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An Example of Piecewise Linear Systems with Infinitely Many Limit Cycles Separated by a Piecewise Linear Curve and Its Perturbations
  
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KeyWord:Piecewise linear system, crossing limit cycle, piecewise linear perturbation, piecewise smooth switching curve, stability
Author NameAffiliation
Qing Zhang Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China 
Zhengdong Du Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China 
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Abstract:
      In this paper, we present an example of piecewise linear systems with infinitely many crossing limit cycles defined in two zones separated by a piecewise linear curve with countable corners. Then we prove that under piecewise linear perturbations, the perturbed system can have infinitely many limit cycles, or exactly $\ell$ limit cycles for any given nonnegative integer $\ell$.