Phase equation with nonlinear excitation for nonlocally coupled oscillators

Strunin, D. V. (2009) Phase equation with nonlinear excitation for nonlocally coupled oscillators. Physica D: Nonlinear Phenomena, 238 (18). pp. 1909-1916. ISSN 0167-2789

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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.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author's version deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 16 Nov 2009 05:25
Last Modified: 02 Jul 2013 23:29
Uncontrolled Keywords: nonlinear excitation; reaction-diffusion systems
Fields of Research : 01 Mathematical Sciences > 0105 Mathematical Physics > 010599 Mathematical Physics not elsewhere classified
01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1016/j.physd.2009.06.022

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