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Dynamic Analysis of Memristor Circuits via Input–Output Techniques

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Memristor Computing Systems

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Abstract

The chapter reviews a recently proposed input–output approach to investigate the dynamics of a class of circuits composed of a linear time-invariant two-terminal element coupled with one ideal flux-controlled memristor. The classical (autonomous) Chua’s and (non-autonomous) Murali–Lakshmanan–Chua’s memristor circuits are employed to discuss the features of the approach, which can be seen as the input–output counterpart of the Flux–Charge Analysis Method (FCAM). It is shown that the dynamics of any circuit of the class admits a first integral, which implies that the circuit dynamics can be obtained by collecting those displayed by a canonical reduced-order input–output system subject to a constant input with a varying amplitude. More specifically, there is a one to one correspondence between the dynamics of the canonical input–output system generated by a fixed amplitude of the constant input and the dynamics displayed by the memristor circuit onto one of the infinite invariant manifolds. It is also shown that the canonical input–output representation of both Chua’s and Murali–Lakshmanan–Chua’s memristor circuits can be implemented via a circuit with a voltage-controlled nonlinear resistor in place of the memristor plus an additional constant voltage source, thus establishing an interesting similarity between memristor circuits and memristor-less circuits. The memristor-less versions are then employed to investigate some features of the dynamics of both Chua’s and Murali–Lakshmanan–Chua’s memristor circuits.

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Notes

  1. 1.

    Throughout the paper, the inverse operator \(\mathcal {D}^{-1}\) is the integral operator (i.e., \(\mathcal {D}^{-1} f(t)=\int _{-\infty }^t f(\tau ) d\tau \)) and \(\mathcal {D}^h f(t_0)\) stands for the value of \(\mathcal {D}^h f(t)\) at \(t=t_0\).

  2. 2.

    \(I_n\) denotes the identity matrix of order n.

  3. 3.

    The symbol \(~^\prime \) stands for derivative.

  4. 4.

    The second equality in (2.26) follows since \(w_i(t)=0\) for \(t< t_0\).

  5. 5.

    For the notational simplicity the explicit dependence of \(\bar{v}_{\text{ nr }}\) on \(\Phi _0\) is omitted.

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Author information

Authors and Affiliations

  1. Department of Information Engineering and Mathematics, University of Siena, Via Roma 56, Siena, 53100, Italy

    Mauro Di Marco & Mauro Forti

  2. Department of Information Engineering, University of Florence, Via S. Marta 3, Firenze, 50139, Italy

    Giacomo Innocenti & Alberto Tesi

Authors
  1. Mauro Di Marco
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  2. Giacomo Innocenti
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  3. Alberto Tesi
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  4. Mauro Forti
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Corresponding author

Correspondence to Mauro Di Marco .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering & Computer Science, University of California, Berkeley, Berkley, CA, USA

    Leon O. Chua

  2. Fundamentals of Electrical Engineering, TU Dresden, Dresden, Germany

    Ronald Tetzlaff

  3. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Angela Slavova

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Di Marco, M., Innocenti, G., Tesi, A., Forti, M. (2022). Dynamic Analysis of Memristor Circuits via Input–Output Techniques. In: Chua, L.O., Tetzlaff, R., Slavova, A. (eds) Memristor Computing Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-90582-8_2

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  • DOI: https://doi.org/10.1007/978-3-030-90582-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-90581-1

  • Online ISBN: 978-3-030-90582-8

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