Impact of Delayed Decaying Corruption Effects on a Socioeconomic System with Economic Growth and Unemployment

This paper is devoted to the study of the dynamical behaviors of a socioeconomic mathematical model with a discrete time delay. The model includes economic growth, corruption, and unemployment, which are some of the main factors driving the economy of a nation. Due to the complex nonlinear nature of the relationships between the variables, our aim is to explore stable steady states, bifurcations, and limit cycles in the parameter space. We prove the existence of multiple limit cycles arising from Hopf bifurcations. In particular, we establish conditions for the existence of Hopf bifurcations and the appearance of economic limit cycles. We find threshold values for the delay in which these Hopf bifurcations occur. We provide additional support to the theoretical findings by performing numerical simulations. Various interesting socioeconomic scenarios are displayed in which limit cycles occur. The discussion and future directions of the research are presented.