On the Predator-Prey Dynamics : Considering the Age-dependent Outlivability of the Prey

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A mathematical model is presented to simulate how the population dynamics of a predator-prey system depends on the prey outlivability distribution due to age difference. The prey population is described by a Lotka-Volterra equation govering the time evolution of the age density; the equation is so formulated as to take account of the age-dependent divergence in the birth/death potential and in the level of predation by the predator. The time evolution of the predator population is modelled by a logistic equation. Numerical simulation reveals that the system given an initial condition far from the equilibrium (EQ) arrives at the EQ via two restoration stages; in the one which finishes almost in a short time approximate to the maximum life span of the prey species, the density of prey age tends to assume a profile analogous to that at the EQ though the total population is still greatly distant from the EQ value, and in the other stage, for both species the total population approaches its EQ exponentially with a time constant greater than that of the preceding stage.

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