Memristor, Hodgkin–Huxley, and Edge of Chaos
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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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If the memductance function G(x,0) is a smooth function of x, then the Continuum-Memory Memristor can be used as a synapse in brain-like machines.
“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]
The Introduction says memristors are suitable components for brain-like machines, and section 3 says continuously tunable memductance is needed to adjust a synapse’s weight. But the paper does not say that smoothness of G(x,0) is the condition that makes a continuum-memory memristor usable as a synapse; its stated criterion for a continuum of non-volatile states is a zero state-change rate when the input is zero (Theorem 1). The indexed passages provide section labels but no page numbers. (LLM, conf=0.86)
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- 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 · 2012: 1
- 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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