Generalized chaotic synchronization in coupled Ginzburg-Landau equations

Abstract

-Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling between the systems are analyzed. The largest spatial Lyapunov exponent is proposed as a new characteristic of the state of a distributed system, and its calculation is described for a distributed oscillatory system. Partial generalized synchronization is introduced as a new type of chaotic synchronization in spatially nonuniform distributed systems. The physical mechanisms responsible for the onset of generalized chaotic synchronization in spatially distributed oscillatory systems are elucidated. It is shown that the onset of generalized chaotic synchronization is described by a modified Ginzburg-Landau equation with additional dissipation irrespective of the type of coupling. The effect of noise on the onset of a generalized synchronization regime in coupled distributed systems is analyzed.

Lyapunov stability of charge transport in miniband semiconductor superlattices

“…The above factors require a development of specific approaches to stability analysis of various spatially extended systems. 16,[19][20][21][22] In this paper, we propose an approach for the calculation of the spectrum of Lyapunov exponents for a system of coupled Poisson and continuity equations, and apply this method to a strongly coupled semiconductor superlattice (SL) operating in the miniband transport regime. 23,24 We should note that for weakly coupled SLs, in which the resonant tunneling transport mechanism dominates, the charge dynamics can be described by a spatially discrete version of the Poisson and continuity equations.…”

Generalized synchronization of chaos for secure communication: Remarkable stability to noise

“…the GS regime appears in unidirectionally coupled dynamical systems in the absence and presence of noise for the same values of the coupling parameter strength [43]. As a consequence, noise may be used to provide the additional masking of the information signal.…”

Generalized spatiotemporal chaos synchronization of the Ginzburg—Landau equation

“…In Ref. [13], the generalized chaos synchronizations of the Ginzburg-Landau equation for different kinds of unidirectionally coupled drive-response systems are analysed numerically. The Ginzberg-Landau equation can be used to study spatiotemporal chaos and pattern formation in various distribution media.…”