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首页> 外文期刊>Mathematical Problems in Engineering >Hidden Coexisting Attractors in a Fractional-Order System without Equilibrium: Analysis, Circuit Implementation, and Finite-Time Synchronization
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Hidden Coexisting Attractors in a Fractional-Order System without Equilibrium: Analysis, Circuit Implementation, and Finite-Time Synchronization

机译：在没有平衡的分数阶系统中隐藏的共存吸引子：分析，电路实现和有限时间同步

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摘要

In this paper, a novel three-dimensional fractional-order chaotic system without equilibrium, which can present symmetric hidden coexisting chaotic attractors, is proposed. Dynamical characteristics of the fractional-order system are analyzed fully through numerical simulations, mainly including finite-time local Lyapunov exponents, bifurcation diagram, and the basins of attraction. In particular, the system can generate diverse coexisting attractors varying with different orders, which presents ample and complex dynamic characteristics. And there is great potential for secure communication. Then electronic circuit of the fractional-order system is designed to help verify its effectiveness. What is more, taking the disturbances into account, a finite-time synchronization of the fractional-order chaotic system without equilibrium is achieved and the improved controller is proven strictly by applying finite-time stable theorem. Eventually, simulation results verify the validity and rapidness of the proposed method. Therefore, the fractional-order chaotic system with hidden attractors can present better performance for practical applications, such as secure communication and image encryption, which deserve further investigation.
机译：本文提出了一种没有平衡的新型三维分数顺序混沌系统，其可以提出呈对称隐藏的共存混沌吸引子。通过数值模拟完全分析了分数级系统的动态特性，主要包括有限时间的本地Lyapunov指数，分叉图和吸引力的盆地。特别是，该系统可以通过不同的订单产生不同的共存吸引子，这呈现充足和复杂的动态特性。并且有很大的安全沟通潜力。然后，分数级系统的电子电路旨在帮助验证其有效性。更重要的是考虑扰动，实现了没有平衡的分数顺序混沌系统的有限时间同步，并且通过应用有限时间稳定定理严格证明改进的控制器。最终，仿真结果验证了所提出的方法的有效性和快速性。因此，具有隐藏吸引子的分数秩序混沌系统可以为实际应用提供更好的性能，例如安全的通信和图像加密，这应该得到进一步的调查。

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  • 来源
    《Mathematical Problems in Engineering》 |2019年第16期|6908607.1-6908607.12|共12页
  • 作者

    Zheng Guangchao; Liu Ling; Liu Chongxin;

  • 作者单位

    Xi An Jiao Tong Univ State Key Lab Elect Insulat & Power Equipment Xian 710049 Shaanxi Peoples R China|Xi An Jiao Tong Univ Sch Elect Engn Xian 710049 Shaanxi Peoples R China|State Grid Hebei Elect Power Supply Co Ltd Baoding Power Supply Branch Baoding 071000 Peoples R China;

    Xi An Jiao Tong Univ State Key Lab Elect Insulat & Power Equipment Xian 710049 Shaanxi Peoples R China|Xi An Jiao Tong Univ Sch Elect Engn Xian 710049 Shaanxi Peoples R China;

    Xi An Jiao Tong Univ State Key Lab Elect Insulat & Power Equipment Xian 710049 Shaanxi Peoples R China|Xi An Jiao Tong Univ Sch Elect Engn Xian 710049 Shaanxi Peoples R China;

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