| In the recent years, the study of mathematical ecology models has widely attractedthe attention of researchers and many good results have been obtained. Some results areon stability, an important feature in describing mathematical ecology models. The studyon stability of populations can provide better guidance in exploiting and transforming thenature.In this paper, using the theory and methods from ordinary diferential equations, wepropose and carefully study four dynamical models.Firstly, a bandicoot population model with competitive reproductive interference underVVIC is established. The sufcient conditions for existence and local asymptotic stabilityof equilibria of the system is attained. The global asymptotic stability of equilibria of thesystem is performed by numerical simulations. By comparison analysis, we get the action ofcompetitively reproductive interference coefcient on bandicoot population number.Secondly, we consider a competition model of sterile control that a kind of mouse popula-tion’s birth and death both have the factor of density restriction,and obtained the existencecondition of system balance point, and have proven the partial approach stability and theoverall situation stability of the balance point.Finally,we have given the numerical simulationof overall situation stable.Thirdly, we have considered a kind of bait which has two species predator sterile-controlmodel , and discussed the system balance point condition of existence, and proved thebalance point partial approach stability and the overall situation stability, and given theoverall situation stable numerical simulation , as well as carried on the analysis discussionto the parameter.Finally, we propose Contraception control Model with Density-dependent Birth pulsesand pulses Harvesting, Using the stroboscopic map ,We obtain an exact cycle of system ,andobtain the threshold conditions for its stability and study the impact of the infertility ratioon the population size. |
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