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Three Fingerprints of Memristor

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This chapter illustrates that for a device to be a memristor it should exhibit three characteristic fingerprints: (1) When driven by a bipolar periodic signal the device must exhibit a “pinched hysteresis loop” in the voltage-current plane, assuming the response is periodic and not symmetrical. (2) Starting from some critical frequency, the hysteresis lobe area should decrease monotonically as the excitation frequency increases, and (3) the pinched hysteresis loop should shrink to a single-valued function when the frequency tends to infinity. Examples of memristors exhibiting these three fingerprints, along with non-memristors exhibiting only a subset of these fingerprints are also presented. In addition , two different types of pinched hysteresis loops; the transversal (self-crossing) and the non-transversal (tangential) loops exhibited by memristors are also discussed with its identification criterion.


  • Memristor
  • Ideal memristor
  • Generalized memristor
  • Memristive device
  • Pinched hysteresis loop
  • Transversal loop
  • Non-transversal loop
  • Lobe area

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  • DOI: 10.1007/978-3-319-76375-0_5
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  1. 1.

    We define the lobe area in the 1st and 3rd quadrant of a voltage controlled memristor by \( A_{1} = \int_{0}^{T/2} {i(t)\left( {dv(t)/dt} \right)} \,dt \) and \( A_{3} = \int_{T/2}^{T} {i(t)\left( {dv(t)/dt} \right)} \,dt \), respectively.

  2. 2.

    Note that the proof of Property 6 in [2] requires that the solution waveform be a periodic function for all \( t \ge 0 \). This implies that \( (x_{1} (t),x_{2} (t), \ldots ,x_{n} (t)) \) has no transient components.


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This work was supported in part by the US Air Force grant number FA9550-10-1-0290 and the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (No. 2010-0006871).

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Correspondence to Hyongsuk Kim .

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Adhikari, S.P., Sah, M.P., Kim, H., Chua, L.O. (2019). Three Fingerprints of Memristor. In: Chua, L., Sirakoulis, G., Adamatzky, A. (eds) Handbook of Memristor Networks. Springer, Cham.

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