Question

Compute a Matlab script:

Suppose we have two species of animals, foxes and rabbits and we wish to model their population Suppose the number of foxes at a given time is given by yn and the number of rabbits is given by rn. Suppose in the absence of predation, rabbits reproduce at a rate proportional to their population rn with constant of proportionality a. Suppose the rate at which foxes eat rabbits is proportional to the number of foxes with constant of proportionality β. Then we can model the population of rabbits by the difference equation In+ Suppose the rate of population growth of the foxes is proportional to the number of rabbits with constant of proportionality and that foxes die off at a rate proportional to the number of foxes with constant γ due to the competition associated with population size. Then the population of foxes if given by the differenceequations These two equations paired together form a simplified predator-prey model. We can write them in matrix form C- yn+1 Suppose we find that the growths rates are α-γ-2, β difference equation: 5, and δ-2. Then we have the matrix valued 1-2 yn Un +1 Start with an initial population of 15 rabbits and 10 foxes. Write a script with calculates the population after ten time steps. Write a script with calculates the population of rabbits and foxes for every time up to n-10 Plot the population of rabbits and foxes on the same axes. Suppose l instead, plot the population of rabbits and foxes on the same axes.

Answer 1

Pnnt . Sequence リ elSe elSe