337,507 research outputs found
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 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
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
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
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
Synchronization of Random Linear Maps
We study synchronization of random one-dimensional linear maps for which the
Lyapunov exponent can be calculated exactly. Certain aspects of the dynamics of
these maps are explained using their relation with a random walk. We confirm
that the Lyapunov exponent changes sign at the complete synchronization
transition. We also consider partial synchronization of nonidentical systems.
It turns out that the way partial synchronization manifests depends on the type
of differences (in Lyapunov exponent or in contraction points) between the
systems. The crossover from partial synchronization to complete synchronization
is also examined.Comment: 5 pages, 6 figure
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