The Control Research And Stability Analysis Based On Species And Innovation Risk Spreading Models

In order to maintain the sustainable development state of nature, it is found that many practics system can be abstracted as mathematics model, and we also learn the character of systems through analyze these mathematical models. In the resources reasonable use and control has far-reaching significance. However, the most important condition to make sure a system work normally is stable. The time delay can destroy the stability of the system at the equilibrium point, make the system produce some behavior more complex dynamic than before, In this paper, two widely studied model--the predator-prey model and innovation risk propagation model based on the time delay were improved, which made the model closer to reality.Firstly, a predator-prey control model with two delays, parameter adjustment and feedback control for the predator is investigated. Choosing the two delays as the bifurcation parameter, according to the Routh-Hurwize discriminant method, we obtained the local stability at the balance, utilizing Hopf bifurcation theorem, the existence of Hopf bifurcation is established. Finally, the effectiveness of the controller is verified by numerical simulation.Secondly, construct a delayed propagation model of within the industrial cluster innovation, the enterprise as the ecological system of the species, constitute the organization of industrial clusters ecosystem and environment. According to the characteristic of biological in the spread of infectious disease in the population, based on the Routh-Hurwize discriminant method, the stability of the model at the equilibrium point is analyzed. By constructing suitable lyapunov function to analyze the global stability of the model. Finally, using numerical simulation to analysis the factors of risk propagation, and propose the risk control strategies.