On global mechanisms of synchronization in networks of coupled chaotic circuits and the role of the voltage-type coupling

TL;DR

This paper investigates synchronization mechanisms in networks of coupled chaotic Nakano circuits with voltage-dependent reset rules, extending stability analysis methods to discontinuous dynamics and exploring the influence of voltage coupling modes.

Contribution

It introduces a generalized master stability function framework for discontinuous networks of spiking oscillators with voltage-type coupling, and demonstrates its application to Nakano circuits.

Findings

Synchronization depends on network topology and reset regimes.

Voltage-type coupling significantly influences synchronization stability.

The saltation-matrix method effectively analyzes discontinuous dynamics.

Abstract

A model for synchronization of coupled Nakano's chaotic circuits is studied. The Nakano circuit consists of a simple RLC circuit with a switch voltage-depending reset rule which generates a discontinuous dynamics. Thus, the model that we study is a network of identical spiking oscillators with integrate-and-fire dynamics. The coupling between oscillators is linear, but the network is subject to a common regime of reset depending on the global state of the oscillator population. This constitutes the simplest way of build pulse-coupled networks with arbitrary topology for this type of oscillators, and it allows the emergence of synchronous states and different reset regimes. The main result is that under certain hypothesis over the weight matrix (that represents the network topology) the different reset regimes match and the formalism of the master stability function can be generalized in order to study the stability of the synchronous state and the discontinuous dynamic of the network. Also, the low dimensionality of the Nakano's circuit allows to implement the saltation-matrix method and numerical simulations can be performed in order to analyze the role of the coupling mode in the synchronization regime of the network and the influence of the voltage-type variables.