一类四阶时滞差分方程的渐近稳定性研究

Study of asympotic stability of a class of 4-th order delay difference equations

运用特征根法等方法,分别研究一类四阶时滞差分方程xn+4-axn+bxn-l=0,当参数l为偶数和奇数时其特征方程所有特征根的分布情况,从而给出方程零解渐近稳定的充要条件。这些结果为解决具有此类模型的实际问题提供了理论依据。

By using the method of characteristic roots and other methods, the distribution of all characteristics roots of the delay difference equation x,＋4 -axn ＋ bxn-1 =0 is studied when the parameters I is even and odd, and thereby, necessary and sufficient conditions are given for asymptotic stability of the zero solution of the delay difference equations. This offers a theoretical basis for solving the practical problems with such models.