期刊:Pramana - Journal of Physics ISSN:03044289 , 年:2016 . 卷:86 . 期:4   页码:801-807

原文链接:http://doi.org/10.1007/s12043-015-1118-1

摘要

In this paper, we construct a novel, 4D smooth autonomous system. Compared to the existing chaotic systems, the most attractive point is that this system does not display any equilibria, but can still exhibit four-wing chaotic attractors. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, bifurcation diagram, and Poincaré maps. There is little difference between this chaotic system without equilibria and other chaotic systems with equilibria shown by phase portraits and Lyapunov exponents. But the bifurcation diagram shows that the chaotic systems without equilibria do not have characteristics such as pitchfork bifurcation, Hopf bifurcation etc. which are common to the normal chaotic systems. The Poincaré maps show that this system is a four-wing chaotic system with more complicated dynamics. Moreover, the physical existence of the four-wing chaotic attractor without equilibria is verified by an electronic circuit. © 2016 Indian Academy of Sciences.

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关键词
Attractive points - Autonomous systems - Bifurcation diagram - Chaotic attractors - Circuit implementation - Hidden attractor - Non equilibrium - Pitch-fork bifurcations

附加关键词:
Bifurcation (mathematics) - Chaos theory - Differential equations - Hopf bifurcation - Lyapunov functions - Lyapunov methods - Phase equilibria - Reconfigurable hardware

作者信息

通讯作者:
     Lin, Yuan(linyuan1001@foxmail.com)
作者机构:
     [1] College of Information Science and Engineering, Hunan University, Changsha, China
     [2] College of Electrical and Information Engineering, Hunan Institute of Engineering, Xiangtan, China