Analog Integrated Circuits and Signal Processing

, Volume 101, Issue 3, pp 379–399 | Cite as

Reversals of period doubling, coexisting multiple attractors, and offset boosting in a novel memristive diode bridge-based hyperjerk circuit

  • Jacques KengneEmail author
  • Gervais Dolvis Leutcho
  • Adélaïde Nicole Kengnou Telem


In this paper, a new memristive diode bridge-based RC hyperjerk circuit is proposed. This new memristive hyperjerk oscillator (MHO) is obtained from the autonomous 4-D hyperjerk circuit (Leutcho et al. in Chaos Solitons Fractals 107:67–87, 2018) by replacing the nonlinear component (formed by two antiparallel diodes) with a first order memristive diode bridge. The circuit is described by a fifth-order continuous time autonomous (‘elegant’) hyperjerk system with smooth nonlinearities. The dynamics of the system is investigated in terms of equilibrium points and stability, phase portraits, bifurcation diagrams and two-parameter Lyapunov exponents diagrams. The numerical analysis of the model reveals interesting behaviors such as period-doubling, chaos, offset boosting, symmetry recovering crisis, antimonotonicity (i.e. concurrent creation and destruction of periodic orbits) and several coexisting bifurcations as well. One of the most attractive features of the new MHO considered in this work is the presence of several coexisting attractors (e.g. coexistence of two, three, four, five, six, seven, or nine attractors) for some suitable sets of system parameters, depending on the choice of initial conditions. Accordingly, the distribution of initial conditions related to each coexisting attractor is computed to highlight different basins of attraction. Laboratory experimental measurements are carried out to verify the theoretical analysis.


Memristive hyperjerk oscillator (MHO) Reversals of period doubling Multistability Offset boosting Experimental study 



The authors would like to thank both the editor and the reviewers for their comments and suggestions that helped to greatly improve the presentation of the present manuscript.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Jacques Kengne
    • 1
    • 2
    Email author
  • Gervais Dolvis Leutcho
    • 1
    • 2
  • Adélaïde Nicole Kengnou Telem
    • 1
    • 2
  1. 1.Research Unit of Laboratory of Automation and Applied Computer (LAIA), Electrical Engineering Department of IUT-FVUniversity of DschangBandjounCameroon
  2. 2.Research Unit of Laboratory of Condensed Matter, Electronics and Signal Processing (URMACETS), Department of Physics, Faculty of SciencesUniversity of DschangDschangCameroon

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