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Limit Cycles in a Family of Planar Piecewise Linear Differential Systems with a Nonregular Separation Line

    https://doi.org/10.1142/S0218127419501098Cited by:17 (Source: Crossref)

    In this paper, we investigate the number of crossing limit cycles in a family of planar piecewise linear differential systems with two zones separated by a nonregular line formed by two rays starting at the origin. By studying the dynamics of each subsystem, a thorough study including the parameteric expressions and main properties of some section maps is performed. Especially, different to the case with a straight separation line, it is proved that each section map can be piecewise with two different pieces and can have at most one inflection point. In addition to this, for the existence of these inflection points, some sufficient and necessary conditions satisfied by the system parameters are obtained. Based on these results, the importance played by these inflection points in increasing the maximum number of limit cycles in such systems is verified by providing a concrete example having five nested limit cycles with two crossing one separation ray and the other three crossing both separation rays. So, the five limit cycles obtained here are different from that obtained in the existing literature, where all the limit cycles cross both separation rays.

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