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Chin. Phys. B, 2012, Vol. 21(3): 030203    DOI: 10.1088/1674-1056/21/3/030203
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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
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.
Keywords:  discrete map      exponential term      parameter plane      Lyapunov fractal  
Received:  10 August 2011      Revised:  18 September 2011      Accepted manuscript online: 
PACS:  02.30.Rz (Integral equations)  
  05.45.Pq (Numerical simulations of chaotic systems)  
  05.45.Ac (Low-dimensional chaos)  
Fund: 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).
Corresponding Authors:  Li Xian-Feng,lixf1979@vip.qq.com     E-mail:  lixf1979@vip.qq.com

Cite this article: 

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 2012 Chin. Phys. B 21 030203

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