Limit Cycles of a Class of Discontinuous Planar Piecewise Linear Systems with Three Regions of Y-Type

Springer Science and Business Media LLC - Tập 18 - Trang 1031-1054 - 2019
Qianqian Zhao1, Jiang Yu1
1School of Mathematical Sciences, Shanghai Jiaotong University, Shanghai, People’s Republic of China

Tóm tắt

In this paper, we investigate the crossing limit cycles of a class of discontinuous planar piecewise linear dynamical systems with three regions of Y-type. We want to find the reason that cause the increase of the number of such limit cycles of the piecewise systems. We obtain the canonical form of such systems with focus–focus–focus type, and prove that the graph of Poincaré map of one of three subsystems has one inflection point. Naturally, we prove that the lower bound of the number of crossing limit cycles for this class systems is 3. We also give an example to simulate the four real crossing limit cycles.

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Springer Science and Business Media LLC

Tập 18

1031-1054

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