About The Stability Of High Order Delay Differential Equations

As discrete-time system, difference equations are widely employed in life sciences, chemistry, physics, economy, cybernetics, computer science, etc. Moreover, as discretization format of differential equations, it is one of the most important ways to solve numerically differential equations in computing mathematics. So, the research of difference equations is arousing the general attention of scholars day by day. Now the research of stability of linear difference equations and rational difference equations is one of the focuses of the research of difference equations theory. In this dissertation, we consider stability of the following rational delay difference equationsand linear delay difference equationswhere the coefficients A are nonzero real number,β_i, B_i, C, a, b are constants, andβ_i= B_i = 0 (0≤i≤3), k > 1 is a positive integer. By using the methods of root-analysis for the characteristic equation and first approximation etc, this paper provides criterions of the asymptotic stability for the zero solution of the above meutioued delay difference equations. These results are represented by parameters of difference equations, which will be convenient for applications and verifications.