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Zbl 1228.92075
Liu, Xuanliang
Bifurcation of an eco-epidemiological model with a nonlinear incidence rate. (English)
[J] Appl. Math. Comput. 218, No. 5, 2300-2309 (2011). ISSN 0096-3003

Summary: A predator-prey system with disease in the prey is considered. Assuming that the incidence rate is nonlinear, we analyse the boundedness of solutions and local stability of equilibria. By using bifurcation methods and techniques, we study Bogdanov-Takens bifurcations near a boundary equilibrium, and obtain a saddle-node bifurcation curve, a Hopf bifurcation curve and a homoclinic bifurcation curve. The Hopf bifurcation and generalized Hopf bifurcation near the positive equilibrium are analyzed, and one or two limit cycles are also discussed.

MSC 2000:: *92D40 Ecology
34C23 Bifurcation (periodic solutions)
34C60 Applications of qualitative theory of ODE
34D20 Lyapunov stability of ODE
65C20 Models (numerical methods)

Keywords: predator-prey system; limit cycle; Hopf bifurcation; Bogdanov-Takens bifurcation

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