Bifurcation of a predator-prey system with generation delay and habitat complexity. (English) Zbl 1392.37095
Summary: In this paper, we study a delayed predator-prey system with Holling type IV functional response incorporating the effect of habitat complexity. The results show that there exist stability switches and Hopf bifurcation occurs while the delay crosses a set of critical values. The explicit formulas which determine the direction and stability of Hopf bifurcation are obtained by the normal form theory and the center manifold theorem.
MSC:
| 37N25 | Dynamical systems in biology |
| 37C75 | Stability theory for smooth dynamical systems |
| 34K18 | Bifurcation theory of functional-differential equations |
| 92B05 | General biology and biomathematics |
| 92D25 | Population dynamics (general) |
| 93D20 | Asymptotic stability in control theory |
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