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Three Fingerprints of Memristor
Abstract
This paper 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. 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.
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“Numerous examples of pinched hysteresis loops of memristors can be found in [3], [13], [22].”
From Everything You Wish to Know About Memristors But Are Afraid to Ask (2015) · cites this paper as [13]
Citations
Cites
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“For the examples presented in [13] it was noted that non-transversal loops occurred when and are even functions of , where , but this was not a necessary condition as transversal pinched hysteresis loops were observed in unipolar resistance switching devices where and were even functions of .”
BackgroundHODGKIN–HUXLEY AXON IS MADE OF MEMRISTORS
CHUA, L., SBITNEV, V., & KIM, H. (2012) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812741230011x · Cited by 319
Self-citationNonlinear circuit foundations for nanodevices, part I: the four-element torus
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Self-citationPinched hysteretic loops of ideal memristors, memcapacitors and meminductors must be ‘self-crossing’
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“The three fingerprints of memristor [3] are as follows:”
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“, the equivalent realization circuit of the memristive diode bridge with LC network is a second-order generalized memristor [28].”
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“In 2008, scientists at Hewlett-Packard laboratories realized the first physical model of memristor using titanium dioxide (TiO2) and platinum electrodes [6-11].”
BackgroundElectromagnetic Interference Effects of Continuous Waves on Memristors: A Simulation Study
Ma, G.-L., Man, M.-H., Zhang, Y.-Q., & Liu, S.-H. (2022) · Italian National Conference on Sensors · doi:10.3390/s22155785 · Cited by 6
“According to the fingerprint characteristic of the memristor [38], the uniformity is due to the fact that the hysteresis line of the memristor shrinks to a single-valued function when the memristor is driven by the high-frequency CW alone.”
BackgroundFPGA Implementation of a Novel Two-internal-State Memristor and its Two Component Chaotic Circuit
Alombah, N. H., Tchendjeu, A. E. T., Romanic, K., Talla, F. C., & Fotsin, H. B. (2021) · Indian Journal of Science and Technology · doi:10.17485/ijst/v14i27.532 · Cited by 6
“L2 = dd∗x(t)+mm∗y(t) +yy∗z(t)(mod p) } (18)”
BackgroundDynamic Behaviors Analysis of a Novel Fractional-Order Chua’s Memristive Circuit
Wu, C.-J., Zhang, Q., Liu, Z., & Yang, N.-N. (2021) · Mathematical Problems in Engineering · doi:10.1155/2021/5896353 · Cited by 6
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“The pinched hysteresis loop is one of the most distinguished fi ngerprints of a memristor (Adhikari et al. (2013), Chua (2014)) and is a re fl ection of its memory effect.”
BackgroundPinched Hysteresis Loops In Nonlinear Resonators
Elwakil, A., Fouda, M., Majzoub, S., & Radwan, A. G. (2020) · IET Circuits Devices Syst. · doi:10.1049/cds2.12003 · Cited by 6
“To identify a device as a memristor, it has to have three fingerprints [27, 26] : 1) a pinched loop in current-voltage plane with 2) a loop area that decreases monotonically with increasing frequency and 3) shrink to a single-valued function when the frequency tends to infinity.”
MethodMixed H2/H∞ stabilization design for memristive neural networks
Zhang, X.-W., & Wu, H.-N. (2019) · Neurocomputing · doi:10.1016/j.neucom.2019.07.002 · Cited by 6
A non-local structural derivative model for memristor
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“By duality, the mathematical definition of the ideal flux (or voltage) -controlled memristor is in the form [18]: where G is the conductance of memristor.”
BackgroundAnalysis of a memristive diode bridge rectifier
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“Beyond a certain critical frequency, the area of the loop decreases monotonically to zero as the frequency f increases to infinity [3].”
BackgroundAnalog Memristive Characteristics and Conditioned Reflex Study Based on Au/ZnO/ITO Devices
Cheng, T.-D., Rao, J., Tang, X.-G., Yang, L.-R., & Liu, N. (2018) · Electronics · doi:10.3390/electronics7080141 · Cited by 6
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Rajamani, V., Yang, C., Kim, H., & Chua, L. O. (2016) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127416300214 · Cited by 9
Self-citationDesign of spatially multi-structure attractors in discrete memristive Hopfield neural networks
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“The mathematical model of (1) accords with the defining equation for the class of ideal flux-controlled memristors and can exhibit a pinched hysteresis loop in the v − i plane as a bipolar periodic voltage stimulus is applied [20].”
BackgroundMethodUpadhyay, V., Kumar, K., Gupta, R. K., Saxena, V., & Ranjan, R. (2026) · Circuits, systems, and signal processing · doi:10.1007/s00034-025-03479-x · Cited by 5
“The memristor, first proposed by Leon Chua in 1971 [13], extends the fundamental trio of passive elements, resistor, capacitor, and inductor by linking magnetic flux and charge through memristance [2].”
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“The second fingerprint of memristor behavior as defined in reference [33] is portrayed in Fig.”
BackgroundResearch Progress in Dielectric-Layer Material Systems of Memristors
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“A current versus voltage characteristics in the form of a pinched hysteresis loop, when excited with a periodic signal, represents the main fingerprint of a memristor [1].”
BackgroundBastani, P., Mohseni, S. M., Jamilpanah, L., Azizi, B., & Gharehbagh, J. S. E. (2022) · Journal of Materials Science Materials in Electronics · doi:10.1007/s10854-022-07812-x · Cited by 5
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BackgroundPolymer Nanocomposites for Resistive Switching Memory
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“A fingerprint of memristors is pinched current–voltage (I–V ) hysteresis loop that is a function of frequency [5], and the hysteresis loop (for given bias polarity) is in either clockwise or counterclockwise direction depending on device configuration and active materials.”
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Pabst, O., Andersen, S., Bhatti, S. A., Brevik, J., Fallaas, S. A., Fjeldstad, M., Gubaidulin, A., Madsen, K. V., Nomedal, M. R., Slettemoen, S. F., et al. (2019) · Journal of Electrical Bioimpedance · doi:10.2478/joeb-2019-0012 · Cited by 5
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“There are three characteristic fingerprints, memdamper should exhibit [11]: 1) The device must exhibit a pinched hysteresis loop in the force-velocity plane for bipolar periodic signal excitation.”
BackgroundRealization of a memristor-based second-order active low-pass filter
Shen, Y., Liu, Y., & Wang, X.-P. (2015) · International Conference on Information and Software Technologies · doi:10.1109/icist.2015.7288995 · Cited by 5
“I shows that the improved model satisfies the three characteristic fingerprints of a mernristor [11].”
BackgroundBiolek, Z., Biolek, D., Biolková, V., & Kolka, Z. (2020) · IEEE Access · doi:10.1109/access.2020.3034802 · Cited by 5
Memristors and Electrical Memory in Plants
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“=3 kΩ, R 3 = 300 Ω, C 1 = 5 pF. Figure 8 shows the first fingerprint (Adhikari et al., 2013) of the proposed memristor emulator.”
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“As explained the three fingerprints of memristor in [24], hysteresis loop shrinks to the linear line as frequency increases.”
BackgroundA Digital Oscilloscope Based Hardware Implementation Approach for Universal Memristor Emulators
Xu, B., Zhao, J., Chen, K., Wang, Y.-F., Yan, Y.-J., & Bai, L.-B. (2023) · IEEE International Conference on Electronic Measurement & Instruments · doi:10.1109/icemi59194.2023.10270663 · Cited by 4
“In summary, the memristor model described in (7) can exhibit the basic characteristics for memristor identification [20].”
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“5(a-c) that area of lobe of pinch hysteresis curves start to decrease as input frequency increase, and finally the proposed memristor emulator changes its nonlinear resistor behavior to a linear resistor at 60 MHz input frequency, these are commonly known as 2 and 3 fingerprints [25] of memristor, which conform that t…”
BackgroundMemristor‐based circuit design of continuously adjustable direct‐current voltage source
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“36,37 The threshold character exists in physical memristor.”
BackgroundSPICE Behaviors of Double Memristor Circuits Using Cosine Window Function
Xu, K., Li, D., Jiang, Y.-N., & Chen, Q. (2020) · Frontiers of Physics · doi:10.3389/fphy.2021.648737 · Cited by 4
“then, many researchers or scholars have focused on the memristor research [3-7] and its numerous potential applications in nonvolatile random access memories [8], neuromorphic systems [9], chaotic circuits [10], reconfigurable logics [11] and RF/microwave devices [12, 13].”
BackgroundLi, X.-T., Tan, Z., Wang, X.-L., & Liu, Y.-D. (2020) · IEEE Transactions on Plasma Science · doi:10.1109/tps.2020.2996662 · Cited by 4
“Such an evolution behavior is opposite to that of memristor mentioned above [50], thus the discharge plasma part in the DBD cannot be described as a memristor.”
BackgroundResultLogistic Function Based Memristor Model With Circuit Application
Abraham, I., Ren, S., & Siferd, R. (2019) · IEEE Access · doi:10.1109/access.2019.2951673 · Cited by 7
“introduced the community to fingerprints of memristors [33].”
BackgroundAn Analytic Approach to Nonlinearity Analysis of Memristor
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“The PHL area here is defined as the area enclosed by the closed IM –VM loop, which is one of the crucial characterizations of the nonlinearity for memristor [22].”
BackgroundMethodPabst, O., Anwar, A., Nieweglowski, A. A., Lindland, C. R., Rahman, H., Siljedal, H., Thorkildsen, H., Camara, I., Mirarkolaei, K. N., Massé, L., et al. (2019) · Journal of Electrical Bioimpedance · doi:10.2478/joeb-2019-0017 · Cited by 5
“Thirdly, the hysteresis loop turns into a single-valued function as the frequency goes toward infinity [3].”
BackgroundCharge-Controlled Memristor Grid for Edge Detection
Sarmiento-Reyes, A., & Velásquez, Y. R. (2018) · Advances in Memristor Neural Networks - Modeling and Applications · doi:10.5772/intechopen.78610 · Cited by 4
“(cid:129) The model must fulfill the fingerprints of the device [10].”
BackgroundMethodInfluentialMemory, Memristors, and Atomristors
Akinwande, D. (2018) · IEEE Micro · doi:10.1109/mm.2018.053631141 · Cited by 4
An accurate analytical memristor model for SPICE simulators
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Complex behavior in memristor circuits based on static nonlinear two-ports and dynamic bipole
Secco, J., Biey, M., Corinto, F., Ascoli, A., & Tetzlaff, R. (2015) · European Conference on Circuit Theory and Design · doi:10.1109/ecctd.2015.7300050 · Cited by 4
Diao, Y., Huang, S.-F., Xing, Y., Zhang, Z.-H., Xiong, X., & Cai, S.-T. (2026) · Information Sciences · doi:10.1016/j.ins.2025.122917 · Cited by 4
Generation and interaction dynamics of target waves in a memristive Rulkov neural network
Mao, M.-Z., Sun, K., Wang, H.-H., & Chen, X.-J. (2026) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2026.118188 · Cited by 4
Memristive Bio-Impedance Modeling of Fruits and Vegetables
Abdelrahman, D. K., Mohammed, R., Fouda, M., Said, L., & Radwan, A. G. (2021) · IEEE Access · doi:10.1109/access.2021.3055480 · Cited by 4
“In [22], two more fingerprints were identified for a device to be called a memristor, the pinched loop shrinks with increasing frequency, and the loop vanishes at infinite frequency.”
BackgroundMemristor Models and Emulators: A Literature Review
Alharbi, A. G., & Chowdhury, M. (2020) · Springer eBooks · doi:10.1007/978-3-030-51882-0_2 · Cited by 4
The Detectors Used in the First Radios were Memristors
Gandhi, G., Aggarwal, V., & Chua, L. (2019) · Handbook of Memristor Networks · doi:10.1007/978-3-319-02630-5_4 · Cited by 4
Self-citationMemristor, Hodgkin-Huxley, and Edge of Chaos
Chua, L. O. (2019) · Handbook of Memristor Networks · doi:10.1007/978-3-319-76375-0_10 · Cited by 4
Self-citationGale, E. (2017) · Emergence, complexity and computation · doi:10.1007/978-3-319-33921-4_19 · Cited by 4
Dai, Y.-Z., Lai, Q., & Huang, J.-N. (2026) · Chaos · doi:10.1063/5.0341096 · Cited by 3
Recording and modeling of pinched hysteresis loops, the fingerprint of a memristor, in neurons
Pabst, O., Schülke, C., Balasingham, I., Krauss, S., Glover, J. C., & Martinsen, Ø. (2025) · Scientific Reports · doi:10.1038/s41598-025-21035-0 · Cited by 3
“Multiple pinched points are possible as long as one is at the origin of coordinates 7,9 .”
A pseudo-random signal generator based on 2D memristor Logistic map
Xu, B., Wang, Y.-F., Zou, S.-T., Bai, L.-B., Chen, K., & Zhao, J. (2024) · International Instrumentation and Measurement Technology Conference · doi:10.1109/i2mtc60896.2024.10561165 · Cited by 3
“The proposed model evidently satisfies the three typical characteristics of the memory resistor as reported in [18].”
MethodA gate‐tunable memristor emulator for motion detection
Zhang, Z., Ma, Y.-B., Shi, G., Li, C., & Liu, G. (2023) · International journal of circuit theory and applications · doi:10.1002/cta.3888 · Cited by 3
Oresanya, B., Si, G.-Q., Xu, X., Gong, J.-H., & Guo, Z. (2023) · International journal of circuit theory and applications · doi:10.1002/cta.3690 · Cited by 3
Review on Different Emulator memristor modelling and application
Soni, K., & Sahoo, S. (2023) · 2023 11th International Conference on Emerging Trends in Engineering & Technology - Signal and Information Processing (ICETET - SIP) · doi:10.1109/icetet-sip58143.2023.10151553 · Cited by 3
Rössler-like Neuronal Firing with Local Amplitude Control
Li, Z.-N., Li, C.-B., Akgul, A., Bi, L., & Jiang, Y.-C. (2022) · Mathematical Problems in Engineering · doi:10.1155/2022/5943376 · Cited by 3
An Embedded Three-Bit-Per-Cell Two-Transistors and One-Ferroelectric-Capacitance Nonvolatile Memory
Hsieh, E., Wang, Z.-Y., Huang, C.-F., & Wu, Y.-S. (2021) · IEEE Electron Device Letters · doi:10.1109/led.2021.3105593 · Cited by 3
“Most importantly, compared to the 2T cell [13], in the 2T1CFE cell, the MOSFETs and the ferroelectric capacitance can be”
BackgroundCurrent Differencing Buffered Amplifier Based Memristive Quadrature Oscillator
Singh, A., Borah, S., & Ghosh, M. (2021) · International Conference on Electronics, Information and Communications · doi:10.1109/iceic51217.2021.9369780 · Cited by 3
“It's memory property and nanometre dimensions provide a very high density, low-power consumption and produces non-linear effects [3-4].”
Takacs Model of Hysteresis in Mathematical Modeling of Memristors
Dautovic, S., Samardzic, N. M., & Juhas, A. (2020) · Radioengineering · doi:10.13164/re.2020.0147 · Cited by 3
“9 presents HLs in the memristance-charge plane and corresponding PHLs for three different driving oddsymmetric periodic current waveforms.”
BackgroundInfluentialArea of Hysteresis Loop of a Generic Memristor Emulator
Pratyusha, N., Mandal, S., Peesa, R. B., & Suhail, M. (2019) · International Conference on Smart and Sustainable Technologies (SpliTech) · doi:10.23919/splitech.2019.8783019 · Cited by 5
“So it satisfies three finger prints of memristor [1].”
BackgroundInfluentialYang, N.-N., Cheng, S., Wu, C.-J., Jia, R., & Liu, C. (2019) · Complex · doi:10.1155/2019/6083853 · Cited by 3
“If the volt-ampere characteristics of the circuit ports have three characteristics fingerprints as described in [12], it can be defined as a memristor.”
Memory effects in the ion conductor Rb2Ti2O5
Federicci, R., Holé, S., Démery, V., & Léridon, B. (2018) · Journal of Applied Physics · doi:10.1063/1.5036841 · Cited by 3
Memristor interpretations based on constitutive relations
Wu, W., & Deng, N. (2017) · Journal of Semiconductors · doi:10.1088/1674-4926/38/10/104005 · Cited by 3
Uniform and Piece-wise Uniform Fields in Memristor ModelsPreprint
Gale, E. (2014) · arXiv.org · doi:10.48550/arxiv.1404.5581 · Cited by 3
“Because I and V are time differentials of q and φ, memristors produce distinctive non-linear I-V curves that have three important features [10]: (1) hysteresis (memory); (2) zero current at zero”
BackgroundWhich Memristor Theory is Best for Relating Devices Properties to Memristive Function?Preprint
Gale, E., Costello, B. D. L. D. L., & Adamatzky, A. (2013) · arXiv.org · doi:10.48550/arxiv.1312.4422 · Cited by 3
“Although the memristor is defined by its constitutive relation between q and φ, it is theoretically predicted to be have a frequency-dependent pinched hysteresis loop [4, 6] in V − I space (note that open-loop versions have been theoretically postulated [7, 8]).”
BackgroundSynchronization in Memristive Small-World Neural Networks Under Electromagnetic Radiation
Ouyang, J.-P., Wu, Y., Sun, Y.-C., & Ma, M.-L. (2025) · Complex System Modeling and Simulation · doi:10.23919/csms.2024.0036 · Cited by 3
Metadata
- Authors
- Adhikari, S. P., Sah, M. P., Kim, H., & Chua, L. O.
- Affiliations
- Jeonbuk National University (KR)
- University of California, Berkeley (US)
- Venue
- IEEE Transactions on Circuits and Systems I: Regular Papers
- Published
- 2013-11
- Volume
- 60
- Issue
- 11
- Pages
- 3008-3021
- ISSN
- 1549-8328 (ISSN-L)
- 1558-0806
- OpenAlex
- W2084914578
- Cited by
- 659
- References
- 0
- Citations by year
- 2026: 34 · 2025: 56 · 2024: 59 · 2023: 70 · 2022: 76 · 2021: 55 · 2020: 60 · 2019: 49 · 2018: 55 · 2017: 36 · 2016: 28 · 2015: 46 · 2014: 28 · 2013: 6
- FWCI
- 21.60
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Transactions on Circuits and Systems I Regular Papers (publishedVersion)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Memory and Neural Computing
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Ferroelectric and Negative Capacitance Devices
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Keywords
- memristors, pinched hysteresis loop, hysteresis loop area, frequency dependence, current-voltage characteristics
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