Solutions For Classes Of Biological Competition Model

Nineteen twenties, kinetic theory is the theory of diferential equations in thebiological sciences was the first application of the United States of America, thediferential equation model of population geneticist Lotka and Italy mathematicianVolterra were established in the study of chemical reaction and fish ecological com-petition system, the interaction between biological population and environmentalecology, the interaction between population and population can also be used todescribe the dynamic method, and the resulting population dynamics, in addition,the human neural network, population genetic, cultivation of microorganism, bi-ological evolution and so on can be used in dynamic approach to research. Weknow life phenomena are very complex, mathematical problems from biology. It isoften very complex, so we need to establish the corresponding mathematical model,quantization group of species between the numbers of growth by the relationshipof environmental constraints, and provide a theoretical basis for the survival anddevelopment of population over the long term.In this paper, by analyzing the relationship between the ecological environmen-t, competition and predation models of several species mainly study and discuss theecological environment. The real form of this relationship in the nature that pop-ulation along with the change of time. On the basis of previous work, this paperstudies a class of N species Lotka-Volterra competition model with impulse andfeedback. Add the pulse condition in the situation with feedback control, the ex-istence of periodic solutions of multi-species competition model by using the fixed point theorem, sufcient conditions for the existence of, and gives the model ofpositive cycle, the paper points out some errors in the reference [24], and corrected.Secondly, we consider the persistence and extinction in the pollution of theenvironment in a class of population predator-prey system model. In the premiseof pulse pollution, join the interference efect of human outside, the efect of pulse.And the diferential equation method, theory and application analysis of pulse togive sufcient conditions for persistence of predator extinction of food bait model,the biological model is closer to the reality of the value, have stronger biologicalresearch, provides the theory basis for biological research.Finally, we study a class of multiple species GilPin-Ayala competition modelwith feedback control, in case the existence of positive periodic, with no fixed pointtheory is given with N species competition model of feedback solutions of cones,the sufcient conditions for the existence of positive periodic model was given.