Phase equation with nonlinear excitation for nonlocally coupled oscillators

Article

Strunin, D. V.. 2009. "Phase equation with nonlinear excitation for nonlocally coupled oscillators." Physica D: Nonlinear Phenomena. 238 (18), pp. 1909-1916. https://doi.org/10.1016/j.physd.2009.06.022
Article Title

Phase equation with nonlinear excitation for nonlocally coupled oscillators

ERA Journal ID352
Article CategoryArticle
Authors
AuthorStrunin, D. V.
Journal TitlePhysica D: Nonlinear Phenomena
Journal Citation238 (18), pp. 1909-1916
Number of Pages8
Year2009
Place of PublicationAmsterdam, Netherlands
ISSN0167-2789
1872-8022
Digital Object Identifier (DOI)https://doi.org/10.1016/j.physd.2009.06.022
Web Address (URL)http://www.sciencedirect.com/science/journal/01672789
Abstract

Some reaction-diffusion systems feature nonlocal interaction and, near the point of Hopf bifurcation, can be represented as a system of nonlocally coupled oscillators. Phase of oscillations satisfies an evolution pde which takes different forms depending on the values of parameters. In the simplest case the equation is
effectively a diffusion equation which is excitation-free. However, more complex forms are possible such as the Nikolaevskii equation and the Kuramoto–Sivashinsky equation incorporating linear excitation. We analyse a situation when the phase equation is based on nonlinear excitation. We derive conditions on the values of the parameters leading to the situation and show that the values satisfying the conditions exist.

Keywordsnonlinear excitation; reaction-diffusion systems
ANZSRC Field of Research 2020490299. Mathematical physics not elsewhere classified
490409. Ordinary differential equations, difference equations and dynamical systems
490105. Dynamical systems in applications
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Byline AffiliationsDepartment of Mathematics and Computing
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