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Title: Recent advances in coupled oscillator theory
We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems with applications to the Izhikevich neuron. We then introduce the idea of isostable reduction to explore behaviours that the weak coupling paradigm cannot explain. In an additional example, we show how bifurcations that change the stability of phase-locked solutions in a pair of identical coupled neurons can be understood using the notion of isostable reduction. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.  more » « less
Award ID(s):
1712922
PAR ID:
10158037
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume:
377
Issue:
2160
ISSN:
1364-503X
Page Range / eLocation ID:
20190092
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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