Isochronal chaos synchronization of delay-coupled optoelectronic oscillators

Abstract

We study experimentally chaos synchronization of nonlinear optoelectronic oscillators with time-delayed mutual coupling and self-feedback. Coupling three oscillators in a chain, we find that the outer two oscillators always synchronize. In contrast, isochronal synchronization of the mediating middle oscillator is found only when self-feedback is added to the middle oscillator. We show how the stability of the isochronal solution of any network, including the case of three coupled oscillators, can be determined by measuring the synchronization threshold of two unidirectionally coupled systems. In addition, we provide a sufficient condition that guarantees global asymptotic stability of the synchronized solution.

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

“…Interestingly, this phenomenon could explain the occurrence of identical synchronization between widely separated cortical regions of the human brain despite of synaptic/dendritic delays [2][3][4][5]. ZLS has also been experimentally demonstrated in delay coupled semiconductor lasers [6], optoelectronic oscillators [7] and in low-dimensional delay coupled chaotic electronic circuits (without intrinsic time-delay) [8] via dynamical relaying. Recently Banerjee et al reported that the coupling threshold for ZLS between the outermost identical oscillators decreases when an impurity (parameter mismatch) is introduced in the relay unit [9].…”

Chaos synchronization in networks of delay-coupled lasers: role of the coupling phases

“…Recently, this structure of the MSF was confirmed experimentally [33] and even utilized to predict the synchronizability of a network from a simpler motif [33,34].…”

Controlling Synchronization Patterns in Complex Networks

“…Besides zero-lag synchronization, a state where all nodes undergo the same dynamics without a phase shift, group and cluster synchronization have received growing interest both in theory [Sorrentino and Ott, 2007;Kestler et al, 2007Kestler et al, , 2008Dahms et al, 2012;Kanter et al, 2011b,a;Golubitsky and Stewart, 2002;Lücken and Yanchuk, 2012;Sorrentino, 2014;Pecora et al, 2014;Poel et al, 2015] and in experiments [Illing et al, 2011;Aviad et al, 2012;Blaha et al, 2013;Williams et al, 2012Williams et al, , 2013aRosin, 2015]. In the case of group synchrony, the network consists of several groups where the nodes within one group are in zero-lag synchrony Dahms et al, 2012].…”

“…Recently, more complex synchronization patterns, including cluster and group synchronization, have received growing interest both in theory [Sorrentino and Ott, 2007;Kestler et al, 2007;Ashwin et al, 2007;Kestler et al, 2008;Kori and Kuramoto, 2001;Lücken and Yanchuk, 2012;Dahms et al, 2012;Kanter et al, 2011b,a;Golubitsky and Stewart, 2002;Sorrentino, 2014;Pecora et al, 2014;Poel et al, 2015] and in experiments [Illing et al, 2011;Aviad et al, 2012;Blaha et al, 2013;Rosin et al, 2013;Williams et al, 2012Williams et al, , 2013aRosin, 2015]. These scenarios appear in many biological systems, examples include dynamics of nephrons [Mosekilde et al, 2002], central pattern generation in animal locomotion [Ijspeert, 2008], or population dynamics [Blasius et al, 1999].…”

“…) was used which is, for example, applicable to lasers [Lang and Kobayashi, 1980] or optoelectronic oscillators [Illing et al, 2011]. Since the focus of this thesis are neural systems, we here use diffusive-like coupling term of the form…”