J Austral Math Soc Ser B 33 pp133--148, 1991.

Hopf bifurcation at infinity with discontinuous nonlinearities

Xiangjian He

Abstract

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.

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Author

Xiangjian He

School of Information Sc. and Tech., Flinders University of S. A., Adelaide S.A., Australia.