Solutions For Several Classes Of Biological Mathematical Models

Biological mathematical model can be used not only to describe the naturalecological phenomenon, express ecological processes and do some quantitative andqualitative researches, but also can help to solve some complex ecological problems,which has a theoretical significance and applied value. Moreover, changes in theenvironment have an important role in many ecosystems, in particular, periodicchanges in the environment. This problem has been extensively studied by manyscholars, see [4]-[35]. In this paper, by using Leggett-Williams fixed point theorem,coincidence degree theory, cone compression and expansion fixed point theorem,we get the existence of positive periodic solutions for several classes of biologicalmathematical models. The dissertation contains three chapters.Chapter 1 investigates a class of n-species competition systems with impulseswhere yi(t) is the population density of the ith species at time t; ri(t) is the intrin-sic exponential growth rate of the ith species at time t. By using the fixed pointtheorem on cone, we obtain the existence of positive periodic solutions. Mean-while, by using the diferential equation comparison theorem and by constructing asuitable Lyapunov function, sufcient conditions are obtained which guarantee the permanence and the global attractivity of the positive periodic solution for a classof n-species competition system with infinite delays.In chapter 2, we consider the existence of triple periodic solutions for impulsivefunctional diferential equations with feedback controlwhere F∈C(Rn+2, [0,∞)) and the above functions areω-periodic in t. The methodused here is Leggett-Williams fixed point theorem. Meanwhile, two examples areworked out to demonstrate the main result and we point out that the impulse playsan important role.In chapter 3, we study a class of ratio-dependent predator-prey systems withharvesting terms and impulsesBy using Mawhin’s continuation theorem of coincidence degree theory, we investi-gate the existence of 2n+mpositive periodic solutions. Here n and m denote thenumber of prey and predator species respectively.