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Implementation and study of the nonlinear dynamics of a memristor-based Duffing oscillator

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Abstract

An electronic model of Duffing oscillator with a characteristic memristive nonlinear element is proposed instead of the classical cubic nonlinearity. The memristive Duffing oscillator circuit system is mathematically modeled, and the stability analysis presents the evolution of the proposed system. The dynamical behavior of this circuit is investigated through numerical simulations, statistical analysis, and real-time hardware experiments, which have been carried out under the external periodic force. The chaotic dynamics of the circuit is studied by means of phase diagram. It is found that the proposed circuit system shows complex behaviors, like bifurcations and chaos, three tori, transient chaos, and intermittency for a certain range of circuit parameters. The observed phenomena and scenario are illustrated in detail through experimental and numerical studies of memristive Duffing oscillator circuit. The existence of regular and chaotic behaviors is also verified by using 0–1 test measurements. In addition, the robustness of the signal strength is confirmed through signal-to-noise ratio. The numerically observed results are confirmed from the laboratory experiment.

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Acknowledgments

S.S. acknowledges University Grants Commission (UGC) for the financial assistance through RFSMS scheme. K.T. acknowledges DST, Govt. of India, for the financial support through the Grant No. SB/EMEQ-077/2013.

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Authors and Affiliations

  1. Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli, Tamilnadu, 620 024, India

    S. Sabarathinam & K. Thamilmaran

  2. Physics Department, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Christos K. Volos

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  1. S. Sabarathinam
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Correspondence to K. Thamilmaran.

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Sabarathinam, S., Volos, C.K. & Thamilmaran, K. Implementation and study of the nonlinear dynamics of a memristor-based Duffing oscillator. Nonlinear Dyn 87, 37–49 (2017). https://doi.org/10.1007/s11071-016-3022-8

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