Solved: In this problem we examine the phase difference between the cyclic variations of

Chapter 9, Problem 6

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In this problem we examine the phase difference between the cyclic variations of the predator and prey populations as given by Eqs. (24) of this section. Suppose we assume that K > 0 and that t is measured from the time that the prey population x is a maximum; then = 0. (a) Show that the predator population y is a maximum at t = /2 ac = T/4, where T is the period of the oscillation. (b) When is the prey population increasing most rapidly? decreasing most rapidly? a minimum? (c) Answer the questions in part (b) for the predator population. (d) Draw a typical elliptic trajectory enclosing the point (c/ , a/), and mark the points found in parts (a), (b), and (c) on it.