ArticlePhilosophical transactions. Series A, Mathematical, physical, and engineering sciences2019
Recent advances in coupled oscillator theory.
Article in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. An erratum has been issued. Cited by 8 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
8 citing papers in PubMed.
- Cross-region neuron co-firing mediated by ripple oscillations supports distributed working memory representations.Nature neuroscience · 2026Article
- Article
- A Phase Model of the Bio-Inspired NbOx Local Active Memristor under Weak Coupling Conditions.Micromachines · 2024Article
- Article
- Collective Oscillations in Coupled-Cell Systems.Bulletin of mathematical biology · 2021Article
- Traveling waves in non-local pulse-coupled networks.Journal of mathematical biology · 2021Article
- Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott-Antonsen theory.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2020Article
- Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2019Article
Corrections and comments
- Erratum issued
Authors and funding
3 authors.
Funding
Abstract
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'.
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