For the delayed logistic equation x _n+1 = ax _n (1 − x _n−2) it is well known that the nontrivial fixed point is locally stable for , and unstable for . We prove that for the fixed point is globally stable, in the sense that it is locally stable and attracts all points of S, where S contains those for which the sequence remains in . The proof is a combination of analytical and reliable numerical methods. The novelty of this article is an explicit construction of a relatively large attracting neighborhood of the nontrivial fixed point of the three-dimensional logistic map by using centre manifold techniques and the Neimark–Sacker bifurcational normal form.

对于延迟逻辑方程x _{n +1} = ax _n (1 − x _{n −2} ) 众所周知，非平凡不动点对于 是局部稳定的，对于是不稳定的。我们证明了对于不动点是全局稳定的，因为它是局部稳定的并且吸引了S 的所有点，其中S包含那些序列保持在 . 证明是分析方法和可靠数值方法的结合。本文的新颖之处在于通过使用中心流形技术和 Neimark-Sacker 分岔范式，显式构造了三维逻辑图的非平凡不动点的相对较大的吸引邻域。