Anticipating, complete and lag synchronizations in RC phase-shift network based coupled Chua’s circuits without delay

Abstract

We construct a new RC phase shift network based Chua's circuit, which exhibits a period-doubling bifurcation route to chaos. Using coupled versions of such a phase-shift network based Chua's oscillators, we describe a new method for achieving complete synchronization (CS), approximate lag synchronization (LS), and approximate anticipating synchronization (AS) without delay or parameter mismatch. Employing the Pecora and Carroll approach, chaos synchronization is achieved in coupled chaotic oscillators, where the drive system variables control the response system. As a result, AS or LS or CS is demonstrated without using a variable delay line both experimentally and numerically.

Anticipating chaotic synchronization via act-and-wait coupling

“…He showed that two identical chaotic systems coupled unidirectionally in a masterslave configuration can synchronize their motion in such a way that the trajectory of a slave system is advanced in time with respect to the trajectory of a T. Pyragienė (B) · K. Pyragas Center for Physical Sciences and Technology, 01108 Vilnius, Lithuania e-mail: pyragiene@pfi.lt master system. Anticipating synchronization has been successfully implemented in diverse systems [2][3][4] and justified experimentally in electronic circuits [5][6][7][8][9][10][11] and chaotic lasers [12]. It has been also observed in excitable systems driven by noise [5,13].…”

The dynamics of the two mutually coupled autonomous Van der Pol Oscillator

“…(3). If there is a coupling between them with a coupling strength ǫ, then one expect x1(t) synchronize x3(t + τ ) in a range of value ǫ, where the delay is τ 6= 0 is the time anticipate which depends on both ǫ and the parameter characterizing the difference between the oscillators [25]. We cannot observe when the two system are identical (same parameter value).…”

“…Van der pol oscillator constitutes the paradigmatic model to study synchronization. Quit recently, it has been discovered that two coupled non identical Van der pol oscillator can exhibit the phenomenon of anticipatory synchronization [22][23][24][25][26] in which the dynamical variable x3(t) anticipate x1(t) specifically given two slightly different oscillator in the Eq. (3).…”

Different types of synchronization in coupled network based chaotic circuits

“…Chua's circuit and its variance are well known chaotic circuits which exhibit a wide variety of nonlinear dynamical phenomena such as bifur-cations and chaos [4,33,34,35,36,37]. Recently, three of the present authors along with others have constructed a new phase shift network based Chua's circuit [38], which exhibits period-doubling bifurcation route to chaotic attractor. In this manuscript, we study the occurrence of different types of chaos synchronization in unidirectionally coupled system of two identical RC phase shift network based Chua's circuits [38].…”