Chaotic oscillations of the Klein-Gordon equation with distributed energy pumping and van der Pol boundary regulation and distributed time-varying coefficients
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 fo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/188/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |