A two-dimensional logistic model for the interaction of demand and supply and its bifurcations

A two-dimensional logistic model is used to describe the interactions and evolution of potential demand and supply. It is assumed that the demand policies will change the growth capacity of the demand and a parameter is introduced to describe its effect. The qualitative analysis shows that the parameter will affect the dynamical behavior of the system. Bifurcations of the system under different conditions are obtained. Under certain conditions, a small shift of policies may cause a sudden change of the demand.