Bifurcations of non-semi-simple eigenvalues and the zero-order approximations of responses at critical points of Hopf bifurcation in nonlinear systems

Yu Dong Chen , Chun Yan Pei , Su Huan Chen

Abstract

This paper deals with the bifurcations of non-semi-simple eigenvalues at critical point of Hopf bifurcation to understand the dynamic behavior of the system. By using the Puiseux expansion, the expression of the bifurcation of non-semi-simple eigenvalues and the corresponding topological structure in the parameter space are obtained. The zero-order approximate solutions in the vicinity of the critical points at which the multiple Hopf bifurcation may occur are developed. A numerical example, the flutter problem of an airfoil in simplified model, is given to illustrate the application of the proposed method.

Key Words

eigenvalue bifurcations; non-semi-simple eigenvalues; Hopf bifurcation; zero-order approximation solution; nonlinear systems

Address

Yu Dong Chen, Chun Yan Pei and Su Huan Chen: College of Mechanical Science and Engineering, Nanling Campus, Jilin University, ChangChun 130025, P.R. China

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