Range of validity and intermittent dynamics of the phase of oscillators with nonlinear self-excitation

Article

Strunin, D. V. and Mohammed, M. G.. 2015. "Range of validity and intermittent dynamics of the phase of oscillators with nonlinear self-excitation." Communications in Nonlinear Science and Numerical Simulation. 29 (1-3), pp. 128-147. https://doi.org/10.1016/j.cnsns.2015.04.024
Article Title

Range of validity and intermittent dynamics of the phase of oscillators with nonlinear self-excitation

ERA Journal ID100
Article CategoryArticle
AuthorsStrunin, D. V. (Author) and Mohammed, M. G. (Author)
Journal TitleCommunications in Nonlinear Science and Numerical Simulation
Journal Citation29 (1-3), pp. 128-147
Number of Pages20
Year2015
Place of PublicationNetherlands
ISSN1007-5704
Digital Object Identifier (DOI)https://doi.org/10.1016/j.cnsns.2015.04.024
Web Address (URL)http://www.sciencedirect.com/science/article/pii/S100757041500163X
Abstract

A range of active systems, particularly of chemical nature, are known to perform self-excited oscillations coupled by diffusion. The role of the diffusion is not trivial so that the differences in the phase of the oscillations through space may persist, depending on the values of the controlling parameters of the system. Firstly, we analyse a 6th-order nonlinear partial differential equation describing such dynamics. We evaluate the range of the parameters leading to different finite versions of the equation, specifically a version based on nonlinear excitation and a version based on linear excitation. In the second part of the work we solve the equation in two spatial dimensions by finite difference discretization in space and subsequent numerical integration of a system of ordinary differential equations in time. A forced variant of the equation is derived and selected exact solutions
are presented. They are also used to verify the numerical code. For the unforced equation, irregular dynamics intermitting with periods of slow evolution are recorded and discussed.

Keywordsactive dissipative system; nonlinear excitation; parametric space; irregular dynamics
ANZSRC Field of Research 2020490303. Numerical solution of differential and integral equations
490105. Dynamical systems in applications
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Byline AffiliationsComputational Engineering and Science Research Centre
Institution of OriginUniversity of Southern Queensland
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