中国物理B ›› 2010, Vol. 19 ›› Issue (7): 70514-070514.doi: 10.1088/1674-1056/19/7/070514

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The analysis of complex behaviours of a novel three dimensional autonomous system

董高高, 郑松, 田立新, 杜瑞瑾, 孙梅   

  1. Research Center for Nonlinear Science, Faculty of Science, Jiangsu University, Zhenjiang 212013, China
  • 修回日期:2010-01-25 出版日期:2010-07-15 发布日期:2010-07-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 10771088), Natural Science Foundation of Jiangsu Province, China (Grant No. 2007098), Outstanding Personnel Program in Six Fields of Jiangsu Province, China (Grant No. 6-A-029), National Natural Science (Youth) Foundation of China (Grant No. 10801140), Youth Foundation of Chongqing Normal University, China (Grant No. 08XLQ04) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 09B_202Z).

The analysis of complex behaviours of a novel three dimensional autonomous system

Dong Gao-Gao (董高高), Zheng Song (郑松), Tian Li-Xin (田立新), Du Rui-Jin (杜瑞瑾), Sun Mei (孙梅)   

  1. Research Center for Nonlinear Science, Faculty of Science, Jiangsu University, Zhenjiang 212013, China
  • Revised:2010-01-25 Online:2010-07-15 Published:2010-07-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 10771088), Natural Science Foundation of Jiangsu Province, China (Grant No. 2007098), Outstanding Personnel Program in Six Fields of Jiangsu Province, China (Grant No. 6-A-029), National Natural Science (Youth) Foundation of China (Grant No. 10801140), Youth Foundation of Chongqing Normal University, China (Grant No. 08XLQ04) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 09B_202Z).

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摘要： This paper introduces a new three dimensional autonomous system with five equilibrium points. It demonstrates complex chaotic behaviours within a wide range of parameters, which are described by phase portraits, Lyapunov exponents, frequency spectrum, etc. Analysis of the bifurcation and Poincaré map is used to reveal mechanisms of generating these complicated phenomena. The corresponding electronic circuits are designed, exhibiting experimental chaotic attractors in accord with numerical simulations. Since frequency spectrum analysis shows a broad frequency bandwidth, this system has perspective of potential applications in such engineering fields as secure communication.

Abstract: This paper introduces a new three dimensional autonomous system with five equilibrium points. It demonstrates complex chaotic behaviours within a wide range of parameters, which are described by phase portraits, Lyapunov exponents, frequency spectrum, etc. Analysis of the bifurcation and Poincaré map is used to reveal mechanisms of generating these complicated phenomena. The corresponding electronic circuits are designed, exhibiting experimental chaotic attractors in accord with numerical simulations. Since frequency spectrum analysis shows a broad frequency bandwidth, this system has perspective of potential applications in such engineering fields as secure communication.

Key words: three dimensional autonomous system, chaotic attractor, electronic circuit, frequency spectrum

中图分类号:  (Low-dimensional chaos)

  • 05.45.Ac
05.45.Pq (Numerical simulations of chaotic systems) 02.30.Yy (Control theory) 02.30.Oz (Bifurcation theory) 89.20.Kk (Engineering)