On The Non-Autonomous Lotka-Volterra Systems

In this paper , we consider the following non-autonomous Lotka-Volterra N-species competitive systemwhere t [0, ), Xi(t) 0 is the population size of the ith species at time t, and zi(tk) = is the impulse of the ith species at time t. According to the theory of differential inequality and the comparision theorem, we will establish some new and more practical criteria of the extinction, uniform persistence and globally asymptotical stability for partial species of the above system. Since the narrate of the main theorem is long, we omit it. To see Section 2 of Chapter 3 for details.In Chapter 4, we consider the following non-autonomous Predator-Prey system with dispersion in a new waywhere x1 and y are the population density of species x and species y in patch 1, and x2 is the density of species x in patch 2. species y is confined to patch 1, while the species x can disperse between two patches. Di(t)(i = l,2)are dispersion coeffcients of species x. we only required that r2(t) is nonnegative and loosen the requests of the functions r1(t) and r (t). we will get some new criteria of the uniform persistence, extinction and attractivity for the above system. Since the narrate of the main theorem is long, we omit it. To see Chapter 4 for details.