Existence of Four-Crossing-Points Limit Cycles in Planar Sector-Wise Linear Systems with Saddle-Saddle Dynamics

• Xiao-Juan Liu ^[1] ; Xiao-Song Yang ^[1] ; Song-Mei Huan ^[1]
  1. [1] Huazhong University of Science and Technology

     Huazhong University of Science and Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • In this paper, we study a family of planar piecewise linear systems with saddle-saddle dynamics and sector-wise separation, which is formed by two rays starting from the same point. We mainly investigate the existence of four-crossing-points limit cycles, which intersect each of the two separation rays at two points. This is a new and complex type of limit cycle that cannot exist in planar piecewise linear systems with two zones separated by a straight line and their existence in planar sector-wise linear systems with saddle-saddle dynamics has not been studied until now. We first obtain some sufficient and necessary conditions for the existence of a special four-crossingpoints limit cycle. Then based on this result, we give some sufficient conditions for the existence of general four-crossing-points limit cycles. Moreover, we show that the four-crossing-points limit cycle and two different types of two-crossing-points limit cycles can exist simultaneously by providing concrete examples.

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