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<p>In this paper, we investigate the maximum number of limit cycles in discontinuous piecewise linear systems separated by two parallel straight lines and formed by a linear system without equilibrium, an Hamiltonian system, and an arbitrary linear system having an isolated singularity in the line of discontinuity. Based on the methods of Poincaré map and first integral, we prove that these systems can have at most four limit cycles. Additionally, we present examples with one, two, three, and four limit cycles.</p>

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Existence of at most four crossing limit cycles in a class of discontinuous piecewise linear systems with three zones

  • 期刊论文

  • 发表日期：

    2025年10月9日

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  • Maroua Ghelmi,
  • Aziza Berbache

摘要

In this paper, we investigate the maximum number of limit cycles in discontinuous piecewise linear systems separated by two parallel straight lines and formed by a linear system without equilibrium, an Hamiltonian system, and an arbitrary linear system having an isolated singularity in the line of discontinuity. Based on the methods of Poincaré map and first integral, we prove that these systems can have at most four limit cycles. Additionally, we present examples with one, two, three, and four limit cycles.