Frequency—Locking in Coupled Chaotic Systems

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.     

Transitions to Long-Resident States in Coupled Chaotic Oscillators

The behaviour of coupled chaotic oscillators before complete synchronization is investigated. Long-time residence of trajectories appears besides one of the saddle foci. The tendency that orbits of the two oscillators get closer becomes faster with the increasing coupling strength. The diffusion of phase difference between the two oscillators is first enhanced and then suppressed. There are exact correspondences among these phenomena. The mechanism of these correspondences is explored. These phenomena uncover the route to synchronization of coupled chaotic oscillators.     

Suppression of Chaos and Phase Locking in Two Coupled Nonidentical Neurons under Periodic Input

Dynamical behaviour of two coupled neurons with at least one of them being chaotic is presented. Bifurcation diagrams and Lyapunov exponents are calculated to diagnose the dynamical behaviour of the coupled neurons with the increasing coupling strength. It is found that when the coupling strength increases, a chaotic neuron can be controlled by the coupling between neurons. At the same time, phase locking is studied by the maxima of the differences of instantaneous phases and average frequencies between two coupled neurons, and the inherent connection of phase locking and the suppression of chaos is formulated. It is observed that the onset of phase locking is closely related to the suppression of chaos. Finally, a way for suppression of chaos in two coupled nonidentical neurons under periodic input is suggested.     

Phase—Locking Dynamics in Coupled Circle—Map Lattices

The phase-locking dynamics in 1D and 2D lattices of non-identical coupled circle maps is explored.A global phase locking can be attained via a cascade of clustering processes with the increase of the coupling strength.Collective spatiotemporal dynamics is observed when a global phase locking is reached.Crisis-induced desynchronization is found,and its consequent spatiotemporal chaos is studied.     

Synchronization of Coupled Oscillators on Newman-Watts Small-World Networks

We investigate the collection behaviour of coupled phase oscillators on Newman-Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with the others following the Kuramoto model We then study the onset of global synchronization of phases and frequencies based on dynamic simulations and finite-size scaling. Both the phase and frequency synchronization are observed to emerge in the presence of a tiny fraction of shortcuts and enhanced with the increases of nearest neighbours and lattice dimensions.     

Phase Desynchronization as a Mechanism for Transitions to High—Dimensional Chaos

Phase is an important degree of freedom in studies of chaotic oscillations.Phase coherence and localization in coupled chaotic elements are studied.It is shown that phase desynchronization is a key mechanism responsible for the transitions from low-to high-dimensional chaos.The route from low-dimensional chaos to high-dimensional toroidal chaos is accompanied by a cascade of phase desynchronizations.Phase synchronization tree is adopted to exhibit the entrainment process.This bifurcation tree implies an intrinsic cascade of order embedded in irregular motions.     

Dynamics of Coupled Quantum-Classical Oscillators

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.     

Information Transmission in Phase Synchronous Chaotic Arrays

We show many versatile phase synchronous configurations that emerge in an array of coupled chaotic elements due to the presence of a periodic stimulus. Then, we explain the relevance of these configurations to the understanding of how information about such a stimulus is transmitted from one side to the other in this array. The stimulus actively creates the ways to be transmitted, by making the chaotic elements to phase synchronize.     

Phase Synchronization in Small World Chaotic Neural Networks

To understand collective motion of real neural networks very well, we investigate collective phase synchronization of small world chaotic Hindmarsh-Rose (HR) neural networks. By numerical simulations, we conclude that small world chaotic HR neural networks can achieve collective phase synchronization. Furthermore, it is shown that phase synchronization of small world chaotic HR neural networks is dependent on the coupling strength,the connection topology (which is determined by the probability ]3), as well as the coupling number. These phenomena are important to guide us to understand the synchronization of real neural networks.     

Phase Locking Phenomena and Electroencephalogram-Like Activities in Dynamic Neuronal Systems

We study signal detection and transduction of dynamic neuronal systems under the influence of external noise,white and coloured. Based on simulations, we show explicitly phase locking phenomena between the output and the input of a single neuron and Electroencephalogram-like activities on neural networks with small-world connectivity. The numerical results prove that the dynamic neuronal system can be adjusted to an optimal sensitive state for signal processing in the presence of additive noise.     

Impulsive Synchronization of Discrete Chaotic Systems

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 theroem,we derives some sufficient conditions for the synchronization of two chaotic Lozi maps via impulsive control.The effectivness of this approach has been demonstrated with chaotic Lozi map.     

Nuclear Chaotic Behavior in a Two—j Shell Coupled with a Rotor Model

The chaotic properties for six particles interacting by a monopole pairing force in a two-j shell model coupled with a deformed core are studied in the frame of particle-rotor model.The nearest-neighbor distribution of energy levels and spectral rigidity in the two-j shell are compared with those in the single-j case.The results show that the system is more regular in the two-j model than that in the single-j case.     

Parametrically Driven Nonlinear Oscillators with an Impurity

By virtue of the method of multiple scales,we study a chain of parametrically driven nonlinear oscillators with a mass impurity.An equation is presented to describe the nonlinear wave of small amplitude in the chain.In our derivation,the equation is applicable to any eigenmode of coupled pendulum.Our result shows that a nonpropagation soliton emerges as the lowest or highest eigenmode of coupled pendulum is excited,and the impurity tends to pin the nonpropagation soliton excitation.     

An Approach to Analyse Phase Synchronization in Oscillator Networks with Weak Coupling

We study phase synchronization in oscillator networks through phase reduced method. The dynamics of networks is reduced to phase equations by this method. Analysing the phase equations through the master stability function method, one obtains that the oscillators with identical frequency can be in-phase synchronized by weak balanced coupling. Similarly, the problem of frequency synchronization of oscillators with different frequencies is transformed to the existence of a locally asymptotically stable equilibrium of the phase error system.     

Time Delay-Enhanced Synchronization and Regularization in Two Coupled Chaotic Neurons

Complete synchronization of two identical chaotic Morris-Lecar (ML) neurons with time-delay coupling is investigated. It is found that the coupled ML neurons may achieve synchronization by an efficient time delay at a low coupling strength. At the same time, the chaotic motion of the coupled neurons may become a regular periodic one during synchronization by the time-delay coupling, that is, the delay time coupling is able to suppress chaos in the process of synchronization. However, the time delay has the effect on enhancement of synchronization and regularization of coupled neurons only in certain coupling strength ranges. Moreover, synchronization of coupled neurons is achieved by time delay after regularization.     

Phase Synchronization as a Mechanism of Controlling Spatiotemporal Chaos via External Periodic Signal

We find that phase synchronization (PS) is a mechanism in which the spatiotemporal chaos (STC) can be suppressed to a spatially regular (SR) state by applying an external periodic signal in a one-dimensional driven drift-wave system.In the driving wave coordinate,the nonlinear system can be transformed to a set of coupled oscillators moving in a periodic potential.In this multi-dimensional system,the internal modes are slaved one by one through PS by the control signal.Two types of responses of the internal modes to the external periodic signal are observed.For some modes,the stabilization is through frequency-locking;while for the other modes,a special kind of PS without frequency-locking,namely multi-looping PS,is developed.     

Phase Space Prediction Model Based on the Chaotic Attractor

A new prediction technique is proposed for chaotic time series.The usefulness of the technique is that it removes some false neighbouring points which are not suitable for the local estimation of the dynamics systems.We use a feedforward neural network to approximate the local dominant Lyapunov exponent,and choose the neighbouring points by the exponent.The model is tested for the convection amplitude of the Lorenz model,and the results indicate that this prediction technique can improve the prediction of chaotic time series.     

Charged Particle Motion in Temporal Chaotic and Spatiotemporal Chaotic Fields

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.     

Periodic and Chaotic Breathers in the Nonlinear Schroedinger Equation

The breathers in the cubic nonlinear Schroedinger equation are investigated numerically by using the symplectic method. We show that the solitonlike wave, the periodic, quasiperiodic and chaotic breathers can be observed with the increase of cubic nonlinear perturbation. Finally, we discuss the breathers in the cubic-quintic nonlinear Schroedinger equation with the increase of quintic nonlinear perturbation.     

Identification of Chaotic Systems with Application to Chaotic Communication

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.