A general framework for the exact stability analysis of love dynamics with four independent time delays

Abstract

We investigate the asymptotic stability of a linear love model with four independent time delays to mimic the complicated human emotions more precisely compared with the classic Strogatz model. These four delays stem from the perception of their own past emotions and their partner's past emotions for both individuals. The central idea is to exactly ascertain the stability switching boundaries where the emotions of these two individuals change in the domain of delays. For this, we propose a general stability analysis framework synthesizing the Dixon resultant theory, the frequency sweeping technique, and the cluster treatment of characteristic roots (CTCR) paradigm. We then present a detailed procedure of this framework to particularly study how one partner reacts to the other. Finally, we demonstrate the effectiveness of this framework through a case study and then provide some suggestions for the couple to achieve a sweet love relationship.