Dynamic Behavior Analysis And Application Of The Single Population Capture Model In The Polluted Environment

The single population is the basic unit of the entire ecosystem.The study of single population model is the basis for the study of multi population models.As we all know,the environmental pollution problem caused by the rapid development of modern industry and agriculture and other production activities have become one of the most important ecological problems.The serious pollution of the ecological environment has threatened the survival of species.In order to study the problem of population survival in the polluted environment,two kinds of single population models and the food chain model in the polluted environment are mainly established,and the dynamic behavior of these models are analyzed in detail.Main works are as follows:In the second chapter,a single population model in contaminated environment is established considering the nonlinear relationship between the intrinsic growth rate of the population and the concentration of toxin in vivo.First of all,the nonnegativity and boundedness of the model solution were proved by the principle of comparison.Then,by using the second comparison theorem of ordinary differential equations and the definition of sequence limit,sufficient conditions for population consistent persistence,population weak persistence and extinction were proved,and the threshold between population persistence and extinction was obtained.The correctness of these theoretical results was verified by numerical simulations.At last,the optimal capture rate and the maximum sustained yield were calculated.In the third chapter,the stochastic single population capture model in the polluted environment is established under the random interference of white noise and color noise.Comprehensive utilization of Ito formula,Chebyshev inequality,stochastic comparison theorem,martingale strong law of large numbers,Borel-Cantalli lemma,the exponential martingale inequality and other related knowl-edges,we analyzed the dynamic behavior of the stochastic single population model,proved that the white noise was not conducive to the growth of population,the sta-tionary distribution of colored noise played a decisive role on the weak persistence and extinction of population.We also obtained sufficient conditions for population stochastic persistence,stochastic averaging weak persistence and extinction,and the threshold between stochastic averaging weak persistence and extinction.Finally,the optimal capture capture rate and the maximum sustained yield are obtained when the input of the toxin is a constant.In the fourth chapter,the food chain model in the polluted environment is established by considering the influence of the contaminated organisms on human health.First,according to the second comparison theorem,the nonnegativity and boundedness of the model solution is proved.On the background of second Songhua River mercury pollution events,accessed to relevant research literature data exten-sively and combined with our model,the release amount of mercury in the next ten years and the daily safety consumption amount of fish for the fishermen near the river were obtained.