Scholarlink

Abstract <p>In this work, we study a family of multiparameter polynomial differential systems of degree eleven. We prove that the considered family has an invariant algebraic curve, which is given explicitly. Subsequently, we demonstrate the integrability of these systems and derive an explicit expression for a first integral. Moreover, we provide sufficient conditions for the systems to possess two limit cycles explicitly given. The applicability of our results is illustrated by a concrete example.</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

Explicit Formulas for Two Limit Cycles of a Family of Planar Differential Systems

  • 期刊论文

  • 发表日期：

    2025年4月1日

查看全文
  • S. E. Hamizi,
  • R. Boukoucha

摘要

Abstract

In this work, we study a family of multiparameter polynomial differential systems of degree eleven. We prove that the considered family has an invariant algebraic curve, which is given explicitly. Subsequently, we demonstrate the integrability of these systems and derive an explicit expression for a first integral. Moreover, we provide sufficient conditions for the systems to possess two limit cycles explicitly given. The applicability of our results is illustrated by a concrete example.