On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings

TL;DR

This paper investigates a novel higher-order ring-star network of Chialvo neurons with diffusive couplings, analyzing its complex dynamical behaviors including chaos, bifurcations, and synchronization patterns using nonlinear dynamics tools.

Contribution

It introduces a new higher-order neuron network model and provides a comprehensive dynamical analysis including bifurcations, chaos quantification, and synchronization measures.

Findings

Coexistence of chaotic attractors observed.

Route to chaos via period-doubling bifurcation.

Synchronization behavior characterized by cross-correlation and Kuramoto measures.

Abstract

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.