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Synchronization, that occurs both for non-chaotic and chaotic systems, is a striking phenomenon with many practical implications in natural phenomena. However, even before synchronization, strong correlations occur in the collective…
Synchronization is a fundamental dynamical state of interacting oscillators, observed in natural biological rhythms and in the brain. Global synchronization which occurs when non-linear or chaotic oscillators placed on the nodes of a…
Synchronization of coupled dynamical systems is a widespread phenomenon in both biological and engineered networks, and understanding this behavior is crucial for controlling such systems. Considerable research has been dedicated to…
The chaotic synchronization regime in coupled dynamical systems is considered. It has been shown, that the onset of synchronous regime is based on the appearance of the phase relation between interacting chaotic oscillators frequency…
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
The synchronization of loosely coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical notion of synchronicity. Effectively unpredictable chaotic systems, coupled through…
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…
Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin…
We study how a coupled array of spiking chaotic systems synchronizes to an external driving in a short time. Synchronization means spike separation at adjacent sites much shorter than the average inter-spike interval; a local lack of…
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…
Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…
Coupled oscillators, even identical ones, display a wide range of behaviours, among them synchrony and incoherence. The 2002 discovery of so-called chimera states, states of coexisting synchronized and unsynchronized oscillators, provided a…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
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 detection of phase synchronization of coupled chaotic oscillators which are not phase-coherent is known to be a challenging task. In this work a method to detect and measure phase synchronization is presented. The procedure uses symbol…
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…
We examine synchronization between identical chaotic systems. A rigorous criteria is presented which, if satisfied, guarantees that the coupling produces linearly stable synchronous motion. The criteria can also be used to design couplings…
The condensation transition, leading to complete mutual synchronization in large populations of globally coupled chaotic Roessler oscillators, is investigated. Statistical properties of this transition and the cluster structure of partially…
The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. We know that the harmonic oscillator is integrable in…