Dynamics of complex-valued fractional-order neural networks

TL;DR

This paper explores the stability and bifurcation behaviors of complex-valued fractional-order neural networks, providing theoretical conditions and numerical simulations to understand their dynamic properties.

Contribution

It derives new stability and bifurcation conditions for complex-valued fractional-order neural networks considering specific connectivity structures.

Findings

Derived conditions for stability and instability based on system parameters.

Identified critical fractional order values for Hopf bifurcations.

Numerical simulations confirmed theoretical stability and bifurcation results.

Abstract

The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the network are derived, based on the complex system parameters and the fractional order of the system, considering simplified neuronal connectivity structures (hub and ring). In some specific cases, it is possible to identify the critical values of the fractional order for which Hopf bifurcations may occur. Numerical simulations are presented to illustrate the theoretical findings and to investigate the stability of the limit cycles which appear due to Hopf bifurcations.