Bifurcation analysis of a modified Holling-Tanner predator-prey model with time delay |
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Authors: | Jia-Fang Zhang |
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Institution: | School of Mathematics and Information Sciences, Henan University, Kaifeng, Henan 475001, People’s Republic of China |
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Abstract: | In this paper, a modified Holling-Tanner predator-prey model with time delay is considered. By regarding the delay as the bifurcation parameter, the local asymptotic stability of the positive equilibrium is investigated. Meanwhile, we find that the system can also undergo a Hopf bifurcation of nonconstant periodic solution at the positive equilibrium when the delay crosses through a sequence of critical values. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included. |
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Keywords: | Predator-prey model Delay Stability Hopf bifurcation Periodic solution |
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