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<p>The goal of this paper is to investigate canard solutions in generalized Liénard equations with a generic or non-generic turning point. We first use a blow-up weight to desingularize the turning point and employ some methods from dynamical systems theory to study the dynamics near the turning point. Then the existence of canard solutions is shown and the first order approximation of the control curve is given by extended Melnikov theory.</p>

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Canards in Generalized Liénard Equations with Turning Points

  • 期刊论文

  • 发表日期：

    2025年11月8日

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  • Jin-hui Yao,
  • Ji-cai Huang

摘要

The goal of this paper is to investigate canard solutions in generalized Liénard equations with a generic or non-generic turning point. We first use a blow-up weight to desingularize the turning point and employ some methods from dynamical systems theory to study the dynamics near the turning point. Then the existence of canard solutions is shown and the first order approximation of the control curve is given by extended Melnikov theory.