Study On The Dynamic Complexity Of Integrated Pest Management Filippov Model With Group Defense

In recent years,the species of pests have increased year by year and the scale has shown a trend of expansion,which has brought many serious negative impacts on agricultural production.Considering that the pest population has group defense behavior and chemical control and biological control are applied,in this thesis,integrated pest management Filippov models with group defense behavior are established,and their dynamic complexities are systematically discussed.In the first chapter,some basic knowledge of this thesis is introduced.In the second chapter,an integrated pest management Filippov model with group defense behavior is established,and we take the population density of pests as the control index of integrated pest management and assume that the releasing rate of natural enemies is linear.Firstly,the dynamics of the two subsystems of Filippov system are analyzed respectively.Next,taking the case where both subsystems have a globally asymptotically stable equilibrium point as an example,the global dynamics of Filippov system are analyzed,which includes the existence conditions of sliding mode,real equilibrium,virtual equilibrium and pseudo equilibrium,the analysis of the globally asymptotic stability of equilibria,the existence region of sliding mode and pseudo equilibrium,boundary equilibrium bifurcation and relevant parameters bifurcation and so on.Finally,we study the complex dynamics for Filippov system when other phenomena such as an unstable interior equilibrium or a stable limit cycle occur in the two subsystems by using numerical simulations.The results show that although there are no closed orbits in the two subsystems,it may exist a stable limit cycle and other complex dynamics for Filippov system after switching perturbation.In the third chapter,considering constant releasing rate of natural enemies,based on the model proposed in the second chapter,an integrated pest management Filippov model with group defense is established.Firstly,the dynamics of the subsystems of Filippov system are analyzed.Next,the sliding mode,the dynamics of the sliding system and the types of equilibria of Filippov system are discussed.Then,the complex dynamics of Filippov system are studied by numerical simulations when there is a globally asymptotically stable limit cycle and a globally asymptotically stable equilibrium in two subsystems,respectively.Finally,the existence region of sliding mode and pseudo equilibrium,and the complex dynamics of Filippov system such as boundary equilibrium bifurcation,the grazing bifurcation,the buckling bifurcation and the crossing bifurcation are analyzed.The research shows that paying attention to the changes of key parameter values for Filippov system,adjusting reasonable control measures can prevent the density of pest populations from exceeding economic injury level and large-scale outbreaks of pest populations and avoid bringing huge economic losses to agricultural production.