Analysis Of The Behavior Of Population Dynamics Of System With Stage Structure In The Effects Of Toxicants

The progress of science and technology not only improves the development of the economy but also improves the level of human life, but it becomes worse that the prob-lem of the pollution, especially with the continuous expansion of industrial produc-tion, further increasing environmental pollution. If we don’t pay attention to this sit-uation, biological populations’living environment will be severely affected.Population ecology has important guiding role and practical significance to people’s daily production practice, it is always a hot topic that many scholars research of the im-pact of environmental pollution with survival of species when the increasing deterioration of the environment.We always only consider the evolution of the species as a whole when species model was studied, which is not reasonable. On the one hand, there is obvious differences that species have different physiology in different life stages, on the other hand, there are interaction factors in different stages of population, all of these factors have different influences with survival of species. It has more practical significance that considering species model with stage structure.So, we should establish a reasonable system to discuss the survival of species. It plays a significant role to maintain the diversity of ecological species. In order to formu-late the corresponding environmental protection measures to make the survival of species permanent, that the method of qualitative analysis can be used to discuss the population model and we can predict the development and change of species under the pollution of the environment.This paper is organized as follows:First of all, the first and second chapter is about the research status and preliminary knowledge.Secondly, the single species population model of two stages was considered in the third chapter (mature and immature populations affected by toxins), with the aid of ordinary differential equations related theory method was applied that we proved that the solutions of the system are ultimate bounded and positive equilibrium point and the origin is stable and the conditions were obtained that the population continued survival and extinction, the global stability for periodic solutions is proved. In the end, the numerical simulations are used to prove the relevant conclusions by matlab software.Thirdly, the interaction between stages structure model of the single species popula-tion affected by toxins was discussed, the boundness of positive solutions is proved, the permanence and extinction is obtained while taking the relevant results of periodic so-lutions into account. Finally, the numerical simulations are used to prove the relevant conclusions.In the fifth chapter, the model of predator-prey with the effects of toxicant is con-sidered, we discussed the same problem with fourth chapter and the relevant conclusions are obtained. Lastly the conclusion of this chapter is proved by numerical simulation.In this chapter, we take the system of predator-prey with the effects of toxicant (prey has two stages and canniblism) into consideration. Discussing the prey-predator system model for survival and periodic solution of relevant conclusions. In the end, the conclusion of this parts is proved by numerical simulation.Finally, the paper was summarized and put forward the direction of the further dis-cussion; acknowledgement; references.