Prey-predator model

Discussion in 'Differential Equations' started by matematician_best, Jan 12, 2024.

  1. matematician_best


    Jan 12, 2024
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    Gause-Rosenzweig-McArthur models for predator-prey interactions, featuring a logistic growth rate for the prey, possess the subsequent configuration:
    H'(t) = r(1-H/K)H-f(H)P
    P'(t) = -uP+gf(H)P
    where r, u and g are constants, f(H) is the functional response (number of preys that a predator eats in a unit of time).
    Suppose f(H) increasing, such that f(0)=0 and that the limit of f(H), as H approaches infinity, is a finite number, that we indicate with m. Show graphically that, if gm>u, then there exists a unique value H* such that gf(H*)=u. Compute the isoclines of the system. Show that the system has a positive equilibrium if and only if K>H*.
    matematician_best, Jan 12, 2024
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