Modeling And Analysis For The Impact Of Toxins On Aquatic Populations

With the rapid development of economy and the growth of population,the consumption of natural resources has risen sharply and the environmental pollution is becoming more and more serious.A large number of toxic substances into water cause many aquatic species diminished even endangered.In order to study the influence of toxins on aquatic species,we established several toxin-dependent population models.We theoretically and numerically analyze the model and discussed the biological significances.The thesis consists of five chapters.In Chapter 1,we introduced biological background,significance and research purposes.Then,the main contents of this thesis and the preliminary knowledge were introduced.In Chapter 2,we considered an aquatic population affected by Allee effect,and constructed a toxin-dependent aquatic population.The boundedness of the solutions of the system was discussed.We found sufficient conditions on the existence and stability of equilibria.Choosing T(the toxin concentration in the aquatic environment)as a parameter,we got threshold conditions of survival and death of the population,and found that a high level of toxin concentration lead to extinction of the population,a low level of toxin concentration has little effect on the long-term behavior of the population,and moderate level of toxin concentration may produce very rich dynamic behaviors including that the survival of the population depends on the number of population at initial time.In Chapter 3,we constructed a model of aquatic population dynamics affected bytoxin with a discrete delay,in which time lag represents the incubation period(the time required for eggs to grow into adults).First of all,the delay system was linearized to obtain the distribution of characteristic roots.Secondly,the stability analysis of equilibrium points and the existence of Hopf branch were studied.The analysis shows that the system has the alternate stability and periodic solutions.Finally,using mathematical software MATLAB,we computed the Hopf bifurcation point of system,made numerical simulations to verify the theoretical results.In Chapter 4,we built a toxin-mediated population model with two discrete delays,in which time delays represent the lag effects of toxins on individual reproduction and death,respectively.We discussed the distribution of characteristic roots of linear system,obtained the sufficient conditions on the stability of equilibrium point and the existence of Hopf branch of the system,and studied the global stability of positive equilibrium point.The theoretical analysis shows when the toxin concentration is low,the reaction time to toxin causing population death can give rise to population fluctuation.Finally,using the dde23 and other function handles in the numerical simulation,we explained the biological significance of the numerical simulation results.In Chapter 5,we briefly reviewed the work and summarized main conclusions,introduced the biological and practical significance of the models in this thesis.Finally,we discussed the shortcomings of the study and suggested future research directions.