The Study Of Effects Of Disease And Impulse On Population Dynamical

Population dynamics as a branch of biological mathematics hasattracted many domestic and foreign scholars; the population dynamicsstudy has made a great progress. In the real world，One specie is not onlyaffected by other species, but also affected by internal factors and externalfactors. Those factors lead to their dynamics change. This paper mainlyconsider disease of internal factors,artificial stocking, human harvesting,pesticide spraying and immune injection of external factors, Inmathematic models, external factors features by impulsive control.This dissertation study of effects of disease and impulse onpopulation dynamical. A brief description for some background andresearch status about the subject is given in Chapter One, in this Chapter,we also given some definitions and lemmas that used in other Chapter.Chapter Two research effects of disease on population dynamicalthrough a predator-prey model with Holling type IV functional responseconsider both the populations affected by diseases. We used Mapleobtained the equilibriums of the system, the most important thing is usethe numerical simulation to see the system’s dynamics. In Chapter Threea predator-prey model with Holling type IV functional response isinvestigated with respect to impulsive control strategies of time. Theresearch of Chapter Three is in order to study effects of impulse onpopulation dynamical. In the course of studying, Firstly, some usefultheorems are obtained by using learned knowledge to make qualitativeanalysis on the models；The most important thing is that the numericalsimulation verified the correctness of qualitative analysis, At this process,bifurcation diagrams and phase plots are drawn to see effects onsystem’s dynamics of different parameters, The parameter which hasgreat influence on choice; The largest Lyapunov exponents arenumerically calculated to make a more accurate assessment on chaos；Finally, the Biological Significance of diagrams from numerical simulation is given. In Chapter Four a predator-prey model isinvestigated with respect to impulsive control strategies of time. Weconsider the survival of predator is not only affected by the population ofprey but also affected by the relative increase of prey, we use somequalitative analysis of the predator-prey model obtained the conditionsfor existence, uniqueness and orbitally asymptotically stable of1-periodic solution. we use numerical analysis to verify the correctnessof mathematical analysis.