Related papers: Synchronization on the accuracy of chaotic oscilla…
We study general random dynamical systems of continuous maps on some compact metric space. Assuming a local contraction condition and uniqueness of the stationary measure, we establish probabilistic limit laws such as the central limit…
In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random…
We report enhancing of complete synchronization in identical chaotic oscillators when their interaction is mediated by a mismatched oscillator. The identical oscillators now interact indirectly through the intermediate relay oscillator. The…
From the flashes of fireflies to Josephson junctions and power infrastructure, networks of coupled phase oscillators provide a powerful framework to describe synchronization phenomena in many natural and engineered systems. Most real-world…
We study a large population of globally coupled phase oscillators subject to common white Gaussian noise and find analytically that the critical coupling strength between oscillators for synchronization transition decreases with an increase…
We consider a line of three mutually coupled lasers with time delays and study chaotic synchronization of the outer lasers. Two different systems are presented: optoelectronically coupled semiconductor lasers and optically coupled fiber…
A method for the quantitative analysis of the degree and parameters of synchronization of the chaotic oscillations in two coupled oscillators is proposed, which makes it possible to reveal a change in the structure of attractors. The…
We study the effect of memory on synchronization of identical chaotic systems driven by common external noises. Our examples show that while in general synchronization transition becomes more difficult to meet when memory range increases,…
By coupling counter--rotating coupled nonlinear oscillators, we observe a ``mixed'' synchronization between the different dynamical variables of the same system. The phenomenon of amplitude death is also observed. Results for coupled…
Synchronization of coupled continuous-time linear systems is studied in a general setting. For identical neutrally-stable linear systems that are detectable from their outputs, it is shown that a linear output feedback law exists under…
This paper is devoted to the problem of synchronization between fractional-order chaotic systems with Gaussian fluctuation by the method of fractional-order sliding mode control. A fractional integral (FI) sliding surface is proposed for…
We experimentally study the synchronization of two chaotic electronic circuits whose dynamics is relayed by a third parameter-matched circuit, to which they are coupled bidirectionally in a linear chain configuration. In a wide range of…
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. As a result, the numerically…
A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical…
The goal of this survey paper is to provide an introduction to chaos synchronization using nonlinear observers and its applications in cryptography. I start with an overview of cryptography. Then, I recall the basics of chaos theory and how…
Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative…
We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to…
Mechanisms of emergence and destruction are analyzed, as well as characteristics of synchronous and asynchronous modes of behavior of ensembles (swarms) of interacting mobile agents moving according to chaotic phase trajectories of Rossler…
In this paper, we report the enhanced stability of induced synchronization by transient uncoupling observed in certain unidirectionally coupled second-order chaotic systems. The stability of synchronization observed in the coupled systems…
Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical…