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We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…

We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest…

We report the occurrence of a self-emerging frequency chimera state in spatially extended systems of coupled oscillators, where the coherence and incoherence are defined with respect to the emergent frequency of the oscillations. This is…

We show that it is possible for chaotic systems to display the main features of coherence resonance. In particular, we show that a Chua model, operating in a chaotic regime and in the presence of noise, can exhibit oscillations whose…

We discuss the possibility of simultaneous and sequential synchronisation in vertical and horizontal arrays of unidirectionally coupled discrete systems. This is realized for the specific case of two dimensional Gumowski-Mira maps. The…

A model for synchronization of globally coupled phase oscillators including ``inertial'' effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsynchronized)…

Auxiliary system approach and various nearest neighbor methods are widely used to detect generalized synchronization in non-identical coupled systems. These methods generally give contradictory results. Therefore one method alone is not…

In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here…

Two remote agents with synchronized clocks may use them to act in concert and communicate. This necessitates some means of creating and maintaining synchrony. One method, not requiring any direct interaction between the agents, is to expose…

We study the emergence of synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and a time delay is…

A solvable model of noise effects on globally coupled limit cycle oscillators is proposed. The oscillators are under the influence of independent and additive white Gaussian noise. The averaged motion equation of the system with infinitely…

Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…

We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the…

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.…

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic…

Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a non-chaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped…

We numerically investigate the dynamics of a closed chain of unidirectionally coupled oscillators in a regime of homoclinic chaos. The emerging synchronization regimes show analogies with the experimental behavior of a single chaotic laser…

The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely…

This paper deals with two types of synchronous behavior of chaotic oscillators -- generalized synchronization and noise--induced synchronization. It has been shown that both these types of synchronization are caused by similar mechanisms…

Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled…