The Persistent Existence Analysis Of A Single-species Population In Toxicant Environment

In this paper, we mainly study the survival properties of a single-species population with stage-structure in toxicant environment in mathematicas, and build corresponding mathematical models. We respectively consider the modes with the effects of toxicant on the whole population and only on the adult individuals, and analyze the persistence and biological significance for the population of each model. This paper is divided into four chapters.In the first chapter, we briefly introduce the background of the ecological toxicolog-ical dynamics, history, significance, research progress, and differential equation stability theory and the related work of this article.In the second chapter, we establish and analyze the mathematical model of a single-species population with stage-structure under a fixed toxins input rate. We obtain the sufficient condition for the stability of the population border equilibrium, and the suffi-cient condition for the persistence of the population, that is the size of toxins input rate determines the population persistence and extinction.In the third chapter, we establish and analyze the mathematical model of a single-species population with stage-structure under a fixed toxins input rate and the effects of toxicant only on the adult individuals. we obtain the conditions for the population strong persistence.In the fourth chapter, we summarizes the main conclusions of the paper, and present the biological explanation and practical significance for these models. Through this paper, it shows that we can control the number of the population by controlling the size of the toxins input rate, so as to achieve our purpose. Finally, we point out the questions and work we should do in the further research.