Complex Dynamics in a Love-Triangle Model with Single-Frequency and Multiple-Frequency External Forcing

Abstract

In this paper, a new version of the nonlinear model with two women competing vehemently for an attractive man in a competitive love-triangle is proposed, which provides more insight into the dynamical behaviors of the complex love-triangle relationship. A notable and important feature of this model is that the effects of the competition, single-frequency and multiple-frequency external periodic forcing terms are introduced into the model, as environmental fluctuation on every individual in the love-triangle relationship. By analyzing the dynamical behaviors of the competitive love-triangle model through analytical techniques and numerical simulation, we find that under some simple parametric conditions, with the effects of external periodic forcing, the model gives rise to the appearance of various phenomena such as stability, quasi-limit cycles, and resonant responses. The results show that system parameters and external periodic forcing play a key role in the love-triangle relationship: system parameters can be the control parameters and their different appropriate values can produce different phenomena, while external periodic forcing can enhance or weaken the oscillations of the feeling density, and moreover, the interesting phenomenon called resonant response can occur under some suitable conditions. In this way, complex types of love feelings can be described and it is closer to the reality.