具周期系数时滞差分方程的全局渐近稳定性

Global asymptotic stability for delay difference equations with periodic coefficients

考虑具周期系数非线性时滞差分方程xn+1-xn+pnxn-k=pnf(x[n/T]T-l),n=0,1,2,…,其中{pn}为T周期正数列,即pn+T=pn,k=sT,k,s,T为自然数.通过讨论对应的齐次线性差分方程的性质,获得了关于零解全局渐近稳定的充分必要条件.

This paper considers the nonlinear delay difference equations with periodic coefficients x_(n+1)-x_n+p_nx_(n-k)=p_nf(x__([n/T]T-l)), n=0,1,2,…, where ｛p_n｝ is a nonnegative sequence with period T, i.e. p_(n+T)=p_n, k=sT, k,s,T are positive integers. By discussing the properties of the correspondence homogeneous linear delay difference equation, the sufficient and necessary condition for the global asymptotic stability of zero solution is obtained.