Fractal structures in a generalized square map with exponential terms

doi:10.1088/1674-1056/21/3/030203

中国物理B ›› 2012, Vol. 21 ›› Issue (3): 30203-030203.doi: 10.1088/1674-1056/21/3/030203

李险峰¹,褚衍东¹,张惠¹ ²

收稿日期:2011-08-10 修回日期:2011-09-18 出版日期:2012-02-15 发布日期:2012-02-15
通讯作者: 李险峰,lixf1979@vip.qq.com E-mail:lixf1979@vip.qq.com

Fractal structures in a generalized square map with exponential terms

Li Xian-Feng(李险峰)^a)†, Chu Yan-Dong(褚衍东)^a), and Zhang Hui(张惠)^a)b)

a. School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China;
b. School of Mechanical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

Received:2011-08-10 Revised:2011-09-18 Online:2012-02-15 Published:2012-02-15
Contact: Li Xian-Feng,lixf1979@vip.qq.com E-mail:lixf1979@vip.qq.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11161027) and the Natural Science Foundation of Gansu Province, China (Grant No. 1010RJZA067).

摘要/Abstract

Abstract: Fractal structures in a generalized squared map with exponential terms are expanded in this paper. We describe how complex behaviors can arise as the parameters change. The appearances of different kinds of fractal structures, in both the attractive and the divergent regions, and most interestingly, on small regular islands embedded in the chaotic region, are manifested to have a variety of extraordinary geometries in the parameter plane.

Key words: discrete map, exponential term, parameter plane, Lyapunov fractal

中图分类号: (Integral equations)

02.30.Rz

05.45.Pq (Numerical simulations of chaotic systems) 05.45.Ac (Low-dimensional chaos)

李险峰, 褚衍东, 张惠. [J]. 中国物理B, 2012, 21(3): 30203-030203.

Li Xian-Feng(李险峰), Chu Yan-Dong(褚衍东), and Zhang Hui(张惠) . Fractal structures in a generalized square map with exponential terms[J]. Chin. Phys. B, 2012, 21(3): 30203-030203.

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Fractal structures in a generalized square map with exponential terms

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