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Thread: Predator-prey system

  1. #1
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    Predator-prey system

    Hello,
    I have to solve the following task with predator-prey method.

    The dynamics of self-regulating "predator-prey" populations in the population is described by the model:
    dN1/dt = (a - bN2 - αN1); dN2/dt = (-c + mN1)N2 (1),
    where α is coefficient of internal victim struggle,
    and a>0,b>0,α>0,c>0,m>0
    With this change N1=k1x, N2=k2y,t=k3z (2) the system (1) can be reduced to: dx/dz=x(E - Ax - y); dy/dz=y(-1 + x) (3)
    And here is the questions:
    1)Find the coefficients ki of element (2), where i =1,3 (irrationals)
    2)Find the relationship/connection between params A and E from (3) and the params from (1)
    3)Find the equilibrium (specific points) of system (3)
    4)Examine the stability of the equilibrium position of (3)
    5)Build a Phase Portrait of (3)

    Thank you in advance!
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  2. #2
    MHF Contributor
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    Re: Predator-prey system

    Since you have to solve it, and not us, perhaps you could tell us what you have managed so far.
    Thanks from topsquark
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