We can modify the logistic population model to include harvesting/hunting of animals: assume that the population...

 

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We can modify the logistic population model to include harvesting/hunting of animals: assume that the population grows logistically while, at the same time, animals are being removed from it at a constant rate h. In appropriately rescaled variables this model may be written as x'(t) = x(1 − x) – h. What are the equilibrium values of x(t) for different values of the parameter h? What is the stability of these equilibria? Draw the phase line portrait for some h < 1/4. Explain how the population varies for different initial conditions, can the population ever become extinct? We can modify the logistic population model to include harvesting/hunting of animals: assume that the population grows logistically while, at the same time, animals are being removed from it at a constant rate h. In appropriately rescaled variables this model may be written as x'(t) = x(1 − x) – h. What are the equilibrium values of x(t) for different values of the parameter h? What is the stability of these equilibria? Draw the phase line portrait for some h < 1/4. Explain how the population varies for different initial conditions, can the population ever become extinct?