通信学报 ›› 2014, Vol. 35 ›› Issue (12): 106-115.doi: 10.3969/j.issn.1000-436x.2014.12.013

• 学术论文 • 上一篇    下一篇

基于反正切的网格混沌吸引子及其保密通信

毛学志1,2,徐勇3,刘建平1,马会泉1   

  1. 1 河北科技师范学院 数学与信息科技学院,河北 秦皇岛 066004
    2 河北科技师范学院 数学与系统科学研究所,河北 秦皇岛 066004
    3 河北工业大学 理学院,天津 300401
  • 出版日期:2014-12-25 发布日期:2017-06-17
  • 基金资助:
    国家自然科学基金资助项目;河北科技师范学院重点学科和科研创新团队建设经费基金资助项目

Grid chaotic attractors based on arc tangent and its secure communication

Xue-zhi MAO1,2,Yong XU3,Jian-ping LIU1,Hui-quan MA1   

  1. 1 College of Mathematics and Information Technology,Hebei Normal University of Science and Technology,Qinhuangdao 066004,China
    2 Institute of Mathematics and Systems Science,Hebei Normal University of Science and Technology,Qinhuangdao 066004,China
    3 School of Science,Hebei University of Technology,Tianjin 300401,China
  • Online:2014-12-25 Published:2017-06-17
  • Supported by:
    The National Natural Science Foundation of China;The Key Disciplines and the Funds for Creative Research Groups of Hebei Normal University of Science and Technology

摘要:

提出了一种用处处光滑的反正切函数序列生成多维多涡卷网格混沌吸引子的方法,可以生成一维n涡卷、二维n×m网格多涡卷和三维n×m×l网格多涡卷混沌吸引子。平衡点分析、数值仿真、Lyapunov指数谱、分岔图和Poincaré映像都表明系统是混沌的。用简单的线性反馈控制实现了同结构网格多涡卷混沌系统之间的同步,可应用于保密通信。简单的理论分析和数值仿真证明了该方法的有效性。

关键词: 混沌同步, 保密通信, 网格多涡卷吸引子, 反正切序列函数

Abstract:

A smooth arc tangent function series approach for creating multi-directional multi-scroll grid chaotic attractors was proposed,including one-directional n-scroll,two-directional n×m-grid scroll,and three-directional n×m×l-grid scroll chaotic attractors.The chotic properties were studied by equilibrium points analysis,numerical simulation,Lyapunov exponents spectrum,bifurcation diagrams and Poincaré section diagrams.Synchronize the two grid multi-scroll chaotic systems with same structure by designing simple linear feedback control lows,which is applied to secure communication.The effectiveness of this method has been verified by simple analysis and numerical simulation.

Key words: chaos synchronization, secure communication, grid multi-scroll chaotic attractors, arc tangent function series