Synchronization of oscillators with random nonlocal connectivity

Abstract

In this paper we study the existing observation in literature about synchronization of a large number of coupled maps with random nonlocal connectivity ͓Chate and Manneville, Chaos 2, 307 ͑1992͔͒. These connectivities which lack any spatial significance can be realized in neural nets and electrical circuits. It is quite interesting and of practical importance to note that a huge number of maps can be synchronized with this connectivity. We show that this synchronization stems from the fact that the connectivity matrix has a finite gap in the eigenvalue spectrum in the macroscopic limit. We give a quantitative explanation for the gap. We compare the analytic results with the ones quoted in the above reference. We also study the departures from this highly collective behavior in the low connectivity limit and show that the behavior is almost statistical for very low connectivity.

Oscillations and synchrony in a cortical neural network

“…Most of the existing work on synchronization of coupled networks assumes that the coupling configuration is completely regular (Heagy et al 1994;Wu and Chua 1995), while a few studies address the issue of synchronization in randomly coupled networks (Gade 1996;Manrubia and Mikhailov 1999). However, many biological, technological and social networks are neither completely regular nor completely random.…”

Delays, Connection Topology, and Synchronization of Coupled Chaotic Maps

“…Usually, such systems have been investigated under the assumption of a certain regularity in the connection topology, where units are coupled to their nearest neighbors or to all other units. Lately, more general networks with random, small-world, scale-free, and hierarchical architectures have been emphasized as appropriate models of interaction [3,4,5,6,7]. On the other hand, realistic modeling of many large networks with non-local interaction inevitably requires connection delays to be taken into account, since they naturally arise as a consequence of finite information transmission and processing speeds among the units.…”

Synchronization of coupled chaotic dynamics on networks

“…The stability of globally coupled maps is well studied in the literature [31][32][33]. An ideal example to consider the stability of the driven synchronized state is a complete bipartite network.…”