Insights into oscillator network dynamics using a phase-isostable framework

Area of Science:

• Nonlinear Dynamics
• Network Science
• Computational Neuroscience

Background:

• Coupled nonlinear oscillators exhibit complex emergent behaviors.
• Standard phase reduction methods fail to capture certain network dynamics and bifurcations.
• Isostable coordinates offer a more comprehensive description of oscillator dynamics.

Purpose of the Study:

• To extend the phase-isostable framework to arbitrary numbers of coupled identical oscillators.
• To derive conditions for the stability of phase-locked states, including synchrony.
• To compare the accuracy of phase-isostable equations against higher-order phase reductions.

Main Methods:

• Development of phase-isostable network equations for N coupled oscillators.
• Analysis of stability conditions for phase-locked states.
• Comparison with higher-order phase reductions using the complex Ginzburg-Landau equation.
• Application to globally linearly coupled Morris-Lecar neuron models.

Main Results:

• Phase-isostable network equations accurately capture bifurcations in phase-locked states.
• The phase-isostable framework demonstrates superior accuracy compared to higher-order phase reductions.
• Qualitative correspondence observed between simulations and phase-isostable descriptions for Morris-Lecar networks.
• The method captures dynamics missed by first-order phase descriptions in small and large networks.

Conclusions:

• The phase-isostable framework provides a more accurate description of coupled oscillator networks than standard phase reduction.
• This approach is effective for analyzing complex dynamics, including synchrony and bifurcations, in various network sizes.
• The study validates the utility of phase-isostable coordinates for understanding emergent phenomena in coupled dynamical systems.