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Networks of nonlinear units with time-delayed couplings can synchronize to a common chaotic trajectory. Although the delay time may be very large, the units can synchronize completely without time shift. For networks of coupled Bernoulli…

Chaotic Dynamics · Physics 2015-03-17 A. Englert , S. Heiligenthal , W. Kinzel , I. Kanter

The conditions for synchronization in unidirectionally coupled chaotic oscillators are revisited. We demonstrate with typical examples that the conditional Lyapunov exponents (CLEs) play an important role in distinguishing between…

Chaotic Dynamics · Physics 2007-05-23 P. Muruganandam , M. Lakshmanan , S. Parthasarathy

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough…

Chaotic Dynamics · Physics 2009-10-31 R. Toral , C. R. Mirasso , E. Hernandez-Garcia , O. Piro

We consider synchronization of chaotic systems coupled indirectly through a common environmnet where the environment has an intrinsic dynmics of its own modulated via feedback from the systems. We find that a rich vareity of synchronization…

Chaotic Dynamics · Physics 2010-05-05 V. Resmi , G. Ambika , R. E. Amritkar

Large deviation inequalities for ergodic sums is an important subject since the seminal contribution of Bernstein for independent random variables with finite variances, followed by the Chernoff method and the Hoefding result for…

Probability · Mathematics 2025-12-12 Miguel Abadi

We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for…

We review some recent work on the synchronization of coupled dynamical systems on a variety of networks. When nodes show synchronized behaviour, two interesting phenomena can be observed. First, there are some nodes of the floating type…

Chaotic Dynamics · Physics 2009-11-11 R. E. Amritkar , Sarika Jalan

An analysis of transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces is presented. The synchronization phenomenon is investigated in the ensemble of particles moving…

chao-dyn · Physics 2015-06-24 B. Kaulakys , F. Ivanauskas , T. Meskauskas

The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter, we demonstrate that the nodes in a second-order Kuramoto model, perform a cascade…

Adaptation and Self-Organizing Systems · Physics 2015-06-15 Peng Ji , Thomas K. DM. Peron , Peter J. Menck , Francisco A. Rodrigues , Jürgen Kurths

It has been known that several objects such as cluster variables, coefficients, seeds, and $Y$-seeds in different cluster patterns with common exchange matrices share the same periodicity under mutations. We call it synchronicity phenomenon…

Rings and Algebras · Mathematics 2024-07-09 Tomoki Nakanishi

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…

Dynamical Systems · Mathematics 2013-06-12 A. Gorban , I. Tyukin , E. Steur , H. Nijmeijer

Globally coupled phase oscillator models, such as the Kuramoto model, exhibit spontaneous collective synchronization. Such models can be restated in terms of interactions within and between subsets of oscillators. An approximation for the…

Adaptation and Self-Organizing Systems · Physics 2015-06-17 David Mertens

A chaotic dynamics is typically characterized by the emergence of strange attractors with their fractal or multifractal structure. On the other hand, chaotic synchronization is a unique emergent self-organization phenomenon in nature.…

We consider complete synchronization of identical maps coupled through a general interaction function and in a general network topology where the edges may be directed and may carry both positive and negative weights. We define mixed…

Chaotic Dynamics · Physics 2009-09-15 Frank Bauer , Fatihcan M. Atay , Juergen Jost

We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting…

Chaotic Dynamics · Physics 2009-10-11 Kazumasa A. Takeuchi , Francesco Ginelli , Hugues Chaté

This paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly…

Systems and Control · Electrical Eng. & Systems 2021-11-05 Zhongchang Liu , Wing Shing Wong , Hui Cheng

We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field…

Statistical Mechanics · Physics 2007-05-23 Deok-Sun Lee

We investigate a transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces. We analyze the synchronization phenomenon in the ensemble of particles moving with friction in…

chao-dyn · Physics 2008-02-03 B. Kaulakys , F. Ivanauskas , T. Meskauskas

This research investigates the intricate domain of synchronization problem among multiple agents operating within a dynamic fast switching network topology. We concentrate on cluster synchronization within coupled linear system under…

Systems and Control · Electrical Eng. & Systems 2024-02-20 Ku Du , Yu Kang

Synchronization of fractional-order chaotic systems is a hot topic in the field of nonlinear study. The co-coupled synchronization between two fractional-order chaotic systems with different initial conditions is investigated in this paper.…

Chaotic Dynamics · Physics 2009-09-15 Kehui Sun , Jian Ren , Shuisheng Qiu