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

Paper

Strunin, Dimitry and Mohammed, Mayada. 2013. "Validity and dynamics in the nonlinearly excited 6th-order phase equation." Costa, David, Feng, Wei and Feng, Zhaosheng (ed.) 9th American Institute of Mathematical Sciences International Conference on Dynamical Systems, Differential Equations and Applications (AIMS 2013). Orlando, United States 01 - 05 Jul 2012 Springfield, MO. United States.

Paper/Presentation Title	Validity and dynamics in the nonlinearly excited 6th-order phase equation
Presentation Type	Paper
Authors	Strunin, Dimitry (Author) and Mohammed, Mayada (Author)
Editors	Costa, David, Feng, Wei and Feng, Zhaosheng
Journal or Proceedings Title	Discrete and Continuous Dynamical Systems: Series S
Number of Pages	10
Year	2013
Place of Publication	Springfield, MO. United States
ISSN	1937-1179
	1937-1632
Web Address (URL) of Paper	http://aimsciences.org/journals/contentsListPro.jsp?pubID=640
Conference/Event	9th American Institute of Mathematical Sciences International Conference on Dynamical Systems, Differential Equations and Applications (AIMS 2013)
Event Details	9th American Institute of Mathematical Sciences International Conference on Dynamical Systems, Differential Equations and Applications (AIMS 2013) Event Date 01 to end of 05 Jul 2012 Event Location Orlando, 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.
Keywords	partial differential equation; nonlinear excitation; dissipation
ANZSRC Field of Research 2020	490409. Ordinary differential equations, difference equations and dynamical systems
	490105. Dynamical systems in applications
Public Notes	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.
Byline Affiliations	School of Agricultural, Computational and Environmental Sciences
Institution of Origin	University of Southern Queensland

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