With Constant Harvest Rate Of Predator - Prey Model For Qualitative Analysis

It is well known that populations are frequently subjected to outside attacks as the nature becomes complex day by day. For example, the changes of natural environment, climatic conditions play important influence on populations. It is par-ticularly important that the biological populations in nature suffer the incursions largely from the human beings. With the development of technology, the influence of human beings'activity on the nature has been enlarged increasingly, such as killing the biological populations, artificial breeding and migration, which all lay much in-fluence on the populations' density, structure and spatial distribution. Concerning the conservation for the long-term benefits of human beings and the sustained use of resources, it is necessary to consider the human beings'factor in the Population Dy-namics to gain insights in the scientific management of renewable resources. Thus, a ratio-dependent predator-prey model, which is subjected to the reaction-diffusion system with constant harvest in the prey, is investigated. where u and v, respectively, stand for population densities of prey and predator; d1, d2, a, b, c, are positive constants, d1, d2 are diffusive coefficients; a, c, b denote the predator capturing rate, death rate and conversion rate. The positive constant h represents the rate of harvesting. The main contents in this paper are as follows.In the first chapter, we study the coexistence of the model with homogeneous Neumann boundary condition First, longtime behavior of solution, the turing instability and asymptotical stability of positive constant solution are given. We get the conclusion that the constant-rate h impacts on the uniform persistence of the solution, and when 0