Optimal And Optimization Control Of The Fold Ecosystem With Impulsive Effects

It is well known that the aphid population does the main damage to the wheat growth,with its higher rate of reproduction, its shorter life and the higher frequency of outbreak.Therefore, the control of aphid population is related to the wheat growth of wheat and theyield of wheat. Under the background, according to the principles of ecology and economicsin this paper, several management models of ecosystem for the aphid population based onfold catastrophe are proposed. Using the optimal impulsive control principle, the optimizationimpulsive control principle and the impulsive control principle, the controllers are designed tomake aphid population reach the level which does not harm to the growth of crops. Thecontents are as follows:Firstly, on the basis of the fold catastrophe model for the aphid population ecosystem,the corresponding optimal management model is given. According to the optimal impulsivecontrol principle, the controller is designed to obtain the optimal impulsive moments and tominimize the cost of spraying pesticide. The study provides the theoretical foundation forcrop management.Second, on the basis of the fold catastrophe model for the aphid population ecosystem,the corresponding optimization management model is got. According to the optimizationimpulsive control principle, controller is designed to eliminate the catastrophe phenomenon ofaphid population ecosystem.Thirdly, on the basis of the fold catastrophe model for the aphid population ecosystem,the corresponding aphid population ecosystem model with impulsive effects is built up. Themodel is analyzed with the qualitative theory of impulsive differential equations. Using theimpulsive control principle, the controller is designed to avoid the catastrophe phenomenon ofaphid population ecosystem and to protect the population diversity.