Stability And Hopf Bifurcation Of A Predator-prey Biological Economic System With Non-selective Harvesting

In recent years, the study of predator-prey biological economic system has obtained many achievements, but most researches of ecological economy model only considering the capture of a single species, and the researches of differential algebraic system with nonselective harvesting are relatively few. Actually, on the one hand, it is difficult to control to capture only a species; On the other hand, to capture more species can obtain better economic benefit. Therefore, the research for predator-prey differential algebraic system has a certain practical significance.This paper mainly studies the modified predator-prey biological economic system with nonselective harvesting, it is on the basis of predecessors’ model and considering the factor of capturing many species. This paper have discussed the model without delay and model with delays respectively, and studied the stability and Hopf branch of the system. The text is divided into four chapters:The first chapter is the introduction, which firstly introduce the research background, practical significance and research status of this paper, and then explain the main work and innovation points of this paper.The second chapter is on the basis of predecessors’ research model, considering the factor of capturing more species, we establish the modified predator-prey biological economic system with nonselective harvesting, by using the standard form and bifurcation theory of differential algebraic system to study its stability and Hopf bifurcation. Corresponding numerical simulation using Matlab are given.The third chapter is on the basis of predecessors’ research model, considering the factors of capturing more species and time delay, we establish modified predator-prey biological economic system with time delay and nonselective harvesting, by using the standard form and bifurcation theory of differential algebraic system to study its stability and Hopf bifurcation, the bifurcation direction have been discussed also. Corresponding numerical simulation using Matlab are given.The fourth chapter is the summary of the work for this article, and puts forward some problems which need to be studied further.