We analyze the problem first discussed by S. Strogatz, which deals with the loving relationship between two people through a dynamical system. A discussion of the concepts and basic tools of Nonlinear Dynamics is done and we focuse on the asymptotic behavior for parameters values that can be interpreted as "opposite feelings" and "opposite personalities" for answer the question "do opposite attract?". We also discuss the influence of an external agent whose dynamics is governed by a nonlinear equation. Our results correspond to the phase planes for the several situations of the model as well as the Hamiltonian function for the cases of center and saddle fixed points. We conclude by quoting some physical systems that are describe by of similar functions.
love hate dynamics; differential equations; vector field; Hamiltonian function
