Synchronization of groups of coupled oscillators with sparse connections

Synchronization of groups of coupled oscillators with sparse connections are explored. It is found that different topologies of intergroup couplings may lead to different synchronizability. In the strong-coupling limit, an analytical treatment and criterion is proposed to judge the synchronization between communities of oscillators, and an optimal connection scheme for the group synchronization is given. By varying the intergroup and intragroup coupling strengths, different synchronous phases, i.e., the unsynchronized state, intragroup synchronization, intergroup synchronization, and global synchronization are revealed. The present discussions and results can be applied to study the pattern formation and synchronization of coupled spatiotemporal systems

Emergence of synchronization induced by the interplay between two prisoner's dilemma games with volunteering in small-world networks

We studied synchronization between prisoner's dilemma games with voluntary participation in two Newman-Watts small-world networks. It was found that there are three kinds of synchronization: partial phase synchronization, total phase synchronization and complete synchronization, for varied coupling factors. Besides, two games can reach complete synchronization for the large enough coupling factor. We also discussed the effect of coupling factor on the amplitude of oscillation of $cooperator$ density.Comment: 6 pages, 4 figure

Neuronal synchrony: peculiarity and generality

Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their “dynamical repertoire” includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale

Parameter mismatches,variable delay times and synchronization in time-delayed systems

We investigate synchronization between two unidirectionally linearly coupled chaotic non-identical time-delayed systems and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent of the relation between the delay time in the coupled systems and the coupling delay time, only retarded synchronization with the coupling delay time is obtained. We show that with parameter mismatch or without it neither complete nor anticipating synchronization occurs. We derive existence and stability conditions for the retarded synchronization manifold. We demonstrate our approach using examples of the Ikeda and Mackey-Glass models. Also for the first time we investigate chaos synchronization in time-delayed systems with variable delay time and find both existence and sufficient stability conditions for the retarded synchronization manifold with the coupling delay lag time. Also for the first time we consider synchronization between two unidirectionally coupled chaotic multi-feedback Ikeda systems and derive existence and stability conditions for the different anticipating, lag, and complete synchronization regimes.Comment: 12 page

Feedback-dependent control of stochastic synchronization in coupled neural systems

We investigate the synchronization dynamics of two coupled noise-driven FitzHugh-Nagumo systems, representing two neural populations. For certain choices of the noise intensities and coupling strength, we find cooperative stochastic dynamics such as frequency synchronization and phase synchronization, where the degree of synchronization can be quantified by the ratio of the interspike interval of the two excitable neural populations and the phase synchronization index, respectively. The stochastic synchronization can be either enhanced or suppressed by local time-delayed feedback control, depending upon the delay time and the coupling strength. The control depends crucially upon the coupling scheme of the control force, i.e., whether the control force is generated from the activator or inhibitor signal, and applied to either component. For inhibitor self-coupling, synchronization is most strongly enhanced, whereas for activator self-coupling there exist distinct values of the delay time where the synchronization is strongly suppressed even in the strong synchronization regime. For cross-coupling strongly modulated behavior is found

Self-synchronization and controlled synchronization

An attempt is made to give a general formalism for synchronization in dynamical systems encompassing most of the known definitions and applications. The proposed set-up describes synchronization of interconnected systems with respect to a set of functionals and captures peculiarities of both self-synchronization and controlled synchronization. Various illustrative examples are give