4. The Dynamics of Romeo and Juliet's Love Affair In this problem, we will study a discrete-time model of the dynamics of Romeo and Juliet's love affair- adapted from Steven H. Strogatz's original paper, Love Affairs and Differential Equations, Mathematics Magazine, 61(1), p.35, 1988, which describes a continuous-time model. Let Run denote Romeo's feelings about Juliet on day n, and let J[n] denote Juliet's feelings about Romeo on day n. The sign of R[n] (or J[n]) indicates like or dislike. For example, if R[n] > 0, it means Romeo likes Juliet. On the other hand, R[n] 0 or hatred if R[n]