Validity and dynamics in the nonlinearly excited 6th-order phase equation

Strunin, Dimitry and Mohammed, Mayada (2013) Validity and dynamics in the nonlinearly excited 6th-order phase equation. In: 9th American Institute of Mathematical Sciences International Conference on Dynamical Systems, Differential Equations and Applications (AIMS 2013), 1-5 Jul 2012, Orlando, FL. United States.


Abstract

A slowly varying phase of oscillators coupled by diffusion is generally described by a partial differential equation comprising infinitely many terms. We consider a particular case when the coupling is nonlocal and, as a result, the equation can be reduced to a finite form with nonlinear excitation and 6th-order dissipation. We fulfilled two tasks: (1) evaluated the range of independent parameters rendering the form valid, and (2) developed and tested the numerical code for solving the equation; some numerical solutions are presented.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: Open access publication. Published source must be acknowledged. Dynamical Systems and Differential Equations, DCDS Supplement 2013 - Proceedings of the 9th AIMS International Conference (Orlando, USA) Editors: David Costa, Wei Feng, Zhaosheng Feng, Xin Lu, Xingping Sun, Masaharu Taniguchi and Antonio Vitolo.
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019)
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019)
Date Deposited: 24 Apr 2014 22:57
Last Modified: 29 Apr 2021 05:03
Uncontrolled Keywords: partial differential equation; nonlinear excitation; dissipation
Fields of Research (2008): 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
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490409 Ordinary differential equations, difference equations and dynamical systems
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490105 Dynamical systems in applications
Socio-Economic Objectives (2008): 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
URI: http://eprints.usq.edu.au/id/eprint/24906

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