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Hopf bifurcation at infinity with discontinuous nonlinearities

Published online by Cambridge University Press:  17 February 2009

Xiangjian He
Xiangjian He
Affiliation:
School of Information Sc. and Tech., Flinders University of S. A., Adelaide S.A., Australia.
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Abstract

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In this paper, we consider the existence of a family of periodic solutions of large amplitude when a pair of eigenvalues of the linear part of a first-order system of ordinary differential equations crosses the imaginary axis. We refer to this problem as a Hopf bifurcation problem at infinity. In our work, the nonlinearities may be discontinuous at the origin, and the proof of existence of periodic solutions is arrived at through the corresponding system of integral equations. The applicability of the result is demonstrated by the study of the dynamics of a train truck wheelset system.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 2 , October 1991 , pp. 133 - 148
Copyright
Copyright © Australian Mathematical Society 1991

References

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