Consider the general dating forecast model for potentially star-crossed lovers,
ID: 2248002 • Letter: C
Question
Consider the general dating forecast model for potentially star-crossed lovers, Romeo and Juliet, given by R' = aR + bJ and J' = cR + dJ. Assume R(t) indicates Romeo’s feelings for Juliet as a function of time (more positive indicates deeper love and more negative indicates deeper hate). Similarly, assume J(t) indicates Juliet’s feelings for Romeo. Suppose now, however, Romeo (R), a newly changed man, adopts a novel strategy in romancing Juliet (J). The resultant dynamical system is given as below:
R' = R + J(1 J 2 )
J' = 4R + J.
Provide an interpretation of Romeo’s new behavior.
Explanation / Answer
R' is a function of R and J, for there to be enough love the function in R with respect to time should be positive.
For R' to be positive R should be positive and R> J (J2-1)
R's behavior depends on J's behavior, if J' decreases then R will have to increase to counter balance it and to maintain R' positive. R' will become negative if R <J (J2-1).
In any case', J is a function of positive coefficient of R and J, hence J' will only decrease if J <-4, when J'decreases the value of J (1-J2) in R' will be negative thus R's value needs to be greater than Juliet's love to maintain the love or it's going to be a hate relationship.