Electron. J. Differential Equations, Vol. 2018 (2018), No. 66, pp. 1-11.

Bifurcation of critical periods of a quintic system

Valery G. Romanovski, Maoan Han, Wentao Huang

Abstract:
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.

Submitted March 17, 2017. Published March 13, 2018.
Math Subject Classifications: 34C23, 34C25, 37G15.
Key Words: Critical period; bifurcation; isochronicity; polynomial systems.

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Valery G. Romanovski
Department of Mathematics
Shanghai Normal University
Shanghai 200234, China
email: valery.romanovsky@uni-mb.si
Maoan Han
Department of Mathematics
Shanghai Normal University
Shanghai 200234, China
email: mahan@shnu.edu.cn
Wentao Huang
School of Science
Guilin University of Aerospace Technology
Guilin, 541004, China
email: huangwentao@163.com

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