Qualitative Analysis Of Multi-Species Ecological Model With Feedback Control

The Lotka-Volterra ecological model describes the growth pattern of biological populations and is a very important type of ecosystem model in population dynamics research.Its research can help humans better understand nature,protect nature,and provide a theoretical basis for realizing the harmonious coexistence of humans and nature.Compared with the traditional Lotka-Volterra ecosystem model,there are still few studies on multi-species ecological models with feedback control.In view of this,based on the previous work,this paper extends the traditional Lotka-Volterra ecological model and analyzes the dynamics of several kinds of ecological models with feedback control.The specific contents are as follows:1.A class of three-species Lotka-Volterra cooperative and competitive model with feedback control and time-delay is studied.By using the comparison theorem of differential equation and other theorems based on the comparison theorem of differential equation,the sufficient conditions for the system to be permanent are obtained.The sufficient conditions for the global asymptotic stability of the system are obtained by constructing a suitable Lyapunov function.Finally,the correctness of the theoretical analysis is verified by the numerical simulation,and compared with the system without feedback control,the effect of feedback control on the system is discussed.2.A class of three-species Lotka-Volterra multi-delay predator-prey model with feedback control and prey diffusion is studied.On the basis of the first part,we add "diffusion term" between two prey-species,the sufficient conditions for the permanent and global asymptotic stability of the system are obtained by using the comparison theorems of differential equation and constructing suitable Lyapunov functions.Finally,the correctness of the theoretical analysis is verified by using the software of MATLAB.3.A class of three-species Lotka-Volterra multi-delay and ratio-dependent food-chain predator-prey model with feedback control is studied.Based on the first part of our study,we introduce the "ratio-dependent term",by using the comparison theorem of differential equation and some inequality techniques to obtain the sufficient conditions for the system to be permanent.The sufficient conditions for the global asymptotic stability of the system are obtained by constructing an appropriate Lyapunov function.Finally,the feasibility of theoretical analysis is verified by numerical simulation.4.A class of three species multi-delay Lotka-Volterra ratio-dependent predator-prey model with feedback control and prey diffusion is investigated.Further improve the model has been discussed,by using the comparison theorem of differential equation and constructing suitable Lyapunov functions and developing some new analytical techniques,some sufficient conditions which guarantees the permanent and global asymptotic stability of this system are obtained.Finally,the system is simulated by MATLAB to verify the correctness of the theoretical analysis.