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<p>There are many papers dedicated to study the limit cycles of either continuous, or discontinuous piecewise linear differential systems separated by one straight line in the plane <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>. Here by first time we shall study the limit cycles of piecewise linear differential systems separated by one straight line in the plane <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {R}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> that are continuous in one component of differential system and discontinuous in the other.</p>

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Limit cycles of continuous-discontinuous piecewise linear differential systems separated by one straight line

  • 期刊论文

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  • 发表日期：

    2026年7月31日

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  • Fernanda Becatti,
  • Jaume Llibre

摘要

There are many papers dedicated to study the limit cycles of either continuous, or discontinuous piecewise linear differential systems separated by one straight line in the plane \(\mathbb {R}^2\) R 2 . Here by first time we shall study the limit cycles of piecewise linear differential systems separated by one straight line in the plane \(\mathbb {R}^2\) R 2 that are continuous in one component of differential system and discontinuous in the other.