Limit cycle and bifurcation of nonlinear problems. (English) Zbl 1093.34520

He, Ji-Huan

Chaos Solitons Fractals 26, No. 3, 827-833 (2005).

The author considers the following nonlinear equation \[ \ddot x+ x+ \varepsilon f(x,\dot x,\ddot x)= 0,\tag{1} \] where the parameter \(\varepsilon\) needs not to be small. The goal of the paper is to find limit cycles of (1) and bifurcation curves. To this end, the author proposes a simple but effective method.

Reviewer: Messoud A. Efendiev (Berlin)

MSC:

34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C23	Bifurcation theory for ordinary differential equations

Keywords:

limit cycles; bifurcation curves; nonlinear problems

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