| Pest prevention and control has been attached great importance by the agricul-tural departments as well as the management departments due to the stochastic out-break and the complexity of control measures.In the early days,chemical pesticides have played important roles in the pest control,mainly because of their convenience,low price and an instant effect.However,the abuse of pesticides can also inevitably bring some negative effects such as the pest resistance,the large-scale outbreak of pests and the pest recurrence,etc.Therefore,a number of control methods have been proposed through long-term practice,including chemical,physical and biologi-cal methods.Integrated Pest Management(IPM)is a combination of the above three tactics,which aims at the maximization of economic benefits.With the combination of the dynamical interaction between pests and their natural enemy populations and the implement of the comprehensive control strategies,the study put,forward the best control measure,in the hope of keeping the pest population under Economic Injury Levels(EIL),The application of those measures has not only timeliness and transient effects,but it also has made a crucial difference in the pest control because of the dynamical interaction based on intra-specific cooperation,and even the en-vironmental randomness.Based on the above-mentioned factors,the core purpose of this study is to creatively develop the ecosystem of natural enemies of pests with transient effect,and then to investigate the effects of environmental randomness on those ecosystems.To achieve these goals,this study proposes a state-dependent pest-natural enemy ecosystem with group defense,a Filippov ecosystem with IPM strategy,and a stochastic perturbation ecosystem with impulsive control strategy.And then after the development of some theoretical derivations,qualitative analysis,numerical simulations the comprehensive and systematic research on the model,the study revealed that t.hose ecosystems have complex and rich biological implications and discussed the optimal strategies for pest control in the hope of providing some suggestions for pest control and ecological management.In the second part,a non-smooth ecosystem with group defense is proposed and analyzed to study the impact of the relationship between pest and natural enemy on IPM strategy.Firstly,the existence and stability of a boundary order-1 periodic solution were investigated and the threshold conditions for a transcritical bifurcation and stable switching related to the boundary order-1 periodic solution were obtained.Furthermore,the definition and properties including monotonicity and discontinuity of the Poincare map determined by the proposed impacting system are discussed,which were used to reveal the existence and global stability of an order-1 periodic solution.The main results indicate that multiple discontinuous point,s of the Poincare map could induce the coexistence of multiple order-1 periodic solutions.Moreover,numerical analyses reveal the complex dynamics of the model including periodic adding and halving bifurcations,which could result in multiple active phases,among them rapid spiking and quiescence phases which can switch from one to another and consequently create complex bursting patterns.The main results reveal that it is beneficial to restore the stability and balance of an ecosystem for species with group defence by moderately reducing population densities and the group defence capacity.However,weak or strong pest control not only increases the amplitude of the pest population,but also aggravates the extinction of natural enemies,even when pesticides have no influence on the latter.Thus,the control strategy should be modest and it is crucial to maintain the balance between pests and natural enemies.Based on a non-smooth ecosystem with group defense,in the third part,Filip-pov non-smoot.h pest-natural enemy model with intermittent IPM strategy is pro-posed to investigate the effects of threshold strategy on IPM.According to the qual-itative analysis techniques and numerical analysis method of Filippov non-smooth system,the proposed model has been analyzed theoretica.lly by taking advantage of qualitat.ive analysis techniques and numerical simulation firstly.Especially,we focus on the sliding mode dynamics,the existence,and stabilit.y of several equilibrium are discussed.The results reveal that two real equilibrium and one pseudo-equilibriun can coexist.After that,we did a further research on the local and global sliding bifurcations including Boundary-Node(Boundary-Focus)bifurcation,Grazing bi-furcation,Crossing bifurcation and Buckling bifurcation(Sliding switching).Those complex sliding bifurcations reveal that the proposed Filippov system exists multi-attractors coexistence including equilibrium and crossing cycle,which indicates that there exists a close relationship between the intermittent control strategy and the initial densities of both populations.Similarly,the global stabilities of real equi-librium and pseudo-equilibrium of sub-systems show that non-smooth pest control strategy can effectively control the pests under the given Economic Threshold(ET)to achieve the aim of IPM strategy.In the last part,this study focuses on the impact of environmental random on IPM strategies.Firstly,a fixed-time stochastic pest-natural enemy ecosystem with IPM strategies is proposed,in which the local,global existence of positive solution and the boundedness of expectation are discussed in detail,and the sufficient condition for the extinction of pest population with probability-1 is given.Then,with the establishment of a state-dependent stochastic predator-prey ecosystem with IPM strategies and the development of the numerical simulations and methods,the effects of ambient noise intensity on pest outbreak are discussed.The result shows that there is a close relationship between the frequency of pest outbreak,ET,the environmental perturbation intensity and control measures.The larger the value of ET is,the slower the pest-outbreak frequency becomes.Besides,the perturbation intensity also has a great impa.ct on pest population.The greater the impact of the perturbation intensity on pest population is,the lower the pest-outbreak frequency becomes.And the opposite is true for their natural enemies.We can also reduce the pest-outbreak frequency by increasing the intensity of control measures.Finally,this study help us to understand the impact of random factors on pest-outbreak frequency by theoretical derivations and numerical simulations,the results have directive significance in the design of an optimal control strategy for the department of ecological agriculture. |
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