 Stability of bifurcating solution of a predator–prey modelMengxin Chen and Hari Mohan Srivastava Chaos, Solitons & Fractals, 2023, vol. 168, issue C Abstract: To explore the role of the prey-taxis in an ecological model, we investigate a predator–prey model with prey-taxis in this paper. Firstly, the local stability of the positive equilibrium and the occurrence conditions of the steady state bifurcation are given. Thereafter, we investigate the existence and stability of the bifurcating solution around the threshold. Precisely, by treating the prey-taxis constant ξ as the bifurcation parameter, we confirm the model possesses the steady state bifurcation at ξ=ξkS for k∈N0/{0}. Also, we set ξkS(ɛ)=ξkS+ɛξ1+ɛ2ξ2+⋅⋅⋅ for small ɛ>0. We show that ξ1=0 and ξ2 determines the stability of the bifurcating solution. Finally, the stable bifurcating solution is observed by using numerical experiments. The findings of this paper are: (i) the repulsive prey-taxis will facilitate the occurrence of the steady state bifurcation. (ii) the bifurcating solution is stable if ξ2<0 and it is unstable if ξ2>0. Keywords: Predator–prey model; Steady state bifurcation; Bifurcating solution; Prey-taxis (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:168:y:2023:i:c:s0960077923000541 DOI: 10.1016/j.chaos.2023.113153 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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