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Small Amplitude Limit Cycles for Cubic Systems

Published online by Cambridge University Press:  20 November 2018

V. Guíñez ,
E. Sáez  and
I. Szántó
V. Guíñez
Affiliation:
Universidad Técnica Federico Santa María Departamento de Matemática Casilla 110-V, Valparaiso Chile
E. Sáez
Affiliation:
Universidad Técnica Federico Santa Maria Departamento de Matemática Casilla 110-V, Valparaíso Chile
I. Szántó
Affiliation:
Universidad de Chile Facultad de Ciencias Casilla 653, Santiago Chile
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Abstract

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In this article we study the simultaneous generation of limit cycles out of singular points and infinity for the family of cubic planar systems

With a suitable choice of parameters, the origin and four other singularities are foci and infinity is a periodic orbit. We prove that it is possible to obtain the following configuration of limit cycles: two small amplitude limit cycles out of the origin, a small amplitude limit cycle out of each of the other four foci, and a large amplitude limit cycle out of infinity. We also obtain other configurations with fewer limit cycles.

Keywords

58F2134C05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 54 - 63
Copyright
Copyright © Canadian Mathematical Society 1993

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