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

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 varia- tion of dynamical systems on eigenvalues of the Frechet matrix. The singularity theory is used to study the engineering unfolding （EU） and t...

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Bibliographic Details
Published in:Applied mathematics and mechanics 2017-09, Vol.38 (9), p.1233-1246
Main Authors: Lu, Kuan, Chen, Yushu, Hou, Lei
Format: Article
Language:English
Subjects:
Applications of Mathematics
Arches
Bifurcation theory
Classical Mechanics
Dynamical systems
Eigenvalues
Engineering
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nonlinear dynamics
Partial Differential Equations
Physical properties
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Summary: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 varia- tion 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 non- linear 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.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-017-2234-8