Chaos Control Of Three Of Discrete Biological Population Systems

The research boom of chaos theory was launched in the middle of the 20 th century,and the chaos control research also appeared in the researchers’ view after the application of OGY method research.Chaos control theory has a wide range of application fields,mainly playing an important role in physics,chemistry,economics,medicine,biology and other fields.As the research progresses and the field of study opens up,chaotic control methods also present diversity: feedback control method,adaptive control method,impulse control method,etc.In this paper,based on two types of discrete population systems with time lag,two types of predator-prey systems,and two types of host-parasite systems,respectively,adaptive control methods based on Backstepping,the trajectory tracking control methods,and chaotic control methods based on BP neural networks are applied to study the chaotic control of the systems.The details of the research are as follows.(1)Chaos control study for two types of discrete population systems with time delay is studied.First,the dynamical properties of the time-delayed ecosystem and the Moran-Ricker model with time-delayed density-dependent birth rate regulation are analyzed separately,and the existence of chaotic attractors is verified by plotting the Lyapunov exponential map and bifurcation diagrams of the two types of systems.Then,the controllers of the two types of chaotic systems are designed separately by using the adaptive control method based on Backstepping.Finally,The effectiveness of the designed controller was verified by numerical simulation with Matlab.(2)Chaos control study for two types of predator-prey systems is studied.First,the dynamical properties of a discrete predator-prey system with prey refuge and food chain systems with Holling-II type and B-D type functional responses are analyzed separately,and the existence of chaotic attractors is verified by plotting the Lyapunov exponential map and bifurcation diagrams of the two types of systems.Then,the controllers of the two types of chaotic systems are designed separately by using the trajectory tracking control method.Finally,The effectiveness of the designed controller was verified by numerical simulation with Matlab.(3)Chaos control study for two types of host-parasite systems is studied.First,the host-parasite system with Hassell growth function and the host-parasitoid model with prolonged diapause for the host are analyzed dynamically and the existence of chaotic attractors is verified by plotting the Lyapunov exponential map and bifurcation diagrams of the two types of systems,respectively.Then,the control method based on BP neural network is used to design a controller.Finally,The effectiveness of the designed controller was verified by numerical simulation with Matlab.