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<p>In this paper, a class of plankton-fish (2,&#xa0;1)-fast-slow system with delay and piecewise smooth on slow variable is studied. A new type of point that loses hyperbolicity on the critical manifold is discussed, and the influence of this point on the large-amplitude oscillation in the system is analyzed. Then, the situation of stability switching in delay systems is discussed, and it is shown that the delay term does not necessarily cause the stability switching of the system. Therefore, when there is no stability switching in the delay system, the conditions of general parameter-induced Hopf bifurcation are given, and the singularity of general parameter-induced Hopf bifurcation is proven by using the center manifold reduction. Finally, the existence and uniqueness of small-amplitude limit cycle and boundary limit cycles are discussed.</p>

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Singular Perturbation Analysis of a Three-dimensional Predator-prey System with Delay and Piecewise Smooth Harvesting

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Xin Ai,
  • Yue Zhang

摘要

In this paper, a class of plankton-fish (2, 1)-fast-slow system with delay and piecewise smooth on slow variable is studied. A new type of point that loses hyperbolicity on the critical manifold is discussed, and the influence of this point on the large-amplitude oscillation in the system is analyzed. Then, the situation of stability switching in delay systems is discussed, and it is shown that the delay term does not necessarily cause the stability switching of the system. Therefore, when there is no stability switching in the delay system, the conditions of general parameter-induced Hopf bifurcation are given, and the singularity of general parameter-induced Hopf bifurcation is proven by using the center manifold reduction. Finally, the existence and uniqueness of small-amplitude limit cycle and boundary limit cycles are discussed.