Question

2.72. A very interesting ecological problem is that of rabbits and foxes in a controlled environ ment. If the number of rabbits were left alone, they would grow indefinitely until the food supply exhausted. Representing the number of rabbits by x(t), their growth rate is given by was t)Ax,(t) However, rabbit-eating foxes in the environment change this relationship to the following: t) Ax,(t)-Bx2(t) where x(t) represents the fox population. In addition, if foxes must have rabbits to exist, then their growth rate is given by t)C(t)Dx2(t), + (a) Assume that A = 1, B = 2, C = 2, and D 4. Determine the state transitions matrix for this eco- logical model. (b) From the state transition matrix, determine the response of this ecological model when x(0) = 100 and x(o) 50. Explain your results.

Answer 1

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