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The dynamics of an age structured predator-prey model with disturbing pulse and time delays. (English) Zbl 1142.34054

Summary: We formulate a general and robust prey-dependent consumption predator-prey model with periodic harvesting (catching or poisoning) for the prey and stage structure for the predator with constant maturation time delay (through-stage time delay) and perform a systematic mathematical and ecological study. We show that the conditions for global attractivity of the ‘predator-extinction’ (‘predator-eradication’) periodic solution and permanence of the population of the model depend on time delay, so, we call it “profitless”. We also show that constant maturation time delay and impulsive catching or poisoning for the prey can bring great effects on the dynamics of system by numerical analysis. In this paper, the main feature is that we introduce time delay and pulse into the predator-prey (natural enemy-pest) model with age structure, exhibit a new modeling method which is applied to investigate impulsive delay differential equations, and give some reasonable suggestions for pest management.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
92D25 Population dynamics (general)
34K25 Asymptotic theory of functional-differential equations
34K20 Stability theory of functional-differential equations
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