The DOI matches its Crossref record; 35 of the 36 references it cites were found in a registry or an index.
Memristor, Hodgkin–Huxley, and Edge of Chaos
Open accessAbstract
From a pedagogical point of view, the memristor is defined in this tutorial as any 2-terminal device obeying a state-dependent Ohm's law. This tutorial also shows that from an experimental point of view, the memristor can be defined as any 2-terminal device that exhibits the fingerprints of 'pinched' hysteresis loops in the v-i plane. It also shows that memristors endowed with a continuum of equilibrium states can be used as non-volatile analog memories. This tutorial shows that memristors span a much broader vista of complex phenomena and potential applications in many fields, including neurobiology. In particular, this tutorial presents toy memristors that can mimic the classic habituation and LTP learning phenomena. It also shows that sodium and potassium ion-channel memristors are the key to generating the action potential in the Hodgkin-Huxley equations, and that they are the key to resolving several unresolved anomalies associated with the Hodgkin-Huxley equations. This tutorial ends with an amazing new result derived from the new principle of local activity, which uncovers a minuscule life-enabling 'Goldilocks zone', dubbed the edge of chaos, where complex phenomena, including creativity and intelligence, may emerge. From an information processing perspective, this tutorial shows that synapses are locally-passive memristors, and that neurons are made of locally-active memristors.
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“In the case where the memductance function G ( x, 0) is a smooth function x , then this memristor can be used as a synapse [3], [32], [35] in brainslike machines.”
From Everything You Wish to Know About Memristors But Are Afraid to Ask (2015) · cites this paper as [32]
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Cites
Hodgkin, A. L., & Huxley, A. F. (1952) · The Journal of Physiology · doi:10.1113/jphysiol.1952.sp004764 · Cited by 23,191
Strukov, D. B., Snider, G. S., Stewart, D. R., & Williams, R. S. (2008) · Nature · doi:10.1038/nature06932 · Cited by 11,828
The chemical basis of morphogenesis
Turing, A. M. (1952) · Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences · doi:10.1098/rstb.1952.0012 · Cited by 11,733
Memristor—The Missing Circuit Element
Chua, L. (1971) · IEEE Transactions on Circuit Theory · doi:10.1109/tct.1971.1083337 · Cited by 10,268
Self-citationBliss, T. V. P., & Gardner-Medwin, A. R. (1973) · The Journal of Physiology · doi:10.1113/jphysiol.1973.sp010274 · Cited by 7,460
Memristive devices and systems
Chua, L. O., & Kang, S. M. (1976) · Proceedings of the IEEE · doi:10.1109/proc.1976.10092 · Cited by 2,604
Self-citationNeuroscience: Exploring the brain
Wood, I. K. (1996) · Journal of Child and Family Studies · doi:10.1007/bf02234670 · Cited by 1,530
Resistance switching memories are memristors
Chua, L. (2011) · Applied Physics A · doi:10.1007/s00339-011-6264-9 · Cited by 1,434
Self-citationChua, L. O. (1987) · Cited by 1,245
Self-citationNeuroscience: Exploring the Brain
Bear, M. F., Connors, B. W., & Paradiso, M. A. (1996) · Cited by 1,050
Research works printed but not linked: 5
- Adhikari S P, 2013, IEEE Trans. Circuits Syst.
- Chua L O, 2009, IEEE Expert Now Educational Course
- Bliss T V P, 1973, J. Physiol., 232, 331, 10.1113/jphysiol.1973.sp010273 · DOI · Paper page
- Bliss T V P, 2004, LTP: Long Term Potentiation
- Smale S, 1974, American Mathematically Society, 6, 15
Cited by
Sorted by citations
Neuromorphic nanoelectronic materials
Sangwan, V. K., & Hersam, M. C. (2020) · Nature Nanotechnology · doi:10.1038/s41565-020-0647-z · Cited by 907
If it's pinched it's a memristor
Chua, L. (2014) · Semiconductor Science and Technology · doi:10.1088/0268-1242/29/10/104001 · Cited by 685
Self-citationBrain-inspired computing needs a master plan
Mehonic, A., & Kenyon, A. J. (2022) · Nature · doi:10.1038/s41586-021-04362-w · Cited by 632
“They may embody some of the functionality of biological dendrites 5 and their dynamic response can generate oscillatory behaviour similar to that of the brain – controversially, operating on the edge of chaos 6,7 .”
Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing
Kumar, S., Strachan, J. P., & Williams, R. S. (2017) · Nature · doi:10.1038/nature23307 · Cited by 620
Everything You Wish to Know About Memristors But Are Afraid to Ask
Chua, L. (2015) · Radioengineering · doi:10.13164/re.2015.0319 · Cited by 481
Self-citation
Metadata
- Authors
- Chua, L.
- Affiliations
- University of California System (US)
- Corresponding author
- Chua, Leon
- ORCID
- Chua, Leon
- Venue
- Nanotechnology
- Publisher
- IOP Publishing
- Published
- 2013-09-02
- Volume
- 24
- Issue
- 38
- Pages
- 383001
- ISSN
- 0957-4484 (ISSN-L)
- 1361-6528
- OpenAlex
- W1973200562
- Cited by
- 253
- References
- 36
- Citations by year
- 2026: 13 · 2025: 31 · 2024: 14 · 2023: 23 · 2022: 24 · 2021: 26 · 2020: 20 · 2019: 28 · 2018: 18 · 2017: 14 · 2016: 16 · 2015: 11 · 2014: 11 · 2013: 3
- FWCI
- 0.94
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Nanotechnology (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Air Force Office of Scientific Research (FA9550-, FA9550-10-1-, FA9550-13-1-0136)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Memory and Neural Computing
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Keywords
- memristors, Hodgkin-Huxley model, edge of chaos, pinched hysteresis, habituation, long-term potentiation, action potential, synapses, neurons, neuromorphic computing, emergence of intelligence
- MeSH terms
- Animals, Aplysia, Electronics, Models, Neurological, Synapses, Nanotechnology
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