Optimal Pulse Control Problems In Pest Control Management

The pest management plays an important part in the agricultural production.Math-ematical models of differential equations are only too significant for describing dynamic behaviors of the pest population.Since the breeding and the harm of pests and people's control behaviors are almost periodical in the real world,especially applying impulsive differential equations to describe dynamic behaviors of the pest population can respect various change rules more reasonably and accurately.The optimal impulsive control problem is always a hot research topic,and it achieves the sound integrated pest man-agement purpose.In this paper,the problems of optimizing variables,numbers and delays in the pest regulation have been analyzed and researched in-depth.In the second section,we investigated the optimal impulsive management of pest growth model aiming at minimizing the amount of pests at the terminal time.In this op-timization process,by means of time-scaling and time translation transformation tech-niques,the gradient formulas of the cost function with respect to impulsive releasing amount and timing of natural enemies are given for three cases.First,the impulsive and optimized releasing amount of natural enemies are supposed to be the same at every fixed release time(amount control).Second,the releasing timing and amount of natu-ral enemies,though equal,are not fixed,and needed to be optimized(timing control).Third,the releasing timing and non-equal amounts of natural enemies are not fixed and to be optimized(mixed control).Based on the gradient formulas and the designed algorithm,we find the optimal impulsive releasing times and amounts of enemies by numerical simulations.And the mixed control strategy is illustrated to be the best strat-egy through comparing the three optimal control strategies with the same initial control parameters.In addition,simulations indicate that the optimization of governance poli-cies may increase the periodic oscillation amplitude of populations,but ultimately it will reduce the amount of pests and lower the cost.Furthermore,our optimal biological interference strategies are superior to those in many literatures in which the enemy is released by the fixed amount at the fixed time.In the third chapter,considering not taking the lag of parasitic eggs,the lag effec-t of pesticide poisoning and the age of releasing natural enemies as control variables,combined with the crop fertility cycle,researches on the optimization problem of pest control models at seedling stage,bud stage and filling stage of crops fill in a gap un-til now.Firstly,a generalized hybrid optimization problem involving state delay with characteristic times and parameter control is presented.Then an algorithm based on gra-dient computation is given.Finally,two examples in agroecological system are given to exhibit the effectiveness of the proposed optimization algorithm.