 Stability and Hopf bifurcation of a multiple delayed predator–prey system with fear effect, prey refuge and Crowley–Martin functionZiwei Liang and Xinyou Meng Chaos, Solitons & Fractals, 2023, vol. 175, issue P1 Abstract: In this paper, we consider a predator–prey model with fear response delay, gestation delay, fear effect, prey refuge, harvesting and Crowley–Martin type functional response. First, we discuss the model without delays and corroborate the positivity and boundedness of the solution. Then, we give some sufficient conditions for the existence and stability of three equilibriums. For the model with delays, we not only analyze the local stability of the positive equilibrium and the occurrence of Hopf bifurcation, but also obtain the crossing curves to study the stability switches of the positive equilibrium on the delays plane. Furthermore, we calculate the normal form of Hopf bifurcation and hence get the direction of Hopf bifurcation and the stability of bifurcated periodic solutions. At last, we support our findings by numerical simulations. Keywords: Fear effect; Hopf bifurcation; Crowley–Martin type functional response; Time delay; Stability switches (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:175:y:2023:i:p1:s0960077923008561 DOI: 10.1016/j.chaos.2023.113955 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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