DELAY INDUCED SUBCRITICAL HOPF BIFURCATION IN A DIFFUSIVE PREDATOR-PREY MODEL WITH HERD BEHAVIOR AND HYPERBOLIC MORTALITY

Xiaosong Tang; Heping Jiang; Zhiyun Deng; Tao Yu

doi:10.11948/2017084

2017 Volume 7 Issue 4

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Xiaosong Tang, Heping Jiang, Zhiyun Deng, Tao Yu. DELAY INDUCED SUBCRITICAL HOPF BIFURCATION IN A DIFFUSIVE PREDATOR-PREY MODEL WITH HERD BEHAVIOR AND HYPERBOLIC MORTALITY[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1385-1401. doi: 10.11948/2017084

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Xiaosong Tang, Heping Jiang, Zhiyun Deng, Tao Yu. DELAY INDUCED SUBCRITICAL HOPF BIFURCATION IN A DIFFUSIVE PREDATOR-PREY MODEL WITH HERD BEHAVIOR AND HYPERBOLIC MORTALITY[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1385-1401. doi: 10.11948/2017084

DELAY INDUCED SUBCRITICAL HOPF BIFURCATION IN A DIFFUSIVE PREDATOR-PREY MODEL WITH HERD BEHAVIOR AND HYPERBOLIC MORTALITY

1 College of Mathematics and Physics, Jinggangshan University, Ji'an 343009, China;
2 School of Mathematics and Statistics, Huangshan University, 245041, China

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Abstract

Abstract

In this paper, we consider the dynamics of a delayed diffusive predator-prey model with herd behavior and hyperbolic mortality under Neumann boundary conditions. Firstly, by analyzing the characteristic equations in detail and taking the delay as a bifurcation parameter, the stability of the positive equilibria and the existence of Hopf bifurcations induced by delay are investigated. Then, applying the normal form theory and the center manifold argument for partial functional differential equations, the formula determining the properties of the Hopf bifurcation are obtained. Finally, some numerical simulations are also carried out and we obtain the unstable spatial periodic solutions, which are induced by the subcritical Hopf bifurcation.
- Predator-prey model with herd behavior /
- hyperbolic mortality /
- delay /
- diffusion /
- Hopf bifurcation /
- periodic solutions
MSC: 35K57;35B10

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References

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