What is it about?
Understanding emergent dynamics in networks of coupled oscillators is a challenging problem, often tackled using reduction to consider only the phase of each oscillator which is relevant only when coupling between oscillators is weak. However, this cannot capture the influential interactions between oscillators when they are away from their limit cycle. In this paper a notion of distance from limit cycle is retained within the reduction in order to reveal the changing emergent dynamics of the network as the coupling strength between the oscillators is varied. Through consideration of example networks we show that this new reduction more accurately predicts stable network states and can reveal phenomena that cannot be described using phase alone.
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Why is it important?
Complex systems that can be described as a network of interacting oscillating units are numerous, with examples including brain networks, power distribution networks, communications networks and laser networks. Understanding the emergence of phenomena such as synchrony and other dynamical states as system parameters are varied is and important but difficult task. We make progress here through novel reduction techniques which are valid beyond the weak coupling limit and can reveal dynamics such as changes in stability of synchrony and the emergence of qusiperiodic states which cannot be found using the standard tool of phase reduction.
Perspectives
Although coupled oscillator networks have been the subject of much research over recent decades, interest in understanding their dynamics remains high due to the wide variety of applications in which they arise. Many questions remain unanswered, especially when considering additional complications such as time delays, heterogeneity and noise. I think that the work instigated here in this work opens up exciting pathways for extension to consider some of these challenges.
Rachel Nicks
University of Nottingham
Read the Original
This page is a summary of: Insights into oscillator network dynamics using a phase-isostable framework, Chaos An Interdisciplinary Journal of Nonlinear Science, January 2024, American Institute of Physics,
DOI: 10.1063/5.0179430.
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