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.


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 / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 24 Apr 2014 22:57
Last Modified: 16 Sep 2014 04:34
Uncontrolled Keywords: partial differential equation; nonlinear excitation; dissipation
Fields of Research : 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 > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences

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