| For the past many years, scholars have studied a large number of age-dependent and individual size-dependent biological systems, and discussed the optimal control problems. The relevant research results have been applied to practice, which guides people to exploit the biological systems and utilize the renewable resources. But little research has been done on the optimal control problems of the biological competitive species affected by the en-vironmental pollution. With the development of China’s modernized industry, there are an increasing amount of pollution. Environmental pollution not only affects the survival and health of human, but also affects the growth of a variety of species. The environmentally polluted biological species have largely attracted people’s attention. Therefore, the study on the polluted biological species is of more practical value. This paper studies the optimal control strategy for the polluted biological competative species, and then discusses the sta-bility conditions of equilibrium solution for a class of nonlinear species with size structure. According to the contents, this paper is divided into three chapters:In the first chapter, we illustrate the background knowledge, including research status.In the second chapter, we demonstrate the optimal control strategy for the non-linear biological competative species under the environmental pollution. We first use the fixed point theorem to prove the uniqueness of the solution to the polluted biological competative species, and then employs the cut-cone method to deduce the optimality conditions of the optimal control.In the third chapter, we f’ocuse on the stability conditions of the equilibrium solution to a class of nonlinear species with size structure. Then it illustrates the uniqueness and ex-pressions of the equilibrium and exploits the characteristic equation of the biological system so as to obtain the equilibrium stability condition. |
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