Dynamics Analysis And Control Of Two Classes Of Fractional Order Three Species Food Chain Systems

It is a hot topic in the biomathematics research to explore the change regulations of species in nature,predict the development trends,take artificial intervention measures actively to regulate the development dynamics of species,and realize the protection of the ecosystem.It is of great theoretical significance and practical value to study the predation relationship among species of the multi-species food chain system,analyze and summarize the internal regulation,gain insights into the change trends of the species in the future,and regulate the stability of the species.Fractional calculus is increasingly used in various fields due to its unique superiority.Applying fractional order calculus to the species system can more accurately describe and analyze the evolution of each species.In the thesis,based on the existing integer order three species food chain system,two classes of three species fractional order food chain system are proposed,and the dynamics behaviors and control of the system are analyzed by the theory of fractional stability.Based on a class of three species integer order food chain system with feedback saturation function,the corresponding fractional order system is presented,the dynamic behavior of the system is studied,and the order domain of the system with chaos is determined.The nonlinear analysis methods such as bifurcation theory and Lyapunov exponents are used to explore the influence of different order parameters on the system dynamics,and the influence of the corresponding environmental conditions on the system is confirmed.At the same time,the nonlinear control terms are added to regulate the fractional order system,the V function is used to determine the range of control parameters that make the controlled system globally asymptotically stable at the positive equilibrium point,and the global stability of the system of the controlled system at the positive equilibrium point is proved,the numerical simulations prove the system is controlled to stable.Based on a class of ratio-related three species integer order food chain model,the corresponding fractional order system is proposed.The state evolution of the fractional order system is studied.The dynamic behaviors of the integer order system and the corresponding fraction order system are compared and analyzed.By designing the control terms and constructing the V function,the global asymptotic stability of the controlled system at the equilibrium point is proved,the ranges of the control parameters are determined,and the correctness of the method is verified by numerical simulation.The study of the fractional order food chain system in the thesis confirms the importance of order selection.The control of the fractional order food chain system provides theoretical guidance for artificial adjusting the dynamics of the food chain system.