Phase reduction approach to synchronisation of nonlinear oscillators

By Hiroya Nakao. 2016

284 citations recorded by the source corpus.

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.

Subfields: Computer Networks and Communications, Plant Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/05e3bb579178c6462b0fc513288257e674d8add2

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In Computer Networks and Communications

In Plant Science

In Statistical and Nonlinear Physics

Citations in the corpus

Recent Advances in Physical Reservoir Computing: A Review (2018, background): “When coupled nonlinear oscillators show limit cycle motions, they can be reduced to coupled phase oscillators under the assumption of weak interactions (Nakao, 2016).”
Networks beyond pairwise interactions: structure and dynamics (2020, methodology): “However, one can obtain phase models that approximate the original dynamics by using phase reduction techniques [390, 391].”
What are higher-order networks? (2021, methodology): “A phase reduction is an approximation of the dynamics of θk on the invariant torus obtained through an asymptotic expansion in the small parameter ε; see [213,232] for”