Study On The Dynamic Properties Of Some Classes Of Nonlinear Difference Equation

The study on difference equations is an important research branch of the mathematical theory, especially in dynamical systems. With the rapid development of computer, the qualitative analysis of difference equations has wide applications in such fields as numerical analysis, economics, ecology, neural network, control theory and so on. The thesis mainly studies the dynamics of several kinds of systems of exponential difference equations.In the first chapter, we mainly state the background of the problem and we investigate its recent development as well as some results related to this thesis.In the second chapter, under some conditions we study the existence of posi-tive solutions, the existence and uniqueness of nonnegative equilibrium, and con-vergence of positive solutions of the following discrete epidemic model: where A,B ? ?0,??. Our results extend some existing ones in the literature.In the third chapter, we study the boundedness character and persistence and obtain the global asymptotic stability of the equilibrium of the following three systems of exponential difference equations: where the parameters ?,?,?,?,? and ?are positive constants and the initial values x₁, x0, y₁ and y0 are positive real constants.