Bifurcation of critical periods of a quintic system

We investigate the critical period bifurcations of the system $$ \dot x = ix + x \bar x ( a x^3 + b x^2 \bar x + \bar x \bar x^2+d \bar x^3) $$ studied in [6]. We prove that at most three critical periods can bifurcate from any nonlinear center of the system.

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Bibliographic Details
Published in:Electronic journal of differential equations 2018-03, Vol.2018 (66), p.1-11
Main Authors: Valery G. Romanovski, Maoan Han, Wentao Huang
Format: Article
Language:English
Subjects:
bifurcation
Critical period
isochronicity
polynomial systems
Online Access:Get full text
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Summary:We investigate the critical period bifurcations of the system $$ \dot x = ix + x \bar x ( a x^3 + b x^2 \bar x + \bar x \bar x^2+d \bar x^3) $$ studied in [6]. We prove that at most three critical periods can bifurcate from any nonlinear center of the system.
ISSN:1072-6691