Theoretical analysis reveals limit cycle bifurcation behavior in generalized piecewise smooth Liénard systems, highlighting expanded criteria for determining origin cyclicity.
We consider a class of generalized Liénard systems and focus on the bifurcation of limit cycles near the origin as parameters vary. We derive the bifurcation function using a generalized polar coordinate transformation and analyze the cyclicity of the system at the origin, generalizing some known results. As an application, we discuss a special piecewise smooth system and study its cyclicity at the origin.
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Hou et al. (2026) studied this question.
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