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1.
Measure synchronization in coupled Hamiltonian systems is a novel
synchronization phenomenon. The measure synchronization on symplectic map is
observed numerically, for identical coupled systems with different
parameters. We have found the properties of the characteristic frequency and
the amplitude of phase locking in regular motion when the measure
synchronization of coupled systems is obtained. The relations between the
change of the largest Lyapunov exponent and the course of phase
desynchronization are also discussed in coupled systems, some useful results
are obtained. A new approach is proposed for describing the measure
synchronization of coupled systems numerically, which is
advantage in judging the measure synchronization, especially for the coupled
systems in nonregular region. 相似文献
2.
本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程. 相似文献
3.
4.
In this paper we briefly report some recent developments on generalized synchronization. We discuss different methods of detecting generalized synchronization. We first consider two unidirectionally coupled systems and then two mutually coupled systems. We then extend the study to a network of coupled systems. In the study of generalized synchronization of coupled nonidentical systems we discuss the Master Stability Function (MSF) formalism for coupled nearly identical systems. Later we use this MSF to construct synchronized optimized networks. In the optimized networks the nodes which have parameter value at one extreme are chosen as hubs and the pair of nodes with larger difference in parameter are chosen to create links. 相似文献
5.
M. S. Baptista S. P. Garcia S. K. Dana J. Kurths 《The European physical journal. Special topics》2008,165(1):119-128
We propose a rationale for experimentally studying the intricate relationship between the rate of information transmission
and synchronization level in active networks, applying theoretical results recently proposed. We consider two non-identical
coupled Chua’s circuit with non-identical coupling strengths in order to illustrate the proceeding for experimental scenarios
of very few data points coming from highly non-coherent coupled systems, such that phase synchronization can only be detected
by methods that do not rely explicitely on the calculation of the phase. A relevant finding is to show that for the coupled
Chua’s circuit, the larger the level of synchronization the larger the rate of information exchanged between both circuits.
We further validate our findings with data from numerical simulations, and discuss an extension to arbitrarily large active
networks. 相似文献
6.
D.V. Senthilkumar M. Lakshmanan J. Kurths 《The European physical journal. Special topics》2008,161(1):35-44
Phase synchronization in unidirectionally coupled Ikeda time-delay systems
exhibiting non-phase-coherent hyperchaotic attractors of complex topology with
highly interwoven trajectories is studied. It is shown that in this set of
coupled systems phase synchronization (PS)does exist in a range of the
coupling strength which is preceded by a transition regime (approximate PS)and
a nonsynchronous regime. However, exact generalized synchronization does not seem
to occur in the coupled Ikeda systems (for the range of parameters we have
studied)even for large coupling strength, in contrast to our earlier studies in
coupled piecewise-linear and Mackey-Glass systems [27,28].
The above transitions are characterized in terms of recurrence based indices,
namely generalized autocorrelation function P(t), correlation of probability
of recurrence (CPR), joint probability of recurrence (JPR)and similarity of
probability of recurrence (SPR). The existence of phase synchronization is also
further confirmed by typical transitions in the Lyapunov exponents of the
coupled Ikeda time-delay systems and also using the concept of localized sets. 相似文献
7.
The dynamics of one-way coupled systems with discrete time is considered. The behavior of the coupled logistic maps is compared to the dynamics of maps obtained using the Poincaré sectioning procedure applied to the coupled continuous-time systems in the phase synchronization regime. The behavior (previously considered as asynchronous) of the coupled maps that appears when the complete synchronization regime is broken as the coupling parameter decreases, corresponds to the phase synchronization of flow systems, and should be considered as a synchronous regime. A quantitative measure of the degree of synchronism for the interacting systems with discrete time is proposed. 相似文献
8.
New results for exponential synchronization of linearly coupled ordinary differential systems 下载免费PDF全文
This paper investigates the exponential synchronization of linearly coupled ordinary differential systems. The intrinsic nonlinear dynamics may not satisfy the QUAD condition or weak-QUAD condition. First, it gives a new method to analyze the exponential synchronization of the systems. Second, two theorems and their corollaries are proposed for the local or global exponential synchronization of the coupled systems. Finally, an application to the linearly coupled Hopfield neural networks and several simulations are provided for verifying the effectiveness of the theoretical results. 相似文献
9.
研究了两个耦合格子动力系统的非线性相互作用。当两个耦合格子系统一样时,则导致完全同步化。而当两个耦合格子系统的参数不一样或者这两个系统不相同时,则导致广义同步化。计算了Lyapunov指数谱。 相似文献
10.
A. E. Hramov A. A. Koronovskii Yu. I. Levin 《Journal of Experimental and Theoretical Physics》2005,100(4):784-794
We consider chaotic oscillator synchronization and propose a new approach for detecting the synchronized behavior of chaotic oscillators. This approach is based on analysis of different time scales in the time series generated by coupled chaotic oscillators. We show that complete synchronization, phase synchronization, lag synchronization, and generalized synchronization are particular cases of the synchronized behavior called time-scale synchronization. A quantitative measure of chaotic oscillator synchronous behavior is proposed. This approach is applied to coupled Rössler systems. 相似文献
11.
Zheng Zhi-gang Feng Xiao-qin Ao Bin Michael C. Cross 《Frontiers of Physics in China》2006,1(4):458-467
In this paper, partial synchronization (PaS) in networks of coupled chaotic oscillator systems and synchronization in sparsely
coupled spatiotemporal systems are explored. For the PaS, we reveal that the existence of PaS patterns depends on the symmetry
property of the network topology, while the emergence of the PaS pattern depends crucially on the stability of the corresponding
solution. An analytical criterion in judging the stability of PaS state on a given network are proposed in terms of a comparison
between the Lyapunov exponent spectrum of the PaS manifold and that of the transversal manifold. The competition and selections
of the PaS patterns induced by the presence of multiple topological symmetries of the network are studied in terms of the
criterion. The phase diagram in distinguishing the synchronous and the asynchronous states is given. The criterion in judging
PaS is further applied to the study of synchronization of two sparsely coupled spatiotemporal chaotic systems. Different synchronization
regimes are distinguished. The present study reveals the intrinsic collective bifurcation of coupled dynamical systems prior
to the emergence of global synchronization. 相似文献
12.
We present a generalized analytical solution to the normalized state equations of a class of coupled simple secondorder non-autonomous circuit systems. The analytical solutions thus obtained are used to study the synchronization dynamics of two different types of circuit systems, differing only by their constituting nonlinear element. The synchronization dynamics of the coupled systems is studied through two-parameter bifurcation diagrams, phase portraits, and time-series plots obtained from the explicit analytical solutions. Experimental figures are presented to substantiate the analytical results. The generalization of the analytical solution for other types of coupled simple chaotic systems is discussed. The synchronization dynamics of the coupled chaotic systems studied through two-parameter bifurcation diagrams obtained from the explicit analytical solutions is reported for the first time. 相似文献
13.
Transition to complete synchronization via near-synchronization in two coupled chaotic neurons 下载免费PDF全文
The synchronization transition in two coupled chaotic Morris-Lecar (ML) neurons with gap junction is studied with the coupling strength increasing. The conditional Lyapunov exponents, along with the synchronization errors are calculated to diagnose synchronization of two coupled chaotic ML neurons. As a result, it is shown that the increase in the coupling strength leads to incoherence, then induces a transition process consisting of three different synchronization states in succession, namely, burst synchronization, near-synchronization and embedded burst synchronization, and achieves complete synchronization of two coupled neurons finally. These sequential transitions to synchronization reveal a new transition route from incoherence to complete synchronization in coupled systems with multi-time scales. 相似文献
14.
Trubetskov D. I. Koronovsky A. A. Khramov A. E. 《Radiophysics and Quantum Electronics》2004,47(5-6):305-331
We present the results of studying the phenomenon of synchronization in distributed electron–wave self-oscillatory systems with a counterpropagating wave. General laws governing the appearance of the classical synchronization in distributed systems are revealed. We propose methods for increasing the synchronization bandwidth by using the distributed input of a signal to the interaction space by means of coupled waveguide structures. Transient processes in nonautonomous self-oscillation regimes are studied. In particular, the effect of ultrafast synchronization is found. The possibility of chaotic synchronization in a gyro-oscillator with a counterpropagating wave under the action of a deterministic chaotic signal is shown. Mutual oscillation regimes in a system of two distributed oscillators with coupled waveguide systems are studied. 相似文献
15.
A. A. Koronovskiĭ P. V. Popov A. E. Hramov 《Journal of Experimental and Theoretical Physics》2006,103(4):654-665
Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling between the systems are analyzed. The largest spatial Lyapunov exponent is proposed as a new characteristic of the state of a distributed system, and its calculation is described for a distributed oscillatory system. Partial generalized synchronization is introduced as a new type of chaotic synchronization in spatially nonuniform distributed systems. The physical mechanisms responsible for the onset of generalized chaotic synchronization in spatially distributed oscillatory systems are elucidated. It is shown that the onset of generalized chaotic synchronization is described by a modified Ginzburg-Landau equation with additional dissipation irrespective of the type of coupling. The effect of noise on the onset of a generalized synchronization regime in coupled distributed systems is analyzed. 相似文献
16.
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. 相似文献
17.
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the identification of phase synchronization in coupled nonidentical piecewise linear and in coupled Mackey-Glass time-delay systems with highly non-phase-coherent regimes. We show that there is a transition from nonsynchronized behavior to phase and then to generalized synchronization as a function of coupling strength. We have introduced a transformation to capture the phase of the non-phase-coherent attractors, which works equally well for both the time-delay systems. The instantaneous phases of the above coupled systems calculated from the transformed attractors satisfy both the phase and mean frequency locking conditions. These transitions are also characterized in terms of recurrence-based indices, namely generalized autocorrelation function P(t), correlation of probability of recurrence, joint probability of recurrence, and similarity of probability of recurrence. We have quantified the different synchronization regimes in terms of these indices. The existence of phase synchronization is also characterized by typical transitions in the Lyapunov exponents of the coupled time-delay systems. 相似文献
18.
19.
The paper investigates synchronization in unidirectionally coupled dynamical systems wherein the influence of drive on response is cumulative: coupling signals are integrated over a time interval τ. A major consequence of integrative coupling is that the onset of the generalized and phase synchronization occurs at higher coupling compared to the instantaneous (τ?=?0) case. The critical coupling strength at which synchronization sets in is found to increase with τ. The systems explored are the chaotic Rössler and limit cycle (the Landau–Stuart model) oscillators. For coupled Rössler oscillators the region of generalized synchrony in the phase space is intercepted by an asynchronous region which corresponds to anomalous generalized synchronization. 相似文献
20.
M. E. Mazurov 《Bulletin of the Russian Academy of Sciences: Physics》2018,82(1):73-77
A general problem of the synchronization and mutual synchronization of relaxational self-oscillating systems is formulated. A direct way of describing the synchronization of relaxational systems on the basis of Kronecker’s inequalities is proposed. The solution to the problem formulated by N. Wiener and A. Rosenbluth of forming a single rhythm in a system of coupled relaxational oscillators is described. Specific transient processes in the synchronization of relaxational systems are considered. Burst synchronization in neural networks and synchronization in distributed relaxational systems are also described. 相似文献