Bifurcation and chaos of an axially accelerating viscoelastic beam

Yang, Xiao‐Dong; Chen, Liqun

doi:10.1016/j.chaos.2004.04.008

Cited by 89 publications

(1 citation statement)

References 21 publications

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“…The chaos of nonlinear system of partial differential equations (PDEs) has become the focus in nonlinear dynamics due to its wide applications in biomedical engineering [1], secure communication [14], physics [30] and so on. The nonlinearity of the system comes from nonlinear PDEs or/and nonlinear boundary condition.…”

Section: Introductionmentioning

confidence: 99%

Chaos of the coupled Klein-Gordon like equations with superlinear boundary conditions

Zhu

Yang

2023

Nonlinear Dyn

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The complicated dynamics is considered for a system of coupled generalized Klein-Gordon equations with two symmetric superlinear boundary conditions. The coupled equations studied here becomes coupled damped Klein-Gordon equations or telegraph equations or wave equations at a certain parameter value. The system is reduced to a discrete iteration of a 2D map differing from the unary map induced by the non-coupled hyperbolic PDEs. In this article, the approach of snapback repeller is applied to establish the sufficient condition on the Li-Yorke chaos of the system. Moreover, by characterizing the asymptotic behavior of the 2D map, the global stability of the system is obtained under a certain range of parameter. In particular, the obtained dynamics not only extends the chaotic results on coupled wave equations with van der Pol type boundary conditions, but also gives the criterion of global stability.

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Section: Introductionmentioning

confidence: 99%