The effect of communication delay and environmental uncertainties on the evolution of love model

Abstract

This paper aims to study the effect of communication delay(the time of the first exchange in which the conflict occurred) and stochastic disturbance on human emotional relationship based on love model. It is characterized by nonlinear stochastic delay differential equations. The delay term and the random term represent the communication interval between two people and the uncertainty of the environment, respectively. Firstly, the characteristic root analysis of linear equation is carried out. Then, the system is effectively reduced by combining the central manifold theory and stochastic averaging method. On this basis, the stochastic dynamic behavior of the system is studied using $\tau$ as the bifurcation parameter. The results of theoretical analysis are verified by numerical analysis. In addition, using the communication interval of two people as a parameter, the variance graph of love between two people is obtained. As you can see, regardless of romantic style, when the communication interval exceeds the threshold, the relationship will fluctuate. So in order for the love to last long, timely communication and frequent meeting is very important. Although this paper is a simple binary relationship model, it lays a foundation for the study of more complex human emotional relationships model.