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

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-Mar). pp. 128-147. ISSN 1007-5704

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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Accepted version deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 21 Apr 2016 02:56
Last Modified: 01 Aug 2016 01:31
Uncontrolled Keywords: active dissipative system; nonlinear excitation; parametric space; irregular dynamics
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1016/j.cnsns.2015.04.024
URI: http://eprints.usq.edu.au/id/eprint/28506

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