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 TypePaper
AuthorsStrunin, Dimitry (Author) and Mohammed, Mayada (Author)
EditorsCosta, David, Feng, Wei and Feng, Zhaosheng
Journal or Proceedings TitleDiscrete and Continuous Dynamical Systems: Series S
Number of Pages10
Year2013
Place of PublicationSpringfield, MO. United States
ISSN1937-1179
1937-1632
Web Address (URL) of Paperhttp://aimsciences.org/journals/contentsListPro.jsp?pubID=640
Conference/Event9th 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.

Keywordspartial differential equation; nonlinear excitation; dissipation
ANZSRC Field of Research 2020490409. 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 AffiliationsSchool of Agricultural, Computational and Environmental Sciences
Institution of OriginUniversity of Southern Queensland
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