Chaotic synchronization in coupled spatially extended beam–plasma systems

Abstract

The appearance of the chaotic synchronization regimes has been discovered for the coupled spatially extended beam-plasma Pierce systems. The coupling was introduced only on the right bound of each subsystem. It has been shown that with coupling increase the spatially extended beam-plasma systems show the transition from asynchronous behavior to the phase synchronization and then to the complete synchronization regime. For the consideration of the chaotic synchronization we used the concept of time scale synchronization described in work [Chaos, 14, 3 (2004) 603-610] and based on the introduction of the continuous set of phases of chaotic signal. In case of unidirectional coupling the generalized synchronization regime has been observed in the spatially extended beam-plasma systems. The generalized synchronization appearance mechanism has been analyzed by means of the offered modified system approach [Phys. Rev. E, 71, 6 (2005) 067201].

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.…”

Brief Tour of Wavelet Theory

“…However, detailed consideration of synchronization theory (in particular, time-scale synchronization based on the continuous wavelet transform) is beyond the scope of this book. The reader can find a detailed description of different aspects of synchronization theory and its applications in [31,32,40,[51][52][53][54][65][66][67][68][69][70].…”

Generalized synchronization in mutually coupled oscillators and complex networks

“…The bidirectional coupling between considered Pierce diodes is realized by the modification of the boundary conditions on the right boundary of the systems, in the same way as it has been done in [26,27] …”