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

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Abstract

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.

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Acknowledgements

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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  1. Research Unit of Laboratory of Automation and Applied Computer (LAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

    Jacques Kengne, Gervais Dolvis Leutcho & Adélaïde Nicole Kengnou Telem

  2. Research Unit of Laboratory of Condensed Matter, Electronics and Signal Processing (URMACETS), Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Jacques Kengne, Gervais Dolvis Leutcho & Adélaïde Nicole Kengnou Telem

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  1. Jacques Kengne
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Kengne, J., Leutcho, G.D. & Telem, A.N.K. Reversals of period doubling, coexisting multiple attractors, and offset boosting in a novel memristive diode bridge-based hyperjerk circuit. Analog Integr Circ Sig Process 101, 379–399 (2019). https://doi.org/10.1007/s10470-018-1372-5

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