Dynamical properties of a small heterogeneous chain network of neurons in discrete time

TL;DR

This paper introduces a novel discrete-time heterogeneous neuron network model combining Chialvo and Rulkov maps, analyzing its complex dynamics, bifurcations, and synchronization properties relevant to neural systems.

Contribution

It presents a new coupled neuron network model with detailed nonlinear analysis, including bifurcation and synchronization studies, advancing understanding of neural dynamics.

Findings

Coexistence of chaotic and periodic attractors

Identification of various bifurcation patterns

Quantification of synchronization behavior

Abstract

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.