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<p>The purpose of this paper is to study the number of limit cycles of canard type in linear regularizations of piecewise linear systems with non-monotonic transition functions. Using the notion of slow divergence integral and elementary breaking mechanisms, we construct systems with an arbitrary finite number of hyperbolic limit cycles. The Hopf breaking mechanism deals with transition functions with precisely one critical point in the interval <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((-1,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. On the other hand, the jump breaking mechanism produces any number of limit cycles using transition functions with precisely three critical points in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((-1,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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An Unbounded Number of Canard Limit Cycles in Linear Regularizations of Piecewise Linear Systems

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  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • Renato Huzak,
  • Otavio Henrique Perez

摘要

The purpose of this paper is to study the number of limit cycles of canard type in linear regularizations of piecewise linear systems with non-monotonic transition functions. Using the notion of slow divergence integral and elementary breaking mechanisms, we construct systems with an arbitrary finite number of hyperbolic limit cycles. The Hopf breaking mechanism deals with transition functions with precisely one critical point in the interval \((-1,1)\) ( - 1 , 1 ) . On the other hand, the jump breaking mechanism produces any number of limit cycles using transition functions with precisely three critical points in \((-1,1)\) ( - 1 , 1 ) .