Bifurcation of an eco-epidemiological model with a nonlinear incidence rate |
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Authors: | Xuanliang Liu |
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Institution: | School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, PR China |
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Abstract: | A predator-prey system with disease in the prey is considered. Assume 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 bifurcation 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 is analyzed, one or two limit cycles is also discussed. |
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Keywords: | Predator-prey system Nonlinear incidence rate Limit cycle Hopf bifurcation Bogdanov-Takens bifurcation |
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