Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory

doi:10.1007/s10483-017-2234-8

Abstract

Abstract:

A method for seeking main bifurcation parameters of a class of nonlinear dynamical systems is proposed. The method is based on the effects of parametric variation of dynamical systems on eigenvalues of the Frechet matrix. The singularity theory is used to study the engineering unfolding (EU) and the universal unfolding (UU) of an arch structure model, respectively. Unfolding parameters of EU are combination of concerned physical parameters in actual engineering, and equivalence of unfolding parameters and physical parameters is verified. Transient sets and bifurcation behaviors of EU and UU are compared to illustrate that EU can reflect main bifurcation characteristics of nonlinear systems in engineering. The results improve the understanding and the scope of applicability of EU in actual engineering systems when UU is difficult to be obtained.

Key words: singularity, rigid line inclusion, elastic circular inclusion, stress intensity factor, interface stress, nonlinear dynamics, bifurcation, universal unfolding (UU), engineering unfolding (EU)

2010 MSC Number:

74H45

Kuan LU, Yushu CHEN, Lei HOU. Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory. Applied Mathematics and Mechanics (English Edition), 2017, 38(9): 1233-1246.

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