Synchronization of fluctuating delay-coupled chaotic networks

Abstract

We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. Focusing on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone, we compare the synchronization properties of static and fluctuating networks in the regime of large delays. We find that random network switching may enhance the stability of synchronized states. Synchronization appears to be maximally stable when fluctuations are much faster than the time-delay, whereas it disappears for very slow fluctuations. For fluctuation time scales of the order of the time-delay, we report a resynchronizing effect in finite-size networks. Moreover, we observe characteristic oscillations in all regimes, with a periodicity related to the time-delay, as the system approaches or drifts away from the synchronized state.

Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology

“…We have developed an analytical formalism within the linearized limit in order to understand synchronization phenomena in the case of delay-coupled networks with a fluctuating topology, studied previously by us in [37].…”

“…We illustrate our results for linear, time-continuous systems in a network of chaotic maps. Similar as in previous work [37], we consider a time-varying network of N delay-coupled Bernouilli maps with a discrete time evolution modelled by…”

“…In a previous publication [37] we numerically studied synchronization properties of delay-coupled networks with a time-varying topology. We considered an interaction network of coupled chaotic maps with a single coupling delay τ , with a topology fluctuating among an ensemble of small-world networks, with a characteristic time-scale T n .…”

“…Here, in order to understand the physics behind the results obtained in [37], we develop an analytical theory in the linearized limit, based on the Master Stability Function. We express the "effective" connectivity as a function of the three time scales: the internal time scale T in , the characteristic time for network fluctuations T n and the interaction delay time τ .…”

Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

“…These works include study of synchronization/antisynchronization for permanent magnet synchronous motors connected in ring topology [11], function projective type synchronization for complex dynamical networks [12], investigation of complete synchronization and antiphase synchronization together [13], hybrid synchronization of networks having heterogeneous systems [14], study of synchronization for fractional-order systems [15], investigation of synchronization for systems with hyperchaotic nature [16,17], and study of synchronization for complex networks [18,19]. Study of hybrid synchronization involves multiple chaotic systems like complete, adaptive, global, projective, and antisynchronization systems [17,[20][21][22][23][24][25][26][27], and synchronization systems in multiple coupled complex networks [28,29]. Currently, hybrid synchronization of several connected chaotic systems is a hot topic of research and the work includes investigation of complex network synchronization for perturbations and delays [30] and a study of neural networks for synchronization [31].…”