Insights into oscillator network dynamics using a phase-isostable framework

Nicks, R.; Allen, R.; Coombes, S.

Abstract

Networks of coupled nonlinear oscillators can display a wide range of emergent behaviors under the variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by the evolution of its phase and slowest decaying isostable coordinate have previously been shown to capture bifurcations and dynamics of the network, which cannot be explained through standard phase reduction. An alternative framework using isostable coordinates to obtain higher-order phase reductions has also demonstrated a similar descriptive ability for two oscillators. In this work, we consider the phase-isostable network equations for an arbitrary but finite number of identical coupled oscillators, obtaining conditions required for the stability of phase-locked states including synchrony. For the mean-field complex Ginzburg–Landau equation where the solutions of the full system are known, we compare the accuracy of the phase-isostable network equations and higher-order phase reductions in capturing bifurcations of phase-locked states. We find the former to be the more accurate and, therefore, employ this to investigate the dynamics of globally linearly coupled networks of Morris–Lecar neuron models (both two and many nodes). We observe qualitative correspondence between results from numerical simulations of the full system and the phase-isostable description demonstrating that in both small and large networks, the phase-isostable framework is able to capture dynamics that the first-order phase description cannot.

Citation

Nicks, R., Allen, R., & Coombes, S. (2024). Insights into oscillator network dynamics using a phase-isostable framework. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(1), Article 013141. https://doi.org/10.1063/5.0179430

• Journal Article Type: Article
• Acceptance Date: Dec 16, 2023
• Online Publication Date: Jan 25, 2024
• Publication Date: Jan 25, 2024
• Deposit Date: Jan 29, 2024
• Publicly Available Date: Jan 29, 2024
• Journal: Chaos: An Interdisciplinary Journal of Nonlinear Science
• Print ISSN: 1054-1500
• Electronic ISSN: 1089-7682
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 1
• Article Number: 013141
• DOI: https://doi.org/10.1063/5.0179430
• Keywords: Nonlinear dynamics modeling and theories, Linear stability analysis, Coupled oscillators, Complex Ginzburg-Landau equation, Asymptotic analysis, Phase space methods, Morris-Lecar model, Neural oscillations, Neuron model
• Public URL: https://nottingham-repository.worktribe.com/output/30152513
• Publisher URL: https://pubs.aip.org/aip/cha/article/34/1/013141/3130838/Insights-into-oscillator-network-dynamics-using-a