Global Asymptotic Stability For Several Nonlinear Rational Difference Equations

Rational difference equations appear as discrete analogues and as numerical solutions of differential and delay differential equations which model various diverse phenomena in biology, ecology, physiology, physics, engineering and economics, whose qualitative analysis has always been the hot spot subject to be studied in recent years. In this dissertation we mainly consider global asymptotical stability of three kinds of rational difference equations.First. in Chapter 2, the global asymptotical stability for a third order rational difference equations was investigated by using "Semicycle Analysis Method", the method which can be used to solve the global asymptotic stability for a kind of rational difference equations, but it is difficult to solve the higher order rational difference equations directly. Some known results are generalized.Second, the global asymptotic stability for a higher order rational difference equations was investigated by using "Subsequence Analysis Method" in Chapter 3, and the "Subsequence Analysis Method" is a extension and supplement of "Semicycle Analysis Method". A set of sufficient conditions for the global stability of higher order rational difference equations are also obtained.Finally, a conjecture presented by Kenneth S.Berenhaut, John D.Foley and Stevo Stevic in "Applied Mathematics letters" was partly solved in Chapter 4. With help of a auxiliary equation, a set of sufficient conditions for the global stability of higher order rational difference equations were obtained.We also give some equations in each chapter of dissertation, Whose global asymptotic stability can be proved by the same method.