School of Mathematical & Statistical Sciences Faculty Publications and Presentations

Chaotic Dynamical Behavior of Coupled One-Dimensional Wave Equations

Document Type

Article

Publication Date

2021

Abstract

In this paper, we consider the chaotic oscillation of coupled one-dimensional wave equations. The symmetric nonlinearities of van der Pol type are proposed at the two boundary endpoints, which can cause the energy of the system to rise and fall within certain bounds. At the interconnected point of the wave equations, the energy is injected into the system through an anti-damping velocity feedback. We prove the existence of the snapback repeller when the parameters enter a certain regime, which causes the system to be chaotic. Numerical simulations are presented to illustrate our theoretical results.

Comments

Copyright World Scientific Publishing Company

Publication Title

International Journal of Bifurcation and Chaos

DOI

10.1142/S0218127421501157

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