Question

Consider the discrete-time chicken and fox population model discussed in class with the following differences. For foxes, during a one-year period, 1/4 of the fox population dies but new foxes are born (due to chicken consumption) in the amount equal to 1/8 of the chicken population. For chickens, during a one-year period, the chicken population decreases by 1/4 of the fox population (due to consumption by foxes) and increases by 1/8 of the current chicken population (the factor is therefore 1 + 1/8 = 9/8). The initial populations are 2000 for foxes and 3000 for chickens. Formulate the model in the form x(t + 1) = Ax(t) where A is a 2 × 2 matrix, then solve for the populations as functions of time using the eigenvalues and eigenvectors of A. Sketch the graphs of the populations as functions of time.

Answer 1