×

More results on the bifurcation of limit cycles for systems of Liénard type. (English) Zbl 0818.34021

Summary: This paper is concerned with the study of second-order differential equations of Liénard type: (A) \(\ddot x+ f(x) \dot x+ g(x)= 0\), where \(f\) and \(g\) are polynomials. The equation (A) can also be written as a system of the form (B) \(\dot x= y- F(x)\), \(\dot y= -g(x)\), where \(F(x)= \int^ x_ 0 f(\xi) d(\xi)\). The results described here apply to systems with a quadratic restoring term, \(g(x)\), and systems with a quadratic damping term, \(f(x)\). By perturbing the coefficients arising in these equations it is possible to bifurcate limit cycles in a small region of the origin. Most of the computations have been carried out on a Silicon Graphics Indigo using MAPLE V.2. Systems with at most seven and eight small-amplitude limit cycles are investigated.

MSC:

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

Software:

Maple
PDFBibTeX XMLCite