Study On The Dynamics Of Non-smooth Filippov Forest-pest Model

Pests will increase the mortality rate of forests,which in turn affects the carbon cycle,leading to air pollution.Thus,it is critical to handle the problem of pest control in forest ecosystems.In order to solve this problem,it is necessary to build a mathematical model to investigate the relationship between forest and pest populations,and consider taking reasonable measures to control pests,so as to achieve the best economic effect and reduce the adverse impact on the environment.This paper is mainly based on integrated pest management strategies,and employing a threshold control strategy to achieve it,that is when the number of pest populations increases and exceeds a certain economic threshold,take measures to reduce its number;when the number of pest populations is less than the threshold,no action is taken.However,the Filippov system can describe this process well.Therefore,this paper considers establishing the Filippov forest-pest model to explore it.The main research results of this paper are as follows:1.Assuming that the pests are herbivorous insects,based on the tree-beetle model,combining the threshold control strategy with the integrated pest management strategy,a Filippov forest-pest model with threshold control strategy is proposed.First,using the Shengjin formula of the one-variable cubic equation and stability theory,not only the existence conditions of equilibria of the two subsystems of the system are obtained,but also their stability conditions.Secondly,using the related theory of the Filippov system,not only the sliding dynamics,the nullclines,and equilibria of the system are discussed,but also the conditions for the coexistence of various equilibria are given.Then,using sliding bifurcations,four cases of the subsystems with different numbers of equilibrium points are discussed,and the influence of the threshold on the system and pest control strategies is further explored.The bifurcation analysis not only reveals the rich dynamics of the system,including sliding limit cycles,bistable states,and stable refuge equilibrium points,but also shows that adopting appropriate strategies can effectively control pest outbreaks.Through detailed analysis of sliding bifurcations,the actual biological significance related to pest control is obtained,which provides ideas for designing better strategies.2.Considering the influence of human factors,based on the forest-pest model,the threshold control strategy and the integrated pest management strategy are combined to establish a Filippov forest-pest model with external periodic disturbances.First,using the related theory of the Filippov system,the sliding dynamics of the system are discussed.The sliding region and sliding period solutions are obtained,and the relationship between them is discussed.Secondly,using the bifurcation of key parameters,it is revealed that the system has abundant dynamic behaviors,including the phenomenon that the bifurcation-adding and chaotic regions alternate,and multiple attractors coexist.Then,using wave coherence,the relationship between the time series of two coexisting attractors in the time-frequency space is detected.Finally,the sensitivity analysis of key parameters shows that these key parameters have impacts on the system and pest control strategies,and play a significant part in exploring the impact of periodic forcing and threshold control strategies on the system and obtaining better control measures.