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- Title
Dynamics of a ratio-dependent stage-structured predator-prey model with delay.
- Authors
Song, Yongli; Yin, Tao; Shu, Hongying
- Abstract
In this paper, we investigate the dynamics of a time-delay ratio-dependent predator-prey model with stage structure for the predator. This predator-prey system conforms to the realistically biological environment. The existence and stability of the positive equilibrium are thoroughly analyzed, and the sufficient and necessary conditions for the stability and instability of the positive equilibrium are obtained for the case without delay. Then, the influence of delay on the dynamics of the system is investigated using the geometric criterion developed by Beretta and Kuang. We show that the positive steady state can be destabilized through a Hopf bifurcation and there exist stability switches under some conditions. The formulas determining the direction and the stability of Hopf bifurcations are explicitly derived by using the center manifold reduction and normal form theory. Finally, some numerical simulations are performed to illustrate and expand our theoretical results.
- Subjects
PREDATION; HOPF bifurcations; BIODIVERSITY; DEATH rate; BIRTH rate; MICHAELIS-Menten equation; MATHEMATICAL models
- Publication
Mathematical Methods in the Applied Sciences, 2017, Vol 40, Issue 18, p6451
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.4467