Bifurcation Curves of Limit Cycles in some Lienard Systems

Details Bifurcation Curves of Limit Cycles in some Lienard Systems Bifurcation Curves of Limit Cycles in some Lienard Systems

2002-05-14

arxiv.org/abs/nlin/0205028v1

Nonlinear Sciences

Pattern Formation and Solitons

25 pages, 0 figures. Published in Int. Journal of Bifurcation and Chaos, vol. 10, 971-980 (2001)

Scientific paper

Lienard systems of the form $\ddot{x}+\epsilon f(x)\dot{x}+x=0$, with f(x) an even continous function, are considered. The bifurcation curves of limit cycles are calculated exactly in the weak ($\epsilon\to 0$) and in the strongly ($\epsilon\to\infty$) nonlinear regime in some examples. The number of limit cycles does not increase when $\epsilon$ increases from zero to infinity in all the cases analyzed.

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