Nonlinear Dynamics

, Volume 89, Issue 3, pp 1877–1887 | Cite as

Chaos-based application of a novel no-equilibrium chaotic system with coexisting attractors

  • Zhen Wang
  • Akif Akgul
  • Viet-Thanh PhamEmail author
  • Sajad Jafari
Original Paper


Novel chaotic system designs and their engineering applications have received considerable critical attention. In this paper, a new three-dimensional chaotic system and its application are introduced. The interesting aspects of this chaotic system are the absence of equilibrium points and the coexisting of limit cycle and torus. Basic dynamics of the no-equilibrium system have been executed by means of phase portraits, bifurcation diagram, continuation, and Lyapunov exponents. Experimental results of the electronic circuit realizing the no-equilibrium system have been reported to show system’s feasibility. By using the chaoticity of the new system without equilibrium, we have developed a random bit generator for practical signal encryption application. Numerical results illustrate the usefulness of the random bit generator.


Chaos Equilibrium Hidden attractor Coexisting attractors Circuit Chaos-based application Random bit generator Encryption 



The authors thank Prof. GuanRong Chen, Department of Electronic Engineering, City University of Hong Kong, for suggesting helpful references. Zhen Wang is supported by the Natural Science Foundation of China (No.61473237), the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2016JM1024), the Scientific Research Program Funded by Shaanxi Provincial Education Department (No.15JK2181), and the Scientific Research Foundation of Xijing University (Grant No.XJ160142). This work was partially supported by Sakarya University Scientific Research Projects Unit under Grants 2016-09-00-008, 2016-50-01-026.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Zhen Wang
    • 1
  • Akif Akgul
    • 2
  • Viet-Thanh Pham
    • 3
    Email author
  • Sajad Jafari
    • 4
  1. 1.Department of Applied SciencesXijing UniversityXi’anChina
  2. 2.Department of Electric and Electronic Engineering, Faculty of TechnologyUniversity of SakaryaSakaryaTurkey
  3. 3.School of Electronics and TelecommunicationsHanoi University of Science and TechnologyHanoiVietnam
  4. 4.Biomedical Engineering DepartmentAmirkabir University of TechnologyTehranIran

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