Several Class Of Higher Order Rational Difference Equation The Global Stability

Difference equations have great number of applications in computer science, economics, ecology, physiology, biology, neural network, control theory, statistical physics, meteorology, social science, etc. The investigation on difference equation is to discuss it's eventually behavior of the solutions, including oscillation, cycle length and global asymptotic stability, etc.This paper directs some open problems and conjectures by G.Ladas and so on. We consider some properties of positive solutions of several kinds of higher order rational difference equation, for example, global asymptotic stability of the positive equilibrium, invariant intervals, oscillation, semicycle analysis and periodicity.The whole paper is composed of four chapters:In the first chapter, we introduce the theoretical and practical background of problems and their research situations. We also list some important notions. And the main works of this paper are also simply introduced.In the second chapter, we consider the global attractivity of the positive equilibrium and boundedness of the solutions of a class of third order rational difference equation. By means of some known results and skills of analyzing we obtain some results.In the third chapter, we study the global stability of the positive equilibrium and invariant intervals of the solutions of a class of (k+1)th order rational difference equation.In the fourth chapter, we investigate the global stability of the positive equilibrium, invariant intervals, semicycle analysis, oscillation and periodicity of the solutions a class of 2k th order rational difference equation.