Mathematical Study On A Single Species Model With Pollution Treatment

With the globalization of economy and trade, environmental pollution increasinglybecomes one of the most serious problems faced by all the countries in the world.Environmental pollution is a major contributor to species extinction or near extinction and thefurther reduction of biodiversity. Based on the biological background mentioned above，toprotect endangered species, in this paper we establish and study a single-species model withperiodic impulsive pollution treatment at fixed time.In Chapter1, we introduce our research background and give some preliminaries.In Chapter2, based on impulsive differential equation, we investigate the dynamics of asingle-species model with impulsive pollution treatment at fixed time in a pollutedenvironment. Sufficient conditions for permanence and extinction of the population areobtained. We show that there exists a unique positive periodic solution which is globalasymptotically stable under permanent condition. Besides, according to practical problems,we will consider constructing a hybrid impulsive single species model combining periodicpollution treatment at fixed time with state-dependent pollution treatment applied when thepollution concentration reaches the given Environment Threshold (ET). and give specificbiological explanations based on numerical simulations and our conclusion will provide thetheoretical decision-making basis for practical problems.In Chapter3, we establish a single-species stage-structured model with impulsivepollution treatment and time delay in a polluted environment. We show that the species ispermanent when the impulsive period is less than some critical value, otherwise the species isextinct.Moreover, at the end of each chapter, by using mathematical software such as Matlaband Maple, we give some numerical simulations results which confirm the theoreticalconclusions.