Limit cycles appearing from perturbations of cubic piecewise smooth center with double invariant real straight lines

2018/08/05 by Yang, Jihua, Zhao, Liqin
#34C07 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.01553

Abstract

This paper investigates the exact number of limit cycles given by the averaging theory of first order for the piecewise smooth integrable non-Hamiltonian system (x, y)=\begincases (-y(x+a)²+ε f⁺(x,y), x(x+a)²+ε g⁺(x,y)), x≥0,
(-y(x+b)²+ε f^-(x,y), x(x+b)²+ε g^-(x,y)), ~ xlt;0,
\endcases where ab≠ 0, 0

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