物理学报2013，Vol.62Issue(2)：138-145,8.DOI:10.7498/aps.62.020510
三维超混沌映射拓扑马蹄寻找算法及应用
Algorithm for finding horseshoes in three-dimensional hyperchaotic maps and its application
摘要
Abstract
Topological horseshoe theory is fundamental for studying chaos rigorously, which, however, has rarely applied to hyperchaos. The reason is that it is too hard to find a topological horseshoe in a hyperchaotic system, due to the high dimension of the system and the multiple expansion directions in the state space. Therefore, in this paper a practical algorithm for three-dimensional (3D) hyperchaotic maps is proposed. Usually, a hyperchaotic system has a large negative Lyapunov exponent, its attractor is often contracted closely to a certain surface. Based on this feature, the algorithm first deducts the dimension along the direction of contraction to obtain a 2D projective system; then it detects a projective horseshoe with 2D expansion; finally, it constructs a 3D horseshoe for the original system. In order to verify the validity of the algorithm, it is applied to the classic hyperchaotic Lorenz system and the famous Saito hyperchaotic circuit, and their horseshoes with 2D expansion are successfully found from the Poincare mapping.关键词
超混沌/拓扑马蹄/Saito超混沌系统/Lorenz超混沌系统Key words
hyperchaos/ topological horseshoes/ Saito hyperchaotic system/ Lorenz hyperchaotic system引用本文复制引用
李清都,唐宋..三维超混沌映射拓扑马蹄寻找算法及应用[J].物理学报,2013,62(2):138-145,8.基金项目
国家自然科学基金(批准号:10972082,61104150)、重庆市科委基金(批准号:cstcjjA40044)和重庆邮电大学博士启动金(批准号:A2009-12)资助的课题. （批准号:10972082,61104150）
