 Multi-scale dynamics of a singularly perturbed piecewise-smooth predator–prey model with weak predator interferenceXiao Wu, Mengyuan Shi and Feng Xie Chaos, Solitons & Fractals, 2025, vol. 199, issue P3 Abstract: In this paper, we focus on the dynamics of a piecewise-smooth predator–prey model with weak predator interference. By non-dimensional transformation, the model can be rewritten as a regular-singular system with a regularly perturbed system for u<1 and a singularly perturbed system for u≥1. Based on the analysis, the regular-singular system has two saddle boundary equilibriums and at most three positive equilibriums. When the positive equilibrium with u<1 is a stable focus, the system undergoes a saddle–node bifurcation and a boundary equilibrium bifurcation. Furthermore, as the parameters cross the bifurcation curves, the system has a small-amplitude hyperbolically unstable limit cycle, which is surrounded by a stable relaxation oscillation cycle, a homoclinic cycle and a heteroclinic cycle, respectively. Finally, we provide the phase portraits to illustrate our theoretical results. Keywords: Predator–prey model; Weak predator interference; Regular-singular system; Relaxation oscillation; Discontinuous equilibrium bifurcation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p3:s0960077925009087 DOI: 10.1016/j.chaos.2025.116895 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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