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<p>In this paper, we investigate a class of planar piecewise linear discontinuous system defined in two zones separated by a straight line. First, we establish necessary conditions for the existence of both crossing and sliding limit cycles in such system. Subsequently, employing the Poincaré compactification technique, we conduct a thorough analysis of the infinite singular points. Finally, we derive the global phase portraits within the Poincaré ball for this class of system, considering five distinct types: <i>C</i>-<i>C</i>, <i>N</i>-<i>N</i>, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N'\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>N</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(N'\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>N</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>, <i>F</i>-<i>F</i>, and <i>S</i>-<i>S</i> configurations.</p>

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Global dynamics of a class of planar piecewise linear discontinuous system with two zones

  • 期刊论文

  • 发表日期：

    2025年11月3日

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  • Qian Tong,
  • Shimin Li

摘要

In this paper, we investigate a class of planar piecewise linear discontinuous system defined in two zones separated by a straight line. First, we establish necessary conditions for the existence of both crossing and sliding limit cycles in such system. Subsequently, employing the Poincaré compactification technique, we conduct a thorough analysis of the infinite singular points. Finally, we derive the global phase portraits within the Poincaré ball for this class of system, considering five distinct types: C-C, N-N, \(N'\) N ′ - \(N'\) N ′ , F-F, and S-S configurations.