Scholarlink

<p>In this paper, we investigate the existence and the number of limit cycles in piecewise linear systems separated by two parallel straight lines, where in one of these straight lines, the piecewise differential system is continuous and in the other it is discontinuous. Based on the methods of the Poincaré map and first integral, we prove that these systems can have at most three limit cycles. Specifically, our results establish upper bounds on the number of limit cycles depending on the configuration: the FSF configuration can exhibit at most three limit cycles; the FCF, CSF, and CCF configurations can have at most two; the FSC and FCC configurations can admit at most one; and no limit cycles exist in the CCC and CSC configurations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

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

  • 期刊论文

  • 发表日期：

    2026年3月25日

查看全文
  • Ines Tababouchet,
  • Aziza Berbache

摘要

In this paper, we investigate the existence and the number of limit cycles in piecewise linear systems separated by two parallel straight lines, where in one of these straight lines, the piecewise differential system is continuous and in the other it is discontinuous. Based on the methods of the Poincaré map and first integral, we prove that these systems can have at most three limit cycles. Specifically, our results establish upper bounds on the number of limit cycles depending on the configuration: the FSF configuration can exhibit at most three limit cycles; the FCF, CSF, and CCF configurations can have at most two; the FSC and FCC configurations can admit at most one; and no limit cycles exist in the CCC and CSC configurations.