Time Delay Effect on the Love Dynamical Model

TL;DR

This paper explores how time delays influence love dynamics models, revealing that delays can induce oscillations and chaos through bifurcations, with theoretical and numerical analysis confirming these phenomena.

Contribution

It provides a detailed analysis of how time delays affect love models, identifying conditions for Hopf bifurcation and chaos, which were not previously characterized.

Findings

Time delay can cause Hopf bifurcation in love dynamics.

Numerical analysis confirms bifurcation predictions.

Identifies a route to chaos via period-doubling bifurcations.

Abstract

We investigate the effect of time delay on the dynamical model of love. The local stability analysis proves that the time delay on the return function can cause a Hopf bifurcation and a cyclic love dynamics. The condition for the occurrence of the Hopf bifurcation is also clarified. Through a numerical bifurcation analysis, we confirm the theoretical predictions on the Hopf bifurcation and obtain a universal bifurcation structure consisting of a supercritical Hopf bifurcation and a cascade of period-doubling bifurcations, i.e., a period doubling route to chaos.