On Piecewise Linear Differential Systems with n Limit Cycles of Arbitrary Multiplicities in Two Zones

Zou, Changwu ^[1] ; Liu, Changjian ^[2] ; Yang, Jiazhong ^[3]
1. [1] Fuzhou University
  
  Fuzhou University
  
  China
2. [2] Sun Yat-sen University
  
  Sun Yat-sen University
  
  China
3. [3] Peking University
  
  Peking University
  
  China
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 1, 2019, págs. 139-151
Idioma: inglés
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Resumen
- In this paper, we demonstrate rich dynamical phenomenon of piecewise linear differential systems having only two zones in the plane. We show that, for any given integer n and any integer tuple m=(m1,m2,⋯,mn), mi≥0, for i=1,⋯,n, there exists an aforementioned system which possesses exactly n limit cycles having multiplicities m1, m2,⋯,mn, respectively. (i.e. there are totally m1+m2+⋯+mn limit cycles taking into account of multiplicities). Moreover, we can even choose the separation boundary of the zones to be an algebraic curve.