Nonlinear Dynamics

, Volume 85, Issue 4, pp 2665–2671 | Cite as

A novel 4D autonomous 2\(\varvec{n}\)-butterfly wing chaotic attractor

  • Fadhil Rahma Tahir
  • Ramzy S. Ali
  • Viet-Thanh PhamEmail author
  • Arturo Buscarino
  • Mattia Frasca
  • Luigi Fortuna
Original Paper


This paper presents a four-dimensional (4D) autonomous chaotic system. The new system is obtained by introducing the state feedback and a novel n-well potential function to the third-order Duffing system. The proposed potential function enables us to create butterfly wing chaotic attractors. The new system can generate n-scroll and 2n-butterfly wing chaotic attractors. The basic dynamical behaviors and properties of this system are investigated, such as equilibriums, stability of equilibrium points, attractors, and Lyapunov exponents. The circuit realization and experimental results are also presented.


Chaos Butterfly wing attractor Autonomous Duffing system Circuit 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Fadhil Rahma Tahir
    • 1
  • Ramzy S. Ali
    • 1
  • Viet-Thanh Pham
    • 2
    Email author
  • Arturo Buscarino
    • 3
  • Mattia Frasca
    • 3
  • Luigi Fortuna
    • 3
  1. 1.Department of Electrical Engineering, College of EngineeringUniversity of BasrahBasrahIraq
  2. 2.School of Electronics and TelecommunicationsHanoi University of Science and TechnologyHanoiVietnam
  3. 3.Dipartimento di Ingegneria Elettrica Elettronica e InformaticaUniversità degli Studi di CataniaCataniaItaly

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