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arXiv · 1808.00409

Global stability for the 2-dimensional logistic map

János Dudás
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Abstract

For the delayed logistic equation $x_{n+1} = a x_n (a-x_{n-1})$ it is well known that the nontrivial fixed point is locally stable for $1 2$. We prove that for $1<a\leq 2$ the fixed point is globally stable, in the sense that it is locally stable and attracts all points of $S$, where $S$ contains those $(x_0,x_1)\in \mathbb{R}_+^2$, for which the sequence $\left\lbrace x_n\right\rbrace \subset \mathbb{R}_+$. The proof is a combination of analytical and reliable numerical methods.

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János Dudás. 2018-08-01. Global stability for the 2-dimensional logistic map. https://arxiv.org/abs/1808.00409

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