Stability switches and multistability coexistence in a delay-coupled neural oscillators system

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory
• Artificial Neural Networks

Background:

• Neural population activity can be modeled using coupled dynamical systems.
• Understanding the influence of time delays and coupling is essential for neural network dynamics.

Purpose of the Study:

• To analyze the stability and bifurcations of a neural network model with two delay-coupled neural oscillators.
• To investigate the emergence of complex dynamics, including coexistence of states and bursting behavior.

Main Methods:

• Analysis of the characteristic equation for local stability of the rest state.
• Hopf and Fold-Hopf bifurcation analysis using central manifold reduction and normal form methods.
• Numerical simulations to explore complex dynamics and parameter-dependent behaviors.

Main Results:

• The system exhibits switching between rest and periodic activity, with Hopf bifurcations identified.
• Fold-Hopf bifurcations were analyzed, showing coexistence of rest states and periodic activities.
• Numerical simulations revealed rich dynamics, including quasi-periodic behavior and bursting activities evolving from periodic ones.

Conclusions:

• The delay-coupled neural oscillator system demonstrates complex neuro-computational properties.
• Parameter choices, particularly time delay, can lead to the coexistence of quasi-periodic and bursting behaviors.
• This model provides insights into the mechanisms underlying diverse neural activities.