Electron. J. Diff. Equ., Vol. 2014 (2014), No. 188, pp. 1-28.

Chaotic oscillations of the Klein-Gordon equation with distributed energy pumping and van der Pol boundary regulation and distributed time-varying coefficients

Bo Sun, Tingwen Huang

Consider the Klein-Gordon equation with variable coefficients, a van der Pol cubic nonlinearity in one of the boundary conditions and a spatially distributed antidamping term, we use a variable-substitution technique together with the analogy with the 1-dimensional wave equation to prove that for the Klein-Gordon equation chaos occurs for a class of equations and boundary conditions when system parameters enter a certain regime. Chaotic and nonchaotic profiles of solutions are illustrated by computer graphics.

Submitted August 1, 2014. Published September 10, 2014.
Math Subject Classifications: 35L05, 35L70, 58F39, 70L05.
Key Words: Chaotic Oscillations; Klein-Gordon equation; distributed energy pumping; van der Pol boundary regulation.

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Bo Sun
Department of Mathematics
Changsha University of Science and Technology
Changsha, Hunan, China
email: sunbo1965@yeah.net
Tingwen Huang
Science Program, Texas A&M University at Qatar
Education City, Doha, Qatar
email: tingwen.huang@qatar.tamu.edu

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