Explore BrainMass
Share

Explore BrainMass

    Differential Equations : Predator / Prey Models

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Part a)

    Given the following predator prey model where x(t) is the predator population and y(t) is the prey population:

    dx/dt = - ax + bxy + (z1)*x

    dy/dt = cy - gxy +(z2)*y

    Here both z1 and z2 can be positive or negative; parameters a, b, c, g are all defined to be positive.

    Parameters z1 and z2 can represent an external introduction of species at a constant rate (positive values) or an external harvesting of the species at a constant rate (a negative values).

    Under what conditions of z1 and z2 can the trivial fixed point (both species evolve to extinction) become stable (in both directions not a saddle node)

    Interpret these results.

    Part b)

    Given the following predator prey model where x(t) is the predator population and y(t) is the prey population:

    dx/dt = - a*x + b*xy -----Q

    dy/dt = c*y - g*xy ------P

    Solve the second equation, equation P, for the predator population (x) and simplify. Then show that the average predator population over one cycle or period T is equal to c/g.

    Note that the populations are periodic so y(T) = y(0) and x(T) = x(0)

    © BrainMass Inc. brainmass.com May 20, 2020, 3:59 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/differential-equations-predator-prey-models-152961

    Solution Summary

    Differential equations and parameters are used to analyze a predator / prey model. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

    $2.19

    ADVERTISEMENT