Cycle Environment And Integrated Control Strategy Of Pest Control

Pest seriously affects production of agriculture, and cause huge losses in econ-omy. Therefore, agro-ecological sector, domestic and foreign experts are very con-cerned about the issues of controlling pest. There are many methods to control pests, such as chemical control, biological control, physical control, and combining a variety of integrated control program. In order to accurately grasp the timing of implementation of integrated pest control strategy, we not only need to understand possible ecological interactions amongst pests, natural enemies and pesticides, as well the dynamic development of pests and natural enemies, but also to know how many natural enemies should be released and how often, when pesticide applications should be made and so on. In order to solve the above problems, establishment of mathematical model for the interaction between pests and natural enemies, consid-ering about the number of various control factors on the impact of development are to be necessary.In recent decades, continuous and discrete pest-natural enemy models concern-ing IPM strategies have been investigated and developed. Such as, in 2010, sanyi Tang and his partners made the following model where x(t), y(t) are the population size of prey and predators at time t, p1 and p2 are the killing rates of pests and predators after chemical control, p3 andÏ„are the proportion and constant release of the predator population that comes from impulsive immigration.Ï„k,λm are time series of spraying insecticide and releasing of natural enemies separately. In that paper, the author studies effects of factors (pest natural enemy ratios, timing of natural enemy releases, and dosages and timing of insecticide application and so on) on IPM control programmers. This result may help people to decide optimum timing for IPM.Therefore, when considering the population growth and pest control strategies, it is necessary to study population dynamics model of periodic environment. For example, in 2002, sanyi Tang and his partners studied the non-autonomous predator-prey model the biological significance of the model's parameters are given in the reference. For the above periodic system, sanyi Tang and his partners studied the existence and stability of boundary periodic solution, as well as the branch of internal periodic solutions and so on.Based on the above two and other pest control models, we concentrate on the integrated pest control strategies that have effect on the pest-free critical conditions in periodic environment, that is, we study a non-autonomous pest-natural enemy model with chemical and biological control tacticsIn section 2, the threshold value R0, which determines the dynamical behavior of a non-autonomous pest-natural enemy system with impulsive effects, was obtained. And according to Comparison Theory and Floquet Theory, we show that if R0< 1 the pest-free periodic solution is globally stable. In section 3, we know that the pest-free periodic solution of the system is unstable with the pest uniformly persistent if R0>1. In section 4, from Standard Bifurcation Theory of impulsive differential equations, we obtain that the positive periodic solution exists when R0â†'1+. In section 5, we carefully discuss the problems that parameters space (such as impulse times, the timing of impulses, residual rates of pests and predators, constant immigration, impulse period and so on) has influence on Ro numerically, initial densities of pest and natural enemy populations have effects on pest control; At last, when a parameter is selected as a branch of the system, the system will appear the phenomenon of coexistence of attractors and other complex dynamic behavior, including:(i) periodic-doubling cascade; (ii) chaos:(iii) periodic-halving cascade; (iv) non-unique dynamics. Numerical results show that when a certain parameter has random perturbation, stable attractors will switch from one attractor to another, this conclusion has clear biological meaning in pest control.