| Dynamic system theory and methods are widely used in many fields such as natural science,engineering technology and social science.In the application of dynamic system theory and method in life science,many branches have been formed,such as cell dynamics,infectious disease dynamics,population dynamics,neural network dynamics,and so on.Among which,infectious disease dynamics and population dynamics are the most classical fields.The dynamic analysis of plant disease model and predator-prey model is an important part of the research content of infectious disease dynamics and population dynamics.In this paper,a model of plant disease caused by tomato spotted wilt virus transmitted by western flower thrips was established by using the method of compartment modeling,and its dynamic behavior was studied.Through sensitivity analysis of system parameters,targeted prevention and control strategies were proposed.Secondly,due to the existence of various disturbances in the real ecosystem,they may lead to fundamental changes in the dynamic behavior of the population.Therefore,this paper studies the dynamic behavior of a discrete-time predator-prey model,and points out that bifurcation phenomenon will occur when the system is disturbed.In addition,since bifurcation is sometimes regarded as a bad phenomenon in practical problems,this paper provides a bifurcation control strategy to control the bifurcation of the system.The first chapter is the introduction.It mainly introduces the research background and current situation of plant disease dynamics and discrete-time population dynamics,and expounds the main work of this paper.The second chapter is the basic theory.It mainly introduces the related theories and concepts of dynamic system,including the concepts of continuous dynamic system and discrete dynamic system;the concepts of equilibrium point and fixed point;the concepts of hyperbolic and non hyperbolic;the concepts of equilibrium point stability and fixed point stability and their judgment theorems;the local bifurcation theory of discrete-time system,for example,saddle node bifurcation,transcritical bifurcation,fork bifurcation and period doubling bifurcation,Neimark-Sacker bifurcation and their generating conditions,and so on.In chapter 3,a 6 dimensional model of plant diseases caused by tomato spotted wilt virus transmitted by western flower thrips is established.Compared with other people’s work,this paper mainly consider the disease resistance factors and the disease exposed period of plants,and adopt different nonlinear incidence rates.In the modeling process,we consider that plants can be infected not only by the infected western flower thrips,but also by the infected plants through the sap.For the established model,we analyze the positive invariance and uniform persistence of the system,and obtain the basic reproduction number R0 to distinguish whether the disease is epidemic or not.The conditions for the existence of the equilibrium point are given.It is prove that the disease-free equilibrium is globally asymptotically stable when R0<1,is unstable when R0>1.Under certain conditions,we prove that the endemic equilibrium is locally asymptotically stable when R0>1,and give a sufficient condition for the endemic equilibrium to be globally asymptotically stable.Finally,numerical simulation is given to verify the correctness of the theoretical analysis,and the effects of plant disease resistance and disease infection rate on R0 are investigated.It is pointed out that improving plant resistance alone is not enough in controlling plant diseases,but also needs to be combined with reducing the contact rate of susceptible plants and infected vectors or infected plants in order to effectively control the spread of disease.In chapter 4,for a discrete-time predator-prey model we prove that the system has at most three fixed points,and give the necessary and sufficient conditions for the existence of different number of fixed points.According to the bifurcation theory,we prove that the system will have transcritical bifurcation and Neimark-Sacker bifurcation.We use a hybrid control strategy based on feedback control strategy and parameter disturbance to control the NeimarkSacker bifurcation.Finally,numerical simulation is given to verify the correctness of the theory and the effectiveness of the control strategy.In chapter 5,the work of this paper is summarized and the future work is prospected. |
