Dynamics of an opinion model with threshold-type delay

Abstract

• We developed a mathematical model of threshold-type delay differential equations • The model describes the relationship between two subpopulations with opposite opinions and the opinion spread dynamics. • We performed mathematical analysis and simulations of the model. • The model exhibits either a forward transcritical or a backward bifurcation. • The model can predict the threshold level of convinced individuals of one opinion that are needed to achieve consensus. • The model is able to study the impact of relevant parameters of the model on the achievement of the consensus. The process of opinion formation rarely boils down to accepting or rejecting the social consensus of others, despite the considerable research (since Sch, 1956 [5] ) that has been focused on such situations. In this paper, we propose a mathematical model of threshold-type delay differential equations describing the relationship between two subpopulations with opposite opinions and the opinion spread dynamics. We study the quantitative as well as qualitative properties of our model, and we present results on positivity and boundedness, local stability of equilibria and global stability of the boundary state under certain conditions. Further analysis of the model show that the system exhibits either a forward transcritical or a backward bifurcation. Furthermore, numerical simulations and sensitivity analysis are performed to study the impact of the relevant parameters of the model on the achievement of the consensus.