Modular networks with delayed coupling: Synchronization and frequency control

Abstract

We study the collective dynamics of modular networks consisting of map-based neurons which generate irregular spike sequences. Three types of intramodule topology are considered: a random Erdös-Rényi network, a small-world Watts-Strogatz network, and a scale-free Barabási-Albert network. The interaction between the neurons of different modules is organized by relatively sparse connections with time delay. For all the types of the network topology considered, we found that with increasing delay two regimes of module synchronization alternate with each other: inphase and antiphase. At the same time, the average rate of collective oscillations decreases within each of the time-delay intervals corresponding to a particular synchronization regime. A dual role of the time delay is thus established: controlling a synchronization mode and degree and controlling an average network frequency. Furthermore, we investigate the influence on the modular synchronization by other parameters: the strength of intermodule coupling and the individual firing rate.

Mean-field dynamics of a population of stochastic map neurons

“…Having developed a viable M F approach, the present research has set the stage for a more systematic exploration of collective dynamics of assemblies of map neurons by analytical means. We believe that the introduced techniques can be successfully applied for treating the emergent behavior of populations in case of chemically and delay-coupled neurons [13]. Moreover, the method may likely be used to explore the effects of parameter inhomogeneity, as well as to study the impact of complex network topologies [13,15].…”

“…Here noise can give rise to a form of dynamics reminiscent of mixed-mode oscillations, cf. So far, models similar to (2) have been applied to address a number of problems associated to collective phenomena in networks of coupled neurons, including synchronization of electrically coupled units with spike-burst activity [49,50], pattern formation in complex networks with modular architecture [13,14,51], transient cluster activity in evolving dynamical networks [16], as well as the basin stability of synchronization regimes in smallworld networks [15]. Within this paper, the collective motion will be described in terms of the global variables…”

Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons

“…The system (1) was used in a number of research papers for modeling the collective activity of different neuronal systems (Refs. [51][52][53][54][55][56]) and studying rather theoretical issues on chaotic dynamics in maps (Refs. [57,58]).…”

Exponential Synchronization for Second-Order Nodes in Complex Dynamical Network with Communication Time Delays and Switching Topologies

“…As one of the most important collective behaviors, synchronization phenomena have been a topic of research. This topic occurs in physical science field and mathematics field for quite some time [3][4][5]. Several books and reviews [6,7] which deal with this topic have also appeared.…”