Bifurcation analysis of a predator–prey model with anti-predator behaviour. (January 2015)

• Record Type: Journal Article
• Authors: Tang, Biao; Xiao, Yanni
• Is Part Of: Chaos, solitons and fractals. Volume 70(2015)
• Page Start: 58
• Page End: 68
• Publication Date: 2015-01
• Subjects: Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2014.11.008
• Languages: English
• ISSNs: 0960-0779

Abstract

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.