Stability and Hopf bifurcation in a delayed predator-prey system with stage structure for prey. (English) Zbl 1203.34132
The authors consider a predator-prey system of Lotka-Volterra type with time delays and stage structure for prey. By analyzing the corresponding characteristic equations, the local stability of the equilibria is investigated and Hopf bifurcations occurring at the positive equilibrium under some conditions are demonstrated. The mathematical tools which enable us to obtain sufficient conditions guaranteeing the global asymptotical stability of the equilibria, are the well-known Kamke comparison theorem and an iteration technique. Numerical simulations are carried out to illustrate the theoretical results.
Reviewer: Hai-Feng Huo (Lanzhou)
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 92D25 | Population dynamics (general) |
| 34K18 | Bifurcation theory of functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K13 | Periodic solutions to functional-differential equations |
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