NUMERICAL STUDY OF COEXISTING ATTRACTORS FOR THE HENON MAP

被引：11

作者：

Galias, Zbigniew ^{[1
]}

Tucker, Warwick ^{[2
]}

机构：

[1] AGH Univ Sci & Technol, Dept Elect Engn, PL-30059 Krakow, Poland

[2] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2013年 / 23卷 / 07期

基金：

瑞典研究理事会;

关键词：

Henon map; periodic orbit; coexisting attractors; interval arithmetic;

D O I：

10.1142/S0218127413300255

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The question of coexisting attractors for the Henon map is studied numerically by performing an exhaustive search in the parameter space. As a result, several parameter values for which more than two attractors coexist are found. Using tools from interval analysis, we show rigorously that the attractors exist. In the case of periodic orbits, we verify that they are stable, and thus proper sinks. Regions of existence in parameter space of the found sinks are located using a continuation method; the basins of attraction are found numerically.

引用

页数：18

共 12 条

[1] SIMPLICIAL AND CONTINUATION METHODS FOR APPROXIMATING FIXED-POINTS AND SOLUTIONS TO SYSTEMS OF EQUATIONS [J].