Global stability of a Lotka–Volterra type predator–prey model with stage structure and time delay. (English) Zbl 1056.92063

Summary: A delayed Lotka-Volterra type predator-prey model with stage structure for the predator is investigated. It is assumed in the model that the individuals in the predator population may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not have the ability to prey. By analyzing characteristic equations and using an iterative technique, a set of easily verifiable sufficient conditions are derived for the local and global stability of the nonnegative equilibria of the model. Numerical simulations are carried out to illustrate the validity of our results.


92D40 Ecology
34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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