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<p>In this paper we consider a class of planar piecewise linear refracting systems with three zones separated by two parallel straight lines. Assume that the system has only one real finite equilibrium point, and the Jacobian matrices of the systems are Hurwitz, that is, all its eigenvalues have negative real parts. Using the Poincaré compactification, we proved that the systems can have&#xa0;18&#xa0;different global topological phase portraits.</p>

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Global Dynamics of Planar Piecewise Linear Refracting System with Three Zones

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Jiang Zhechen,
  • Li Shimin

摘要

In this paper we consider a class of planar piecewise linear refracting systems with three zones separated by two parallel straight lines. Assume that the system has only one real finite equilibrium point, and the Jacobian matrices of the systems are Hurwitz, that is, all its eigenvalues have negative real parts. Using the Poincaré compactification, we proved that the systems can have 18 different global topological phase portraits.