一类非线性Lyness差分方程的定性分析

Investigation of the stability of a sort of nonlinear Lyness difference equations

研究了一类非线性二阶Lyness差分方程,利用解的不变区间的技巧,证明了解的全局渐近稳定性。将证明所得结论推广到k阶Lyness差分方程上,进一步讨论了k阶Lyness差分方程解的全局渐进稳定性,并给出了两个具体的数值算例。

Abstract：The stability of solutions of a sort of non-linear second order Lyness difference equations was investigated in this paper.Using the invariant interval technique,we proved the global asymptotic stability of the solution.Then,the conclusion for the 2-order Lyness difference equation was generalized to k-order Lyness difference equation.Furthermore,we got the global asymptotic stability of the solution of k-order Lyness equation.In the end,two numerical experimentations were carried out.