Chaotic Oscillations of Solutions of the Klein-Gordon Equation Due to Imbalance of Distributed and Boundary Energy Flows Academic Article

abstract

• Chaos in physical systems governed by nonlinear PDEs have been amply observed and reported. However, rigorous proofs for their occurrences are challenging. In particular, for a second order PDE of hyperbolic type with a van der Pol cubic nonlinearity in one of the boundary conditions and a spatially distributed antidamping term in a linear governing equation, no proof for the onset of chaos was available even though chaos was expected to occur when the antidamping term becomes sufficiently strong. In this paper, we use an operator-factoring technique together with the analogy with the one-dimensional wave equation to prove that for the KleinGordon 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.

authors

• Chen, Goong
• Huang, Tingwen

published proceedings

• INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

author list (cited authors)

• Chen, G., Sun, B. o., & Huang, T.

citation count

• 16

complete list of authors

• Chen, Goong||Sun, Bo||Huang, Tingwen

publication date

• July 2014

publisher

• World Scientific Publishing  Publisher

published in

• International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  Journal

keywords

• Chaotic Oscillations In Pdes
• Distributed Antidamping
• Klein-gordon Equations
• Operator-factoring
• Van Der Pol Nonlinearity

Digital Object Identifier (DOI)

• 10.1142/S0218127414300213

start page

• 1430021

end page

• 1430021

volume

• 24

issue

• 7

URL

• http://dx.doi.org/10.1142/s0218127414300213