A delay dynamic model of love affair with cautious partners

We investigate love dynamics of two individuals in a delay love affair model in which both are assumed to be cautious, the most natural romantic style. The local stability analysis proves first that the steady state is fairly stable when there are no delays and second that solving the characteristic equation generates a set of positive delays for which the steady state loses stability. Through numerical analysis, we confirm the following three main results: (1) cyclic oscillations of love feeling emerge via Hopf bifurcation; (2) multiple delays cause the double edge effect implying that alternation of stability and instability repeatedly occurs; (3) complicated dynamics involving chaotic oscillations emerges and then merges to a limit cycle as the length of one delay increases with fixed values of the other delay.