from NASA's Spitzer Space Telescope shows the Large Magellanic Cloud, a satellite galaxy to our own Milky Way galaxy. The infrared image, a mosaic of more than 100,000 individual tiles, offers astronomers a unique chance to study the lifecycle of stars and dust in a single galaxy. Nearly one million objects are revealed for the first time in this Spitzer view, which represents about a 1,000-fold improvement in sensitivity over previous space-based missions. Most of the new objects are dusty stars of various ages populating the Large Magellanic Cloud; the rest are thought to be background galaxies. The blue color in the picture, seen most prominently in the central bar, represents starlight from older stars. The chaotic, bright regions outside this bar are filled with hot, massive stars buried in thick blankets of dust. The red clouds contain cooler interstellar gas and molecular-sized dust grains illuminated by ambient starlight. The Large Magellanic Cloud, located 160,000 light-years from Earth, is one of a handful of dwarf galaxies that orbit our own Milky Way. It is approximately one-third as wide as the Milky Way, and, if it could be seen in its entirety, would cover the same amount of sky as a grid of about 480 full moons. About one-third of the whole galaxy can be seen in the Spitzer image. This picture is a composite of infrared light captured by Spitzer's infrared array camera. Light with wavelengths of 8 and 5.8 microns is red and orange: 4.5-micron light is green; and 3.6-micron light is blue.
How chaotic are strange non-chaotic attractors?
Glendinning, Paul; Jäger, Tobias H.; Keller, Gerhard
2006-09-01
We show that the classic examples of quasiperiodically forced maps with strange non-chaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit sensitive dependence on initial conditions, both on the whole phase space and restricted to the attractor. The results also remain valid in more general classes of quasiperiodically forced systems. Further, we include an elementary proof of a classic result by Glasner and Weiss on sensitive dependence, and we clarify the structure of the attractor in an example with two-dimensional fibres also introduced by Grebogi et al.
Synchronization of Cross-Well Chaos in Coupled Duffing Oscillators
Vincent, U. E.; Njah, A. N.; Akinlade, O.; Solarin, A. R. T.
Numerical simulations have been used to investigate the synchronization behavior of a unidirectionally coupled pair of double-well duffing oscillators (DDOs). The DDOs were simulated in their structurally stable chaotic zone and their state variables were found to completely synchronized. The essential feature of the transition to the synchronous state is shown to correspond to a boundary crisis in which the cross-well chaotic attractor is destroyed.
Synchronization of indirectly coupled Lorenz oscillators: An experimental study
Indian Academy of Sciences (India)
Amit Sharma; Manish Dev Shrimali
2011-11-01
The dynamics of indirectly coupled Lorenz circuits is investigated experimentally. The in-phase and anti-phase synchronization of indirectly coupled chaotic oscillators reported in Phys. Rev. E 81, 046216 (2010) is veriﬁed by physical experiments with electronic circuits. Two chaotic systems coupled through a common dynamic environment shows the verity of synchronization behaviours such as anti-phase synchronization, in-phase synchronization, identical synchronization, anti-synchronization, etc.
Detecting variation in chaotic attractors.
Carroll, T L
2011-06-01
If the output of an experiment is a chaotic signal, it may be useful to detect small changes in the signal, but there are a limited number of ways to compare signals from chaotic systems, and most known methods are not robust in the presence of noise. One may calculate dimension or Lyapunov exponents from the signal, or construct a synchronizing model, but all of these are only useful in low noise situations. I introduce a method for detecting small variations in a chaotic attractor based on directly calculating the difference between vector fields in phase space. The differences are found by comparing close strands in phase space, rather than close neighbors. The use of strands makes the method more robust to noise and more sensitive to small attractor differences.
Chaotic eigenfunctions in phase space
Nonnenmacher, S
1997-01-01
We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann-Husimi representations for quantum states, as well as their stellar parametrization, which encodes states through a minimal set of points in phase space (the constellation of zeros of the Husimi density). We rigorously prove that a semiclassical uniform distribution of Husimi densities on the torus entails a similar equidistribution for the corresponding constellations. We deduce from this property a universal behavior for the phase patterns of chaotic Bargmann eigenfunctions, which reminds of the WKB approximation for eigenstates of integrable systems (though in a weaker sense). In order to obtain more precise information on ``chaotic eigenconstellations", we then model their properties by ensembles of random states, generalizing former results on the 2-sphere to the torus geometry. This approach yields statistical predictions fo...
The Statistics of Chaotic Tunnelling
Creagh, S C; Creagh, Stephen C.; Whelan, Niall D.
2000-01-01
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on using the properties of a semiclassical tunnelling operator together with random matrix theory arguments about wave function overlaps. The resulting distribution depends on the stability of a specific tunnelling orbit and is therefore not universal. However it does reduce to the universal Porter-Thomas form as the orbit becomes very unstable. For some choices of system parameters there are systematic deviations which we explain in terms of scarring of certain real periodic orbits. The theory is tested in a model symmetric double well problem and possible experimental realisations are discussed.
The chaotic marriage of physics and financial economics
Gilmore, Claire
2013-01-01
By the early 1980s interest in chaos theory was spreading from mathematics and the sciences to other fields, including economics and finance. Initial results, based on the metric approach to testing for chaos in time series data, appeared to lend support to the presence of chaotic behavior in a variety of economic phenomena and in financial markets. Subsequently, a topological approach to the analysis of chaos was developed which led to tests for chaotic behavior more suited to the relatively small, noisy data sets typically available in these fields. This close returns test is demonstrated here and is applied to data from several financial markets. The qualitative topological test does not support evidence of a chaotic generating mechanism in these series. The quantitative form of the close returns test indicates nonchaotic nonlinear behavior that cannot be fully explained by current financial models.
Communication Scheme via Cascade Chaotic Systems
Institute of Scientific and Technical Information of China (English)
HUA Chang-Chun; GUAN Xin-Ping
2004-01-01
@@ A new chaotic communication scheme is constructed. Different from the existing literature, cascade chaotic systems are employed. Two cascade modes are considered. First, we investigate the input to state cascade mode;cascade systems between different kinds of chaotic systems are considered. Then the parameter cascade case of chaotic system is studied. Under the different cases, the corresponding receivers are designed, which can succeed in recovering the former emitted signal. Simulations are performed to verify the validity of the proposed main results.
Impulsive Synchronization of Discrete Chaotic Systems
Institute of Scientific and Technical Information of China (English)
郑永爱; 年漪蓓; 刘曾荣
2003-01-01
Impulsive synchronization of two chaotic maps is reformulated as impulsive control of the synchronization error system. We then present a theorem on the asymptotic synchronization of two chaotic maps by using synchronization impulses with varying impulsive intervals. As an example and application of the theorem, we derives some sufficient conditions for the synchronization of two chaotic Lozi maps via impulsive control. The effectiveness of this approach has been demonstrated with chaotic Lozi map.
A new multi-scroll chaotic generator
Institute of Scientific and Technical Information of China (English)
Wang Fa-Qiang; Liu Chong-Xin
2007-01-01
In this paper a new simple multi-scroll chaotic generator is studied. The characteristic of this new multi-scroll chaotic generator is that it is easy to generate different number of scroll chaotic attractors through modifying the nature number n after fixing the suitable system parameters and it does not need complex mathematical derivation. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on Electronic Workbench (EWB).
Chaotic zones around gravitating binaries
Shevchenko, Ivan I
2014-01-01
The extent of the continuous zone of chaotic orbits of a small-mass tertiary around a system of two gravitationally bound bodies (a double star, a double black hole, a binary asteroid, etc.) is estimated analytically, in function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the binary periods. The binary's mass ratio, above which such a chaotic zone is universally present, is also estimated.
Modeling of deterministic chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Lai, Y. [Department of Physics and Astronomy and Department of Mathematics, The University of Kansas, Lawrence, Kansas 66045 (United States); Grebogi, C. [Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States); Grebogi, C.; Kurths, J. [Department of Physics and Astrophysics, Universitaet Potsdam, Postfach 601553, D-14415 Potsdam (Germany)
1999-03-01
The success of deterministic modeling of a physical system relies on whether the solution of the model would approximate the dynamics of the actual system. When the system is chaotic, situations can arise where periodic orbits embedded in the chaotic set have distinct number of unstable directions and, as a consequence, no model of the system produces reasonably long trajectories that are realized by nature. We argue and present physical examples indicating that, in such a case, though the model is deterministic and low dimensional, statistical quantities can still be reliably computed. {copyright} {ital 1999} {ital The American Physical Society}
Theoretical Investigations of Chaotic Dynamics
1993-10-31
INVESTIGATIONS OF CHAOTIC DYNAMICS" PROFESSOR JAMES A YORKE CELSO GREBOGI UNIVERSITY OF MARYLAND COLLEGE PARK MD 20742-2431 F49620-92-J-0033 I PREFACE This...publication. d. "Evolution of Attractor Boundaries of Two-Dimensional Noninvertible Maps", W. Chin, I. Kan and C. Grebogi , Random & Comp. Dyn. L 349-370...1993). e "How often are chaotic saddles nonhyperbolic?", Y-C. Lai, C. Grebogi , and J. A Yorke, Nonlinearity, 6., 779-797 (1993). f. "A Geometric
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.
Observers for a Class of Chaotic Systems
Institute of Scientific and Technical Information of China (English)
ZHOU Ping
2006-01-01
The design of observers for a class of practical physical chaotic systems is discussed.By using only one state variable and its time derivatives,a control law is constructed to achieve the synchronization between the investigated chaotic systems and their observers,and the results are proved theoretically.Several observers of chaotic systems are designed by using this method.
Directory of Open Access Journals (Sweden)
Manuel Tobias Munz
2015-08-01
Full Text Available Background: Behavioral inhibition, which is a later-developing executive function (EF and anatomically located in prefrontal areas, is impaired in attention-deficit and hyperactivity disorder (ADHD. While optimal EFs have been shown to depend on efficient sleep in healthy subjects, the impact of sleep problems, frequently reported in ADHD, remains elusive. Findings of macroscopic sleep changes in ADHD are inconsistent, but there is emerging evidence for distinct microscopic changes with a focus on prefrontal cortical regions and non-rapid eye movement (non-REM slow-wave sleep. Recently, slow oscillations (SO during non-REM sleep were found to be less functional and, as such, may be involved in sleep-dependent memory impairments in ADHD. Objective: By augmenting slow-wave power through bilateral, slow oscillating transcranial direct current stimulation (so-tDCS, frequency = 0.75 Hz during non-REM sleep, we aimed to improve daytime behavioral inhibition in children with ADHD. Methods: 14 boys (10-14 yrs diagnosed with ADHD were included. In a randomized, double-blind, cross-over design, patients received so-tDCS either in the first or in the second experimental sleep night. Inhibition control was assessed with a visuomotor go/no-go task. Intrinsic alertness was assessed with a simple stimulus response task. To control for visuomotor performance, motor memory was assessed with a finger sequence tapping task. Results: SO-power was enhanced during early non-REM sleep, accompanied by slowed reaction times and decreased standard deviations of reaction times, in the go/no-go task after so-tDCS. In contrast, intrinsic alertness and motor memory performance were not improved by so-tDCS. Conclusion: Since behavioral inhibition but not intrinsic alertness or motor memory was improved by so-tDCS, our results suggest that lateral prefrontal slow oscillations during sleep might play a specific role for executive functioning in ADHD.
Relaxing Oscillation of the Machine-Unit
Directory of Open Access Journals (Sweden)
Bohumil Skala
2008-01-01
Full Text Available To understand the behavior of the Earth´s geomagnetic field, many theories have been created. One of the possible approaches is the Rikitake dynamo and chaotic theory. This paper describes the first step, i.e. how to verify the chaotic theory simulated result by a practical test. This first step is the oscillating machine unit. The asynchronous motor working point is moving from the stable part of its torque characteristic to the labile part due to the enormous loading. In the labile part the speed slows down and loading has to be decreased. Then the motor moves back to the stable part of characteristic.
Houdek, G
2010-01-01
In this short review on stellar convection dynamics I address the following, currently very topical, issues: (1) the surface effects of the Reynolds stresses and nonadiabaticity on solar-like pulsation frequencies, and (2) oscillation mode lifetimes of stochastically excited oscillations in red giants computed with different time-dependent convection formulations.
Analysis of chaotic FM system synchronization for bistatic radar
Pappu, Chandra S.; Verdin, Berenice; Flores, Benjamin C.; Boehm, James; Debroux, Patrick
2015-05-01
We propose a scheme for bistatic radar that uses a chaotic system to generate a wideband FM signal that is reconstructed at the receiver via a conventional phase lock loop. The setup for the bistatic radar includes a 3 state variable drive oscillator at the transmitter and a response oscillator at the receiver. The challenge is in synchronizing the response oscillator of the radar receiver utilizing a scaled version of the transmitted signal sr(t, x) = αst(t, x) where x is one of three driver oscillator state variables and α is the scaling factor that accounts for antenna gain, system losses, and space propagation. For FM, we also assume that the instantaneous frequency of the received signal, xs, is a scaled version of the Lorenz variable x. Since this additional scaling factor may not be known a priori, the response oscillator must be able to accept the scaled version of x as an input. Thus, to achieve synchronization we utilize a generalized projective synchronization technique that introduces a controller term -μe where μ is a control factor and e is the difference between the response state variable xs and a scaled x. Since demodulation of sr(t) is required to reconstruct the chaotic state variable x, the phase lock loop imposes a limit on the minimum error e. We verify through simulations that, once synchronization is achieved, the short-time correlation of x and xs is high and that the self-noise in the correlation is negligible over long periods of time.
Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil
Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris
2016-01-01
Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.
New Canards Bursting and Canards Periodic-Chaotic Sequence
Institute of Scientific and Technical Information of China (English)
YOOER Chi-Feng; XU Jian-Xue; ZHANG Xin-Hua
2009-01-01
A trajectory following the repelling branch of an equilibrium or a periodic orbit is called a canards solution. Using a continuation method, we find a new type of canards bursting which manifests itself in an alternation between the oscillation phase following attracting the limit cycle branch and resting phase following a repelling fixed point branch in a reduced leech neuron model. Via periodic-chaotic alternating of infinite times, the number of windings within a canards bursting can approach infinity at a Gavrilov-Shilnikov homoclinic tangency bifurcation of a simple saddle limit cycle.
Loss of lag synchronization in coupled chaotic systems
DEFF Research Database (Denmark)
Sosnovtseva, Olga; Balanov, A G; Vadivasova, T E
1999-01-01
Lag synchronization denotes a particular form of synchronization in which the amplitudes of two interacting, nonidentical chaotic oscillators are correlated but there is a characteristic time delay between them. We study transitions to and between different forms of synchronization...... for the attractors defined as "in-phase" and "out-of-phase" and investigate the processes by which lag synchronization is lost in two coupled Rössler systems. With a small frequency mismatch between the two systems, these processes are related to the occurrence of a peculiar form of basin structure as more and more...
Loss of lag synchronization in coupled chaotic systems
DEFF Research Database (Denmark)
Sosnovtseva, O.V.; Balanov, A.G.; Vadivasova, T.E.
1999-01-01
Lag synchronization denotes a particular form of synchronization in which the amplitudes of two interacting, nonidentical chaotic oscillators are correlated but there is a characteristic time delay between them. We study transitions to and between different forms of synchronization...... for the attractors defined as "in-phase" and "out-of-phase" and investigate the processes by which lag synchronization is lost in two coupled Rossler systems. With a small frequency mismatch between the two systems, these processes are related to the occurrence of a peculiar form of basin structure as more and more...
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
How long is the chaotic boundary of a billiard?
Bäcker, Arnd; Löck, Steffen; Schanz, Holger
2010-01-01
For two-dimensional quantum billiards we derive Weyl's law, i.e. the average density of states, for a subset of eigenstates concentrating on an invariant region $\\Gamma$ of phase space. The leading term is proportional to the area of the billiard times the phase-space fraction of $\\Gamma$. The boundary term is proportional to the fraction of the boundary where parallel trajectories belong to $\\Gamma$. Our result is numerically confirmed for the mushroom billiard, where we determine the boundary lengths associated with chaotic and regular states, and for the elliptical billiard, where we consider rotating and oscillating states.
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.
Dynamical chaos in chip-scale optomechanical oscillators
Wu, Jiagui; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Xia, Guangqiong; Wong, Chee Wei
2016-01-01
Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here we report the first generation of dynamical chaos in silicon optomechanical oscillators, enabled by the strong and coupled nonlinearities of Drude electron-hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the complexity of chaos. The correlation dimension D2 is determined at ~ 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate about 2.94*the fundamental optomechanical oscillation. The corresponding nonlinear dynamical maps demonstrate the plethora of subharmonics, bifurcations, and stable regimes, along with distinct transitional routes into chaotic states. The chaos generation in our mesoscopic...
Chaos Control and Synchronization of a Novel Chaotic System Based upon Adaptive Control Algorithm
Directory of Open Access Journals (Sweden)
Israr Ahmad
2014-08-01
Full Text Available Controlling chaos is stabilizing one of the unstable periodic orbits either to its equilibrium point or to a stable periodic orbit by means of an appropriate continuous signal injected to the system. On the other hand, chaos synchronization refers to a procedure where two chaotic oscillators (either identical or nonidentical adjust a given property of their motion to a common behavior. This research paper concerns itself with the Adaptive Control and Synchronization of a new chaotic system with unknown parameters. Based on the Lyapunov Direct Method, the Adaptive Control Techniques are designed in such a way that the trajectory of the new chaotic system is globally stabilized to one of its equilibrium points of the uncontrolled system. Moreover, the Adaptive Control Law is also applied to achieve the synchronization state of two identical systems and two different chaotic systems with fully unknown parameters. The parameters identification, chaos control and synchronization of the chaotic system have been carried out simultaneously by the Adaptive Controller. All simulation results are carried out to corroborate the effectiveness and the robustness of the proposed methodology and possible feasibility for synchronizing two chaotic systems by using mathematica 9.
Chaotic domains: A numerical investigation
Cross, M. C.; Meiron, D.; Tu, Yuhai
1994-01-01
We study the chaotic domain state in rotating convection using a model equation that allows for a continuous range of roll orientations as in the experimental system. Methods are developed for extracting the domain configuration from the resulting patterns that should be applicable to a wide range of domain states. Comparison with the truncated three mode amplitude equation description is made.
Chaotic Dynamics in Hybrid Systems
P.J. Collins (Pieter)
2008-01-01
htmlabstractIn this paper we give an overview of some aspects of chaotic dynamics in hybrid systems, which comprise different types of behaviour. Hybrid systems may exhibit discontinuous dependence on initial conditions leading to new dynamical phenomena. We indicate how methods from topological
Chaotic dynamics in hybrid systems
P.J. Collins (Pieter)
2008-01-01
htmlabstractIn this paper we give an overview of some aspects of chaotic dynamics in hybrid systems, which comprise different types of behaviour. Hybrid systems may exhibit discontinuous dependence on initial conditions leading to new dynamical phenomena. We indicate how methods from topological
Chaotic Dispersal of Tidal Debris
Price-Whelan, Adrian M; Valluri, Monica; Pearson, Sarah; Kupper, Andreas H W; Hogg, David W
2015-01-01
Several long, dynamically cold stellar streams have been observed around the Milky Way Galaxy, presumably formed from the tidal disruption of globular clusters. In integrable potentials---where all orbits are dynamically regular---tidal debris phase-mixes close to the orbit of the progenitor system. However, cosmological simulations of structure formation suggest that the Milky Way's dark matter halo is expected not to be fully integrable; an appreciable fraction of orbits will be chaotic. This paper examines the influence of chaos on the phase-space morphology of cold tidal streams. We find very stark results: Streams in chaotic regions look very different from those in regular regions. We find that streams (simulated using test particle ensembles of nearby orbits) can be sensitive to chaos on a much shorter time-scale than any standard prediction (from the Lyapunov or frequency-diffusion times). For example, on a weakly chaotic orbit with a chaotic timescale predicted to be >1000 orbital periods (>1000 Gyr)...
Chaotic communication scheme with multiplication
Bobreshov, A. M.; Karavaev, A. A.
2007-05-01
A new scheme of data transmission with nonlinear admixing is described, in which the two mutually inverse operations (multiplication and division) ensure multiplicative mixing of the informative and chaotic signals that provides a potentially higher degree of security. A special feature of the proposed scheme is the absence of limitations (related to the division by zero) imposed on the types of informative signals.
Learning in a Chaotic Environment
Goldman, Ellen; Plack, Margaret; Roche, Colleen; Smith, Jeffrey; Turley, Catherine
2009-01-01
Purpose: The purpose of this study is to understand how, when, and why emergency medicine residents learn while working in the chaotic environment of a hospital emergency room. Design/methodology/approach: This research used a qualitative interview methodology with thematic data analysis that was verified with the entire population of learners.…
Chaotic dynamics, fluctuations, nonequilibrium ensembles.
Gallavotti, Giovanni
1998-06-01
The ideas and the conceptual steps leading from the ergodic hypothesis for equilibrium statistical mechanics to the chaotic hypothesis for equilibrium and nonequilibrium statistical mechanics are illustrated. The fluctuation theorem linear law and universal slope prediction for reversible systems is briefly derived. Applications to fluids are briefly alluded to. (c) 1998 American Institute of Physics.
Controlling chaos with localized heterogeneous forces in oscillator chains.
Chacón, Ricardo
2006-10-01
The effects of decreasing the impulse transmitted by localized periodic pulses on the chaotic behavior of homogeneous chains of coupled nonlinear oscillators are studied. It is assumed that when the oscillators are driven synchronously, i.e., all driving pulses transmit the same impulse, the chains display chaotic dynamics. It is shown that decreasing the impulse transmitted by the pulses of the two free end oscillators results in regularization with the whole array exhibiting frequency synchronization, irrespective of the chain size. A maximum level of amplitude desynchrony as the pulses of the two end oscillators narrow is typically found, which is explained as the result of two competing universal mechanisms: desynchronization induced by localized heterogeneous pulses and oscillation death of the complete chain induced by drastic decreasing of the impulse transmitted by such localized pulses. These findings demonstrate that decreasing the impulse transmitted by localized external forces can suppress chaos and lead to frequency-locked states in networks of dissipative systems.
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.
Visibility graphlet approach to chaotic time series.
Mutua, Stephen; Gu, Changgui; Yang, Huijie
2016-05-01
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.
Color image encryption based on Coupled Nonlinear Chaotic Map
Energy Technology Data Exchange (ETDEWEB)
Mazloom, Sahar [Faculty of Electrical, Computer and IT Engineering, Qazvin Islamic Azad University, Qazvin (Iran, Islamic Republic of)], E-mail: sahar.mazloom@gmail.com; Eftekhari-Moghadam, Amir Masud [Faculty of Electrical, Computer and IT Engineering, Qazvin Islamic Azad University, Qazvin (Iran, Islamic Republic of)], E-mail: eftekhari@qazviniau.ac.ir
2009-11-15
Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by conventional methods. The desirable cryptographic properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. Therefore, recent researches of image encryption algorithms have been increasingly based on chaotic systems, though the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper proposes a Coupled Nonlinear Chaotic Map, called CNCM, and a novel chaos-based image encryption algorithm to encrypt color images by using CNCM. The chaotic cryptography technique which used in this paper is a symmetric key cryptography with a stream cipher structure. In order to increase the security of the proposed algorithm, 240 bit-long secret key is used to generate the initial conditions and parameters of the chaotic map by making some algebraic transformations to the key. These transformations as well as the nonlinearity and coupling structure of the CNCM have enhanced the cryptosystem security. For getting higher security and higher complexity, the current paper employs the image size and color components to cryptosystem, thereby significantly increasing the resistance to known/chosen-plaintext attacks. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.
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.
Synchronizing chaotic dynamics with uncertainties based on a sliding mode control design.
Yang, Tao; Shao, Hui He
2002-04-01
The synchronization of two chaotic systems with uncertainties is studied in this paper. A feedback controller is provided based on a sliding mode control design. A kind of extended state observer is used to compensate for the systems' uncertainties, such as the structure difference or parameter mismatching, using only the available synchronizing error. Then the feedback controller becomes physically realizable based on the states of the observer, and can be used to synchronize two continuous chaotic systems. Illustrative examples of the synchronization of Duffing and Van der Pol oscillators as well as two Lorenz systems with parameter mismatching are proposed to show the effectiveness of this method.
Anti-synchronization on autonomous and non-autonomous chaotic systems via adaptive feedback control
Energy Technology Data Exchange (ETDEWEB)
Li Ruihong [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)], E-mail: llylrh8077@mail.nwpu.edu.cn; Xu Wei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)], E-mail: weixu@nwpu.edu.cn; Li Shuang [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2009-05-15
In this paper, the anti-synchronization of a general class of chaotic systems is investigated. A simple adaptive feedback scheme is proposed to anti-synchronize many familiar chaotic systems, including autonomous systems and non-autonomous systems. Lyapunov analysis for the error system gives the asymptotic stability conditions based on the invariance principle of differential equations. The schemes are successfully applied to three groups of examples: the van der Pol-Duffing oscillator, the parametrically harmonically excited 4D system, and the additionally harmonically excited Murali-Lakshmanan-Chua circuit. Numerical results are presented to justify the theoretical analysis in this paper.
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.
Chaotic flavor evolution in an interacting neutrino gas
Hansen, Rasmus Sloth
2014-01-01
Neutrino-neutrino refraction can lead to non-periodic flavor oscillations in dense neutrino gases, and it has been hypothesized that some solutions are chaotic in nature. This is of particular interest in the case of neutrino emission from core-collapse supernovae where the measurement of the spectral shape for different flavors can provide crucial information about both neutrino physics and the physical conditions close to the proto-neutron star. Whether a system is chaotic or not can be assessed by the Lyapunov exponents which quantify the rate of divergence of nearby trajectories in the system. We have done a numerical case study for a simple toy model of two neutrino flavors with two momentum states traveling against each other which is known to exhibit flavor transition instabilities. We find the leading Lyapunov exponent to be positive in all cases, confirming the chaoticity of the system for both the normal and the inverted neutrino mass hierarchy. However, more Lyapunov exponents were approximately ze...
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.
Analysis and implementation of memristor chaotic circuit%忆阻混沌电路的分析与实现
Institute of Scientific and Technical Information of China (English)
包伯成; 胡文; 许建平; 刘中; 邹凌
2011-01-01
具有记忆功能的忆阻器是除电阻器、电容器和电感器之外的第四种基本二端电路元件.提出了由φ-q平面上的一条三次单调上升的非线性曲线来确定的光滑磁控忆阻器,它有着斜＂8＂字形的类紧磁滞回线的伏安特性曲线.采用此忆阻器和负电导构成的有源忆阻器替换蔡氏混沌电路中的蔡氏二极管,导出了一个基于忆阻器的混沌振荡电路.此外,利用常规的运算放大器和乘法器等元器件给出了有源忆阻器的等效电路实现形式.理论分析、数值仿真和电路仿真结果一致,均表明忆阻混沌电路的动力学行为依赖于忆阻器的初始状态,在不同初始状态下存在混沌振荡、周期振荡或稳定的汇等不同的运行轨道.%Memristor with memory function is the fourth fundamental two-terminal circuit element,besides resistor,capacitor and inductor.In this paper,a smooth flux-controlled memristor is described by a monotone-increasing nonlinearity curve in the φ-q plane,and it has an italic type ＂8＂ like voltage current relation curve that looks like a pinched hysteresis loop characteristics.By replacing Chua＇s diode with an active memristor consisting of a smooth flux-controlled memristor and a negative conductance,a memristor based chaotic oscillation is derived from Chua＇s circuit.Furthermore,the equivalent circuit implementation form for the active memristor is designed by utilizing conventional components such as operational amplifiers and multipliers.The results from theoretical analysis,numerical simulations and circuit simulations are completely identical with each other,and demonstrate that the dynamical behaviors of the memristor chaotic circuit are dependent on the memristor initial state,showing different orbits such as chaotic oscillation,periodic oscillation and stable sink under different initial states.
Experimental observation of partial amplitude death in coupled chaotic oscillators
Institute of Scientific and Technical Information of China (English)
Liu Wei-Qing; Yang Jun-Zhong; Xiao Jing-Hua
2006-01-01
The dynamics of coupled Lorenz circuits is investigated experimentally. The partial amplitude death reported in Phys. Rev. E 72, 057201 (2005) is verified by physical experiments with electronic circuits. With the increase of coupling constant, the coupled circuits undergo the transition from the breakdown of both the reflection symmetry and the translational symmetry to the partial amplitude death. Its stability is also confirmed by analysing the effects of noise.
Chaotic Diffusion of Resonant Kuiper Belt Objects
Tiscareno, Matthew S
2008-01-01
We carried out extensive numerical orbit integrations to probe the long-term chaotic dynamics of the two strongest mean motion resonances of Neptune in the Kuiper belt, the 3:2 (Plutinos) and 2:1 (Twotinos). Our primary results include a computation of the relative volumes of phase space characterized by large- and small-resonance libration amplitudes, and maps of resonance stability measured by mean chaotic diffusion rate. We find that Neptune's 2:1 resonance has weaker overall long-term stability than the 3:2 -- only 15% of Twotinos are projected to survive for 4 Gyr, compared to 28% of Plutinos. We find that Pluto has only a modest effect, causing a ~4% decrease in the Plutino population that survives to 4 Gyr. Given current observational estimates, we conclude that the primordial populations of Plutinos and Twotinos formerly made up more than half the population of the classical and resonant Kuiper Belt. We also conclude that Twotinos were originally nearly as numerous as Plutinos, consistent with models ...
On closure parameter estimation in chaotic systems
Directory of Open Access Journals (Sweden)
J. Hakkarainen
2012-02-01
Full Text Available Many dynamical models, such as numerical weather prediction and climate models, contain so called closure parameters. These parameters usually appear in physical parameterizations of sub-grid scale processes, and they act as "tuning handles" of the models. Currently, the values of these parameters are specified mostly manually, but the increasing complexity of the models calls for more algorithmic ways to perform the tuning. Traditionally, parameters of dynamical systems are estimated by directly comparing the model simulations to observed data using, for instance, a least squares approach. However, if the models are chaotic, the classical approach can be ineffective, since small errors in the initial conditions can lead to large, unpredictable deviations from the observations. In this paper, we study numerical methods available for estimating closure parameters in chaotic models. We discuss three techniques: off-line likelihood calculations using filtering methods, the state augmentation method, and the approach that utilizes summary statistics from long model simulations. The properties of the methods are studied using a modified version of the Lorenz 95 system, where the effect of fast variables are described using a simple parameterization.
Applications of tripled chaotic maps in cryptography
Energy Technology Data Exchange (ETDEWEB)
Behnia, S. [Department of Physics, IAU, Urmia (Iran, Islamic Republic of)], E-mail: s.behnia@iaurmia.ac.ir; Akhshani, A. [School of Physics, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia); Akhavan, A. [School of Computer Science, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia); Mahmodi, H. [School of Physics, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia)
2009-04-15
Security of information has become a major issue during the last decades. New algorithms based on chaotic maps were suggested for protection of different types of multimedia data, especially digital images and videos in this period. However, many of them fundamentally were flawed by a lack of robustness and security. For getting higher security and higher complexity, in the current paper, we introduce a new kind of symmetric key block cipher algorithm that is based on tripled chaotic maps. In this algorithm, the utilization of two coupling parameters, as well as the increased complexity of the cryptosystem, make a contribution to the development of cryptosystem with higher security. In order to increase the security of the proposed algorithm, the size of key space and the computational complexity of the coupling parameters should be increased as well. Both the theoretical and experimental results state that the proposed algorithm has many capabilities such as acceptable speed and complexity in the algorithm due to the existence of two coupling parameters and high security. Note that the ciphertext has a flat distribution and has the same size as the plaintext. Therefore, it is suitable for practical use in secure communications.
Archetypal oscillator for smooth and discontinuous dynamics.
Cao, Qingjie; Wiercigroch, Marian; Pavlovskaia, Ekaterina E; Grebogi, Celso; Thompson, J Michael T
2006-10-01
We propose an archetypal system to investigate transitions from smooth to discontinuous dynamics. In the smooth regime, the system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. At the discontinuous limit, however, there is a substantial departure in the dynamics from the standard one. In particular, the velocity flow suffers a jump in crossing from one well to another, caused by the loss of local hyperbolicity due to the collapse of the stable and unstable manifolds of the stationary state. In the presence of damping and external excitation, the system has coexisting attractors and also a chaotic saddle which becomes a chaotic attractor when a smoothness parameter drops to zero. This attractor can bifurcate to a high-period periodic attractor or a chaotic sea with islands of quasiperiodic attractors depending on the strength of damping.
Identification of Chaotic Systems with Application to Chaotic Communication
Institute of Scientific and Technical Information of China (English)
FENG Jiu-Chao; QIU Yu-Hui
2004-01-01
@@ We propose and develop a novel method to identify a chaotic system with time-varying bifurcation parameters via an observation signal which has been contaminated by additive white Gaussian noise. This method is based on an adaptive algorithm, which takes advantage of the good approximation capability of the radial basis function neural network and the ability of the extended Kalman filter for tracking a time-varying dynamical system. It is demonstrated that, provided the bifurcation parameter varies slowly in a time window, a chaotic dynamical system can be tracked and identified continuously, and the time-varying bifurcation parameter can also be retrieved in a sub-window of time via a simple least-square-fit method.
All-optical chaotic MQW laser repeater for long-haul chaotic communications
Institute of Scientific and Technical Information of China (English)
Senlin Yan
2005-01-01
We present an all-optical chaotic multi-quantum-well (MQW) laser repeater system to be used in long-haul chaotic communications. Chaotic synchronization is achieved among transmitter, repeater, and receiver. Chaotic repeater communications with a sinusoidal signal of 0.2-GHz modulation frequency and a digital signal of 0.4-Gb/s bit rate are numerically simulated, respectively. Calculation results illustrate that the signals are well decoded by the chaotic repeaters. Its bandwidth and the characteristics at much high bit rate are also analyzed. Simulation shows that the repeater can improve decoding quality, especially in higher bit rate chaotic communications.
The study of fuzzy chaotic neural network based on chaotic method
Institute of Scientific and Technical Information of China (English)
WANG Ke-jun; TANG Mo; ZHANG Yan
2006-01-01
This paper proposes a type of Fuzzy Chaotic Neural Network (FCNN). Firstly, the model of recurrent fuzzy neural network (RFNN) is considered, which adds a feedback in the second layer to realize dynamic map. Then, the Logistic map is introduced into the recurrent fuzzy neural network, so as to build a Fuzzy Chaotic Neural Network (FCNN). Its chaotic character is analyzed, and then the training algorithm and associate memory ability are studied subsequently. And then, a chaotic system is approximated using FCNN; the simulation results indicate that FCNN could approach dynamic system preferably. And owing to the introducing of chaotic map, the chaotic recollect capacity of FCNN is increased.
Strange Nonchaotic Oscillations in The Quasiperiodically Forced Hodgkin-Huxley Neuron
Lim, Woochang; 10.1088/1751-8113/42/26/265103
2011-01-01
We numerically study dynamical behaviors of the quasiperiodically forced Hodgkin-Huxley neuron and compare the dynamical responses with those for the case of periodic stimulus. In the periodically forced case, a transition from a periodic to a chaotic oscillation was found to occur via period doublings in previous numerical and experimental works. We investigate the effect of the quasiperiodic forcing on this period-doubling route to chaotic oscillation. In contrast to the case of periodic forcing, new type of strange nonchaotic (SN) oscillating states (that are geometrically strange but have no positive Lyapunov exponents) are found to exist between the regular and chaotic oscillating states as intermediate ones. Their strange fractal geometry leads to aperiodic "complex" spikings. Various dynamical routes to SN oscillations are identified, as in the quasiperiodically forced logistic map. These SN spikings are expected to be observed in experiments of the quasiperiodically forced squid giant axon.
Strange nonchaotic oscillations in the quasiperiodically forced Hodgkin-Huxley neuron
Energy Technology Data Exchange (ETDEWEB)
Lim, Woochang; Kim, Sang-Yoon [Department of Physics, Kangwon National University, Chunchon, Kangwon-Do 200-701 (Korea, Republic of)], E-mail: wclim@kangwon.ac.kr, E-mail: sykim@kangwon.ac.kr
2009-07-03
We numerically study dynamical behaviors of the quasiperiodically forced Hodgkin-Huxley neuron and compare the dynamical responses with those for the case of periodic stimulus. In the periodically forced case, a transition from a periodic to a chaotic oscillation was found to occur via period doublings in previous numerical and experimental works. We investigate the effect of the quasiperiodic forcing on this period-doubling route to chaotic oscillation. In contrast to the case of periodic forcing, a new type of strange nonchaotic (SN) oscillating states (that are geometrically strange but have no positive Lyapunov exponents) is found to exist between the regular and chaotic oscillating states as intermediate ones. Their strange fractal geometry leads to aperiodic 'complex' spikings. Various dynamical routes to SN oscillations are identified, as in the quasiperiodically forced logistic map. These SN spikings are expected to be observed in experiments of the quasiperiodically forced squid giant axon.
Aniksztejn, L; Sciancalepore, M; Ben Ari, Y; Cherubini, E
1995-04-01
1. The single-electrode voltage-clamp technique was used to study the effects of the metabotropic glutamate receptors (mGluRs) agonist 1S,3R-1-aminocyclopentane-1,3-dicarboxylic acid (1S,3R-ACPD, ACPD, 3-10 microM) on CA3 hippocampal neurons during the 1st 10 days of postnatal (P) life and in adulthood. 2. Repeated applications of 1S,3R-ACPD, in the presence of tetrodotoxin (TTX, 1 microM), tetraethylammonium chloride (TEACl 10 mM), and CsCl (2 mM), induced in immature but not in adult neurons periodic inward currents (PICs) that persisted for several hours after the last application of the agonist. 3. PICs, which were generated by nonspecific cationic currents, reversed polarity at 2.8 +/- 3 (SD) mV. They were reversibly blocked by kynurenic acid (1 mM), suggesting that they were mediated by glutamate acting on ionotropic receptors. They were also abolished in a nominally Ca(2+)-free medium. 4. PICs were irreversibly abolished by thapsigargin (10 microM) but were unaffected by ryanodine (10-40 microM). Caffeine (2 mM) also reversibly blocked PICs; this effect was independent from adenosine 3',5'-cyclic monophosphate (cAMP) accumulation, inhibition of voltage-dependent Ca2+ current, or blockade of adenosine receptors. 5. We suggest that, in neonatal slices, mGluRs-induced PICs are triggered by elevation of [Ca2+]i, after mobilization of Ca2+ from inositol 1,4,5-trisphosphate (InsP3)-sensitive stores. This will lead to a persistent, pulsatile release of glutamate from presynaptic nerve terminals, a phenomenon that is probably maintained via a calcium-induced-calcium release process.
Communications with chaotic optoelectronic systems cryptography and multiplexing
Rontani, Damien
With the rapid development of optical communications and the increasing amount of data exchanged, it has become utterly important to provide effective architectures to protect sensitive data. The use of chaotic optoelectronic devices has already demonstrated great potential in terms of additional computational security at the physical layer of the optical network. However, the determination of the security level and the lack of a multi-user framework are two hurdles which have prevented their deployment on a large scale. In this thesis, we propose to address these two issues. First, we investigate the security of a widely used chaotic generator, the external cavity semiconductor laser (ECSL). This is a time-delay system known for providing complex and high-dimensional chaos, but with a low level of security regarding the identification of its most critical parameter, the time delay. We perform a detailed analysis of the in uence of the ECSL parameters to devise how higher levels of security can be achieved and provide a physical interpretation of their origin. Second, we devise new architectures to multiplex optical chaotic signals and realize multi-user communications at high bit rates. We propose two different approaches exploiting known chaotic optoelectronic devices. The first one uses mutually coupled ECSL and extends typical chaos-based encryption strategies, such as chaos-shift keying (CSK) and chaos modulation (CMo). The second one uses an electro-optical oscillator (EOO) with multiple delayed feedback loops and aims first at transposing coded-division multiple access (CDMA) and then at developing novel strategies of encryption and decryption, when the time-delays of each feedback loop are time-dependent.
Recovering chaotic properties from small data.
Shao, Chenxi; Fang, Fang; Liu, Qingqing; Wang, Tingting; Wang, Binghong; Yin, Peifeng
2014-12-01
Physical properties are obviously essential to study a chaotic system that generates discrete-time signals, but recovering chaotic properties of a signal source from small data is a very troublesome work. Existing chaotic models are weak in dealing with such case in that most of them need big data to exploit those properties. In this paper, geometric theory is considered to solve this problem. We build a smooth trajectory from series to implicitly exhibit the chaotic properties with series-nonuniform rational B-spline (S-NURBS) modeling method, which is presented by our team to model slow-changing chaotic time series. As for the part of validation, we reveal how well our model recovers the properties from both the statistical and the chaotic aspects to confirm the effectiveness of the model. Finally a practical chaotic model is built up to recover the chaotic properties contained in the Musa standard dataset, which is used in analyzing software reliability, thereby further proves the high credibility of this model in practical time series. The effectiveness of the S-NURBS modeling leads us to believe that it is really a feasible and worthy research area to study chaotic systems from geometric perspective. For this reason, we reckon that we have opened up a new horizon for chaotic system research.
Design of a novel current-controlled CMOS oscillator circuit%一种新型电流控制CMOS振荡器电路设计
Institute of Scientific and Technical Information of China (English)
徐慧敏; 戴庆元; 罗超
2012-01-01
设计了一种基于华虹0.35μm BCD工艺的新型电流控制CMOS振荡器电路,中心频率为1 MHz,宽温度范围内具有占空比高稳定性.不同于传统电流控制CMOS振荡器拓扑,结构简单,通过反相器阈值电压控制电流对电容的充放电状态切换,消除了延迟时间引起的上冲、下冲问题,具有良好的可移植性.Cadence Spectre仿真结果表明:-45～125℃范围内,振荡频率和占空比相对中心值的上下偏差分别为5.01％(-)到3.31％(+)、1 95％(-)到1.84％(+)；方差分别为0.000 9、0.000 1.%A novel current-controlled CMOS oscillator circuit with 1 MHz frequency was designed based on 0.35 μm BCD process which realized high stability of frequency and duty cycle. The key aspect of the circuit with a simple structure and good portability, was the different topology with conventional CMOS oscillator, in which the capacitor charge state switching was controlled by the inverter threshold voltage, eliminating the overshoot and undershoot caused by delay. The results from the Cadence spectra simulation show that, with temperature range from —45 ℃ to 125 ℃, the proposed oscillator has a frequency deviation of 5.01%(—) to 3.31%(+) and a duty cycle variation of 1.95%(-) to 1.84%(+), while variance are 0.0009 and 0.0001, respectively.
Energy Technology Data Exchange (ETDEWEB)
Sulyma, Christopher M. [Department of Physics, Clarkson University, Potsdam, NY 13699-5820 (United States); Roy, Dipankar, E-mail: samoy@clarkson.ed [Department of Physics, Clarkson University, Potsdam, NY 13699-5820 (United States)
2010-09-15
Anodic corrosion of Ta is examined for potential applications in electrochemical-mechanical planarization (ECMP) of diffusion barriers. This strategy involves electro-oxidation of Ta in the presence of NO{sub 3}{sup -} (or Br{sup -}) to form mechanically weak surface-oxide films, followed by mechanical removal of the latter. The voltammetric currents exhibit oscillatory behaviour with frequencies that are signature attributes of localised pitting by Br{sup -} or general surface corrosion by NO{sub 3}{sup -}. SEM, voltammetry, and impedance spectroscopy are used to probe these corrosion mechanisms. Apart from their relevance for ECMP, the results also address certain fundamental aspects of pitting and general corrosion of valve metals.
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.
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.
Study on Super-Twisting synchronization control of chaotic system based on U model
Directory of Open Access Journals (Sweden)
Jianhua ZHANG
2016-06-01
Full Text Available A U model based Super-Twisting synchronization control method for chaotic systems is proposed. The chaos control of chaotic systems is prescribed, then, based on the current research status of chaotic systems and some useful research results in nonlinear system design, some new methods for chaos control and synchronization are provided, and the controller is designed to achieve the finite time chaos synchronization. The numerical simulations are carried out for Lorenz system and Chen system, and the result proves the effectiveness of the method.
A new spatiotemporally chaotic cryptosystem and its security and performance analyses
Lü, Huaping; Wang, Shihong; Li, Xiaowen; Tang, Guoning; Kuang, Jinyu; Ye, Weiping; Hu, Gang
2004-09-01
A one-way-coupled chaotic map lattice is proposed for cryptography of self-synchronizing stream cipher. The system performs basic floating-point analytical computation on real numbers, incorporating auxiliarily with few simple algebraic operations on integer numbers. Parallel encryption (decryption) operations of multiple chaotic sites are conducted. It is observed that the system has high practical security, fast encryption (decryption) speed with software realization, and excellent reliability against strong channel noise, and its overall cryptographic properties are considerably better than both known chaotic cryptosystems and currently used conventional cryptosystems, including the advanced encryption standard.
Illusion optics in chaotic light
Zhang, Su-Heng; Gan, Shu; Xiong, Jun; Zhang, Xiangdong; Wang, Kaige
2010-08-01
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
Energy Technology Data Exchange (ETDEWEB)
Bouallegue, Kais, E-mail: kais-bouallegue@yahoo.fr [Department of Electrical Engineering, Higher Institute of Applied Sciences and Technology of Sousse, Sousse (Tunisia)
2015-07-15
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.
The convergence of chaotic integrals
Bauer, O; Bauer, Oliver; Mainieri, Ronnie
1995-01-01
We review the convergence of chaotic integrals computed by Monte Carlo simulation, the trace method, dynamical zeta function, and Fredholm determinant on a simple one-dimensional example: the parabola repeller. There is a dramatic difference in convergence between these approaches. The convergence of the Monte Carlo method follows an inverse power law, whereas the trace method and dynamical zeta function converge exponentially, and the Fredholm determinant converges faster than any exponential.
Chaotic behavior in dopamine neurodynamics.
King, R; Barchas, J.D.; Huberman, B A
1984-01-01
We report the results of the dynamics of a model of the central dopaminergic neuronal system. In particular, for certain values of a parameter k, which monitors the efficacy of dopamine at the postsynaptic receptor, chaotic solutions of the dynamical equations appear--a prediction that correlates with the observed increased variability in behavior among schizophrenics, the rapid fluctuations in motor activity among Parkinsonian patients treated chronically with L-dopa, and the lability of moo...
Chaotic principle an experimental test
Bonetto, F; Garrido, P L
1996-01-01
The chaotic hypothesis discussed in [GC1] is tested experimentally in a simple conduction model. Besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which, as the forcing strength grows, the attractor ceases to be an Anosov system and becomes an Axiom A attractor. A first test of the new predictions is also attempted.
Stabilization of generalized fractional order chaotic systems using state feedback control
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M. E-mail: wajdi@sharjah.ac.ae; El-Khazali, Reyad E-mail: khazali@ece.ac.ae; Al-Assaf, Yousef E-mail: yassaf@aus.ac.ae
2004-10-01
In this paper, we address the problem of chaos control of three types of fractional order systems using simple state feedback gains. Electronic chaotic oscillators, mechanical 'jerk' systems, and the Chen system are investigated when they assume generalized fractional orders. We design the static gains to place the eigenvalues of the system Jacobian matrices in a stable region whose boundaries are determined by the orders of the fractional derivatives. We numerically demonstrate the effectiveness of the controller in eliminating the chaotic behavior from the state trajectories, and driving the states to the nearest equilibrium point in the basin of attraction. For the recently introduced Chen system, in particular, we demonstrate that with a proper choice of model parameters, chaotic behavior is preserved when the system order becomes fractional. Both state and output feedback controllers are then designed to stabilize a generalized fractional order Chen system.
Rigatos, Gerasimos
2016-07-01
The Derivative-free nonlinear Kalman Filter is used for developing a communication system that is based on a chaotic modulator such as the Duffing system. In the transmitter's side, the source of information undergoes modulation (encryption) in which a chaotic signal generated by the Duffing system is the carrier. The modulated signal is transmitted through a communication channel and at the receiver's side demodulation takes place, after exploiting the estimation provided about the state vector of the chaotic oscillator by the Derivative-free nonlinear Kalman Filter. Evaluation tests confirm that the proposed filtering method has improved performance over the Extended Kalman Filter and reduces significantly the rate of transmission errors. Moreover, it is shown that the proposed Derivative-free nonlinear Kalman Filter can work within a dual Kalman Filtering scheme, for performing simultaneously transmitter-receiver synchronisation and estimation of unknown coefficients of the communication channel.
Correlation analysis of chaotic trajectories from Chua's system
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iatapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico)], E-mail: jjar@xanum.uam.mx; Rodriguez, Eduardo; Echeverria, Juan Carlos; Puebla, Hector [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iatapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico)
2008-06-15
Chaotic systems exhibit an erratic behavior reflected by a strong divergence of trajectories with arbitrarily close initial condition. In this way, similar to trajectories from pseudorandom number generators, chaotic trajectories can be seen as noise with some degree of correlation. This work focuses on the study of some correlation properties (i.e., scaling) of chaotic trajectories from the Chua's system. This is done by using detrended fluctuation analysis, which is a method designed for the detection of correlations in stochastic time series. It is found that, in general, Chua's trajectories behave as a Brownian motion for small time scales, while they can display a white noise-like behavior or be dominated by harmonic oscillations for large time scales.
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.
CHAOTIC ZONES AROUND GRAVITATING BINARIES
Energy Technology Data Exchange (ETDEWEB)
Shevchenko, Ivan I., E-mail: iis@gao.spb.ru [Pulkovo Observatory of the Russian Academy of Sciences, Pulkovskoje ave. 65, St. Petersburg 196140 (Russian Federation)
2015-01-20
The extent of the continuous zone of chaotic orbits of a small-mass tertiary around a system of two gravitationally bound primaries of comparable masses (a binary star, a binary black hole, a binary asteroid, etc.) is estimated analytically, as a function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges (above a threshold in the primaries' mass ratio) due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the central binary periods. In this zone, the unlimited chaotic orbital diffusion of the tertiary takes place, up to its ejection from the system. The primaries' mass ratio, above which such a chaotic zone is universally present at all initial eccentricities of the tertiary, is estimated. The diversity of the observed orbital configurations of biplanetary and circumbinary exosystems is shown to be in accord with the existence of the primaries' mass parameter threshold.
Kuusela, Tom A.
2017-09-01
A He-Ne laser is an example of a class A laser, which can be described by a single nonlinear differential equation of the complex electric field. This laser system has only one degree of freedom and is thus inherently stable. A He-Ne laser can be driven to the chaotic condition when a large fraction of the output beam is injected back to the laser. In practice, this can be done simply by adding an external mirror. In this situation, the laser system has infinite degrees of freedom and therefore it can have a chaotic attractor. We show the fundamental laser equations and perform elementary stability analysis. In experiments, the laser intensity variations are measured by a simple photodiode circuit. The laser output intensity time series is studied using nonlinear analysis tools which can be found freely on the internet. The results show that the laser system with feedback has an attractor of a reasonably high dimension and that the maximal Lyapunov exponent is positive, which is clear evidence of chaotic behaviour. The experimental setup and analysis steps are so simple that the studies can even be implemented in the undergraduate physics laboratory.