The Global Behavior Of Two Classes Of Difference Equations

Difference equations(or recursive sequences) are considered as the discretization and numerical solutions of differential equations and delay differential equations,which have great number of applications in economics,ecology,physiology,biology,physics,engineering, neural network,social sciences,etc.The investigation on difference equation is to discuss its eventually behavior of the solutions,including oscillation,cycle length and global asymptotic stability,etc.This paper mainly studies the global behavior of two classes of nonlinear difference equations.In the first chapter,the historical background,the recent development tendency of the difference equations and some relative known results are introduced briefly.In the second chapter,we consider the oscillation and cycle length under certain conditions for solutions of a kind of nonlinear difference equationwhere k ∈ {1,2,…}.Some results for the the oscillation and cycle length of the difference equation are obtained,which improve some known results.In the third chapter,we study the following higher order nonlinear difference equationwhere with the initial conditions and for any Several properties of the equation are obtained and we prove that its equilibrium is globally asymptotically stable.