4-D Memristive Chaotic System with Different Families of Hidden Attractors

  • Dimitrios A. Prousalis
  • Christos K. Volos
  • Viet-Thanh Pham
  • Ioannis N. Stouboulos
  • Ioannis M. Kyprianidis
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 133)


The design of systems without equilibrium or with line of equilibrium points is a subject which has started to attract the interest of the research community the last decade. In this direction, various chaotic systems with hidden attractors, which are based on memristors or memristive systems, have been proposed. In this chapter a new 4-D memristive system is presented. The peculiarity of the model is that it displays a line of equilibrium points for a range of the parameters as well as no-equilibrium for another range of the parameters. System in both occasions presents a chaotic behavior with hidden attractors. The behavior of the proposed system is investigated through numerical simulations, by using phase portraits, Lyapunov exponents and bifurcation diagrams. The adaptive control scheme of the system is presented in order to prove that the memristive system’s dynamical behavior can be controlled. Also, we have designed an electronic circuit to confirm the feasibility of the system in both cases.


Memristive system Hidden attractor Chaos control 


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Dimitrios A. Prousalis
    • 1
  • Christos K. Volos
    • 1
  • Viet-Thanh Pham
    • 2
  • Ioannis N. Stouboulos
    • 1
  • Ioannis M. Kyprianidis
    • 1
  1. 1.Department of PhysicsAristotle University of ThessalonikiThessalonikiGreece
  2. 2.School of Electronics and TelecommunicationsHanoi University of Science and TechnologyHanoiVietnam

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