Nonlinear Dynamics

, Volume 89, Issue 3, pp 1673–1687 | Cite as

Dynamics, circuit realization, control and synchronization of a hyperchaotic hyperjerk system with coexisting attractors

  • Xiong Wang
  • Sundarapandian Vaidyanathan
  • Christos Volos
  • Viet-Thanh Pham
  • Tomasz Kapitaniak
Original Paper


Although different hyperjerk systems have been discovered, a few hyperjerk systems can exhibit hyperchaotic behavior. In this work, we introduce a new hyperjerk system with hyperchaotic attractors. By investigating dynamics of the system, we have observed the different coexisting attractors such as coexistence of period-2 attractors, or coexistence of period-2 attractor and quasiperiodic attractor. It is worth noting that this striking phenomenon is rarely reported in a hyperjerk system. The proposed system has been realized with electronic components. The agreement between the simulation and experimental results indicates the feasibility of the hyperjerk system. Moreover, chaos control and synchronization of such hyperjerk system have been also reported.


Hyperchaos Hyperjerk system Quasiperiodic dynamics Coexisting attractor Circuit Control Synchronization 



The authors thank Prof. GuanRong Chen, Department of Electronic Engineering, City University of Hong Kong for suggesting helpful references. This work has been supported by the Polish National Science Centre, MAESTRO Programme—Project No 2013/08/A/ST8/00/780. The author Xiong Wang was supported by the National Natural Science Foundation of China (No. 61601306) and Shenzhen Overseas High Level Talent Peacock Project Fund (No. 20150215145C).


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Xiong Wang
    • 1
  • Sundarapandian Vaidyanathan
    • 2
  • Christos Volos
    • 3
  • Viet-Thanh Pham
    • 4
    • 5
  • Tomasz Kapitaniak
    • 5
  1. 1.Institute for Advanced StudyShenzhen UniversityShenzhenChina
  2. 2.R & D CentreVel Tech UniversityChennaiIndia
  3. 3.Department of PhysicsAristotle University of ThessalonikiThessaloníkiGreece
  4. 4.School of Electronics and TelecommunicationsHanoi University of Science and TechnologyHanoiVietnam
  5. 5.Division of DynamicsLodz University of TechnologyLodzPoland

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