Related papers: Synchronizing Chaos with Imperfections
This paper deals with the chaotic oscillator synchronization. A new approach to the synchronization of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by…
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…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…
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 present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of…
In networks of nonlinear oscillators, symmetries place hard constraints on the system that can be exploited to predict universal dynamical features and steady-states, providing a rare generic organizing principle for far-from-equilibrium…
Coupling of chaotic oscillators has evidenced conditions where synchronization is possible, therefore a nonlinear system can be driven to a particular state through input from a similar oscillator. Here we expand this concept of control of…
We report erosion of synchronization in networks of coupled phase oscillators, a phenomenon where perfect phase synchronization is unattainable in steady-state, even in the limit of infinite coupling. An analysis reveals that the total…
We study chaotic systems with multiple time delays that range over several orders of magnitude. We show that the spectrum of Lyapunov exponents (LE) in such systems possesses a hierarchical structure, with different parts scaling with the…
Synchrony is inevitable in many oscillating systems -- from the canonical alignment of two ticking grandfather clocks, to the mutual entrainment of beating flagella or spiking neurons. Yet both biological and manmade systems provide…
We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise…
We consider the phenomenon of mutual synchronization in a fundamental quantum system of two detuned quantum harmonic oscillators dissipating into the environment. We identify the conditions leading to this spontaneous phenomenon showing…
Generalized synchronization of chaos is a type of cooperative behavior in directionally-coupled oscillators that is characterized by existence of stable and persistent functional dependence of response trajectories from the chaotic…
The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov…
A particular example of chaos can be conceived in the interaction of non-linear oscillator with a harmonic gravitational wave. When we replace the linear potential forces by the therm SIN(x), the type of solution becomes subject to external…
Synchronization of network-coupled dynamical units is important to a variety of natural and engineered processes including circadian rhythms, cardiac function, neural processing, and power grids. Despite this ubiquity, it remains poorly…
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume…
We study synchronization of $N$ oscillators indirectly coupled through a medium which is inhomogeneous and has its own dynamics. The system is formalized in terms of a multilayer network, where the top layer is made of disconnected…
Chaos is associated with stochasticity, complex, irregular motion, etc. It has some peculiar properties such as ergodicity, highly initial value sensitivity, non-periodicity and long-term unpredictability. These pseudo random features lead…