Clustering and Synchronization in an Array of Repulsively Coupled Phase Oscillators

Clustering and synchronization in an array of repulsively coupled phase oscillators are numerically investigated. It is found that oscillators are divided into several clusters according to the symmetry in the structure.Synchronization occurs between oscillators in each cluster, while those oscillators belonging to different clusters remain asynchronous. Such synchronization may collapse for all clusters when the dynamics of only one oscillator is altered properly. The synchronous state may return back after a short period of transient process. This is determined by the strength of the oscillator altered. Its application in the communication of one-to-several is suggested.     

Alternate Phase Synchronization in Coupled Chaotic Oscillators

Phase locking dynamics in coupled chaotic oscillators is investigated.For chaotic systems with a poorly coherent phase variable,the imperfect phase locking can be observed befor the onset of a complete phase synchronization.The temporal alternations among n:n phase lockings are found,which originate from an overlap of m:n Arnold tongues.     

Phase Synchronization of Coupled Rossler Oscillators: Amplitude Effect

Phase synchronization of two linearly coupled Rossler oscillators with parameter misfits is explored.It is found that depending on parameter mismatches,the synchronization of phases exhibits different manners.The synchronization regime can be divided into three regimes.For small mismatches,the amplitude-insensitive regime gives the phase-dominant synchronization; When the parameter misfit increases,the amplitudes and phases of oscillators are correlated,and the amplitudes will dominate the synchronous dynamics for very large mismatches.The lag time among phases exhibits a power law when phase synchronization is achieved.     

Synchronization of Phase Oscillators in Networks with Certain Frequency Sequence

Synchronization of Kuramoto phase oscillators arranged in real complex neural networks is investigated. It is shown that the synchronization greatly depends on the sets of natural frequencies of the involved oscillators. The influence of network connectivity heterogeneity on synchronization depends particularly on the correlation between natural frequencies and node degrees. This finding implies a potential application that inhibiting the effects caused by the changes of network structure can be bManced out nicely by choosing the correlation parameter appropriately.     

Synchronization of Spatiotemporal Chaos in Coupled Complex Ginzburg-Landau Oscillators

Synchronization of spatiotemporal distributed system is investigated by considering the model of 1D dif-fusively coupled complex Ginzburg-Landau oscillators. An itinerant approach is suggested to randomly move turbulentsignal injections in the space of spatiotemporal chaos. Our numerical simulations show that perfect turbulence synchro-nization can be achieved with properly selected itinerant time and coupling intensity.     

Transition to Amplitude Death in Coupled System with Small Number of Nonlinear Oscillators

In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.     

Dynamics of a Ring of Diffusively Coupled Lorenz Oscillators

We study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a stable fixed state in arbitrarily large rings for a fixed coupling strength. This suggests that coherent behavior in networks of diffusively coupled systems may appear at a coupling strength that is independent of the size of the network.     

Synchronization Regimes in an Ensemble of Phase Oscillators Coupled Through a Diffusion Field

Radiophysics and Quantum Electronics - We consider an ensemble of identical phase oscillators coupled through a common diffusion field. Using the Ott–Antonsen reduction, we develop dynamical...     

Discrete Breathers in Lattices of Coupled Oscillators

Discrete breathers are generic solutions for the dynamics of nonlinearly coupled oscillators. We show that discrete breathers can be observed in low-dimensional and high-dimensional lattices by exploring the sinusoidally coupled pendulum. Loss of stability of the breather solution is studied. We also find the existence of discrete breather in lattices with parameter mismatches. Breather phase synchronization is exhibited for the coupled chaotic oscillators.     

Long-Time Behavior of Weakly Coupled Oscillators

We consider small perturbations of a simple completely integrable system with many degrees of freedom: a collection of independent one-degree-of-freedom oscillators (in the perturbed system the individual oscillators are no longer independent). We show that the long-time behavior of such a system, even in the case of purely deterministic perturbations, should, in general, be described as a stochastic process. The limiting stochastic process is a Markov process on an open book space corresponding to the collection of first integrals of the non-perturbed system.     

Synchronization of Chaotic Intensities and Phases in an Array of N Lasers

A linear array of N mutually coupled single-mode lasers is investigated. It is shown that the intensities of N lasers are chaotically synchronized when the coupling between lasers is relatively strong. The chaotic synchronization of intensities depends on the location of the lasers in the array. The chaotic synchronization appears between two outmost lasers, the second two outmost lasers, etc. There is no synchronization between nearest neighbors of the lasers. If the number of N is odd, the middle laser is never synchronized between any lasers. The chaotic synchronization of phases between nearest lasers in the array is examined by using the analytic signal and the Gaussian filter methods based on the peak of the power spectrum of the intensity. It can be seen that the message of chaotic intensity synchronization is conveyed through the phase synchronization.     

Synchronization of oscillators in complex networks

Theory of identical or complete synchronization of identical oscillators in arbitrary networks is introduced. In addition, several graph theory concepts and results that augment the synchronization theory and a tie in closely to random, semirandom, and regular networks are introduced. Combined theories are used to explore and compare three types of semirandom networks for their efficacy in synchronizing oscillators. It is shown that the simplest k-cycle augmented by a few random edges or links are the most efficient network that will guarantee good synchronization.      

Phase Properties of Photon-Added Coherent States for Nonharmonic Oscillators in a Nonlinear Kerr Medium

The potential of nonharmonic systems has several applications in the field of quantum physics. The photonadded coherent states for annharmonic oscillators in a nonlinear Kerr medium can be used to describe some quantum systems. In this paper, the phase properties of these states including number-phase Wigner distribution function,Pegg-Barnett phase distribution function, number-phase squeezing and number-phase entropic uncertainty relations are investigated. It is found that these states can be considered as the nonclassical states.     

Path Integral for a Pair of Time-Dependent Coupled and Driven Oscillators

The propagator for a certain class of two time-dependent coupled and driven harmonic oscillators with time-varying angular frequencies and masses is evaluated by path integration. This is simply done through suitably chosen generalized canonical transformations and without presupposing the knownledge of any auxiliary equation. The time-dependent oscillators system with exponentially growing masses and coupling coefficient in time may be considered as a particular case.     

Phase Dynamics in Nonlinear Coupled Oscillators

We discuss the phase dynamics in the system of a set of nonlinear coupled oscillators. We find a direct and simple geometric method to observe the geometric phase for this system, and it provides a possibility for the experimental measurements.     

Synchronization in Coupled Oscillators with Two Coexisting Attractors

Dynamics in coupled Dufling oscillators with two coexisting symmetrical attractors is investigated. For a pair of Dufl~ng oscillators coupled linearly, the transition to the synchronization generally consists of two steps： Firstly, the two oscillators have to jump onto a same attractor, then they reach synchronization similarly to coupled monostable oscillators. The transition scenarios to the synchronization observed are strongly dependent on initial conditions.     

Spin Number Coherent States and the Problem of Two Coupled Oscillators

From the definition of the standard Perelomov coherent states we introduce the Perelomov number coherent states for any su(2) Lie algebra. With the displacement operator we apply a similarity transformation to the su(2) generators and construct a new set of operators which also close the su(2) Lie algebra, being the Perelomov number coherent states the new basis for its unitary irreducible representation. We apply our results to obtain the energy spectrum, the eigenstates and the partition function of two coupled oscillators. We show that the eigenstates of two coupled oscillators are the SU(2) Perelomov number coherent states of the two-dimensional harmonic oscillator with an appropriate choice of the coherent state parameters.     

Finite Lifetime Eigenfunctions of Coupled Systems of Harmonic Oscillators

We consider a vector-valued Hermite-type basis for which the eigenvalue problem associated to the operator H _A,B :=B(; _x ² )+Ax ² acting on becomes a three-terms recurrence. Here A and B are 2 × 2 constant positive definite matrices. Our main result provides an explicit characterization of the eigenvectors of H _A,B that lie in the span of the first four elements of this basis when AB BA.This revised version was published online in March 2005 with corrections to the cover date.     

Synchronization in complex clustered networks

Synchronization in complex networks has been an active area of research in recent years. While much effort has been devoted to networks with the small-world and scale-free topology, structurally they are often assumed to have a single, densely connected component. Recently it has also become apparent that many networks in social, biological, and technological systems are clustered, as characterized by a number (or a hierarchy) of sparsely linked clusters, each with dense and complex internal connections. Synchronization is fundamental to the dynamics and functions of complex clustered networks, but this problem has just begun to be addressed. This paper reviews some progress in this direction by focusing on the interplay between the clustered topology and network synchronizability. In particular, there are two parameters characterizing a clustered network: the intra-cluster and the inter-cluster link density. Our goal is to clarify the roles of these parameters in shaping network synchronizability. By using theoretical analysis and direct numerical simulations of oscillator networks, it is demonstrated that clustered networks with random inter-cluster links are more synchronizable, and synchronization can be optimized when inter-cluster and intra-cluster links match. The latter result has one counterintuitive implication: more links, if placed improperly, can actually lead to destruction of synchronization, even though such links tend to decrease the average network distance. It is hoped that this review will help attract attention to the fundamental problem of clustered structures/synchronization in network science.      

Analysis on Patterns of Globally Coupled Phase Oscillators with Attractive and Repulsive Interactions

The Hong-Strogatz (HS) model of globally coupled phase oscillators with attractive and repulsive interactions reflects the fact that each individual (oscillator) has its own attitude (attractive or repulsive) to the same environment (mean field). Previous studies on HS model focused mainly on the stable states on Ott-Antonsen (OA) manifold. In this paper, the eigenvalues of the Jacobi matrix of each fixed point in HS model are explicitly derived, with the aim to understand the local dynamics around each fixed point. Phase transitions are described according to relative population and coupling strength. Besides, the dynamics off OA manifold is studied.