Article ID Journal Published Year Pages File Type
5774847 Journal of Mathematical Analysis and Applications 2017 11 Pages PDF
Abstract
In this paper, we mainly consider the chaotic behaviors of the initial-boundary value problems of 1D wave equation on an interval. The boundary conditions at the left and right endpoints have nonlinearities of van der Pol type, both of which cause the total energy of the system to rise and fall within certain bounds. We show that the interactions of these nonlinear boundary conditions can cause chaotic oscillations of the wave equation when the parameters enter a certain regime, which can be taken as a new way to lead to the onset of chaos. We further prove that for any given initial data and parameters, the variables “force” and “velocity” will fall into a bounded region as time increases. Numerical simulations are presented to illustrate the theoretical outcomes.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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