Bifurcation analysis of a predator–prey model with anti-predator behaviour

Biao Tang and Yanni Xiao

Chaos, Solitons & Fractals, 2015, vol. 70, issue C, 58-68

Abstract: We investigated a predator–prey model with a nonmonotonic functional response and anti-predator behaviour such that the adult prey can attack vulnerable predators. By analyzing the existence and stability of all possible equilibria and conducting a bifurcation analysis, we obtained the global dynamics of the proposed system. The system could undergo a saddle-node bifurcation, (supercritical and subcritical) Hopf bifurcation, homoclinic bifurcation and a Bogdanov–Takens bifurcation of codimension 2. Further, we obtained a generic family unfolding for the system by choosing the environmental carrying capacity of the prey and the death rate of the predator as bifurcation parameters. Numerical studies showed that anti-predator behaviour not only makes the coexistence of the prey and predator populations less likely, but also damps the predator–prey oscillations. Therefore, anti-predator behaviour helps the prey population to resist predator aggression.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:70:y:2015:i:c:p:58-68

DOI: 10.1016/j.chaos.2014.11.008

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