Research on a 3D Predator-Prey Evolutionary System in Real Estate Market

الملخص EN

This paper establishes a model on the upstream and downstream relationship among private enterprises, provincial and local officials, and the central government in the real estate market using the population ecology theory of mutual relations among individual species from the perspective of business ecosystem.

A dynamic model is introduced and the complex dynamical behaviors of such a predator-prey model are investigated by means of numerical simulation.

The local stability conditions and complex dynamics are investigated, and the existence of chaos is discussed in the sense of Marotto theorem; bifurcation diagrams, Lyapunov exponents, sensitivity analysis for initial values, and time history figure of the system are mapped out and discussed.

This shows that there are two routes to complicated dynamics, one of which is the cascade of flip bifurcations resulting in periodic cycles (and chaos), and the other one is Neimark-Sacker bifurcation which produces attractive invariant closed curves.

We arrive at conclusions that the phenomenon of chaos is harmful to private enterprises, and unstable behavior is often unfavorable.

Thus, linear feedback control is applied to drive the model to a stable state when the system exhibits chaotic behaviors, achieving the goal of eliminating the negative effects to a large extent.