Memristive System¶
An electrical one-port model whose evolving internal state changes a multiplicative resistance or conductance response to current or voltage.
Core Idea¶
A memristive system is an electrical one-port model: current or voltage updates an internal state, which changes resistance or conductance. Chua and Kang pair a state-update law with an output law in which this response multiplies the input. Memory without that port/readout form is outside this class.[^ref-3f46af413f22]
The generalized class is wider than an ideal charge-only memristor. Temperature or gating can supply extra state; a loop or device label does not prove charge-only ideality.[ref-3f46af413f22][ref-3e70f35028e9][^ref-4d46a290599e]
Chua’s 1971 ideal element relates accumulated charge and flux. Charge- and flux-controlled forms name response quantities called memristance and memductance. These narrower quantities neither name every generalized system nor prove an ideal physical device.[^ref-6eac539475bf]
Scope of Application¶
The 1975 report gives two unlike theoretical model classifications:
- Thermistor. Electrical power changes body temperature, which changes resistance multiplying current: a first-order current-controlled model.[^ref-3f46af413f22]
- Ionic channel branches. Voltage-driven potassium and sodium gating states change channel conductance, which multiplies driving voltage. The report classifies their branches as first- and second-order voltage-controlled models.[^ref-3f46af413f22]
These are model settings, not independent experiments. The whole membrane is not one branch; a physical device needs separate constitutive evidence.
Strukov and colleagues later reported a switching-device model, simulations, and an experimental comparison attributed to earlier work; their 2009 corrigendum fixes affected Figure 2a and window-function material. This context is not a third complete case here.[ref-a8a638341ce3][ref-584b3011d23d]
Valov and colleagues report nanobattery-driven nonzero-crossing behavior needing an extended model. Separate theory discusses non-finite response. Both are beyond this finite multiplicative subclass; neither invalidates every wider use of “memristor.”[ref-99056f939844][ref-462e90de5acb]
Clarity¶
Four questions test the class: Which current/voltage port? Which operative state? How is it updated? How does it multiply the input in the terminal response? An externally varied resistor or unrelated additive output fails this test.[^ref-3f46af413f22]
Memcapacitive and meminductive systems use different constitutive pairs, respectively charge–voltage and flux–current. They are neighboring memory-element classes, not aliases for the resistive one-port identity.[^ref-3e70f35028e9]
Manages Complexity¶
Separate state update from terminal readout. In a thermistor, heat flow updates temperature before it changes port resistance. In an ionic branch, gating updates conductance before it changes current. The coefficients differ, but both map the four roles.[^ref-3f46af413f22]
Abstract Reasoning¶
Within the 1975 report's continuous, finite-response model, the multiplicative output law yields zero output at zero input. Other results need extra premises: passivity includes a resistance-sign restriction; DC nonlinear-resistor equivalence needs a unique globally asymptotically stable equilibrium per DC input; the high-frequency linear limit needs time-invariant Eq. 4, bounded-input bounded-state stability, and periodic operation. None is an unconditional device law.[^ref-3f46af413f22]
The catalog places this bounded model as a provisional unparented root. A state, loop, or feedback analogy proves no full parent signature or Prime status.
Knowledge Transfer¶
The four-role test transfers between thermal and channel models; their mechanisms and numbers do not. For a proposed device, inspect port, state, update, and readout. Ideal charge-only claims need stronger evidence than a pinched loop.[ref-3f46af413f22][ref-4d46a290599e]
Neighborhood in Abstraction Space¶
Memristive System sits in a sparse region of the domain-specific corpus (95th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2721 abstractions)
Nearest neighbors
- Controlled Invariant Subspace — 0.78
- Quantum Operation — 0.77
- DEVS — 0.77
- Network Synthesis — 0.77
- Lorenz System — 0.76
Computed from structural-signature embeddings · 2026-10-17
References¶
[^ref-6eac539475bf]: Leon O. Chua, “Memristor—The Missing Circuit Element,” IEEE Transactions on Circuit Theory 18(5):507–519 (1971). Original journal scan: https://ethw-images.s3.us-east-va.perf.cloud.ovh.us/ethw/b/bd/Memristor_chua_article.pdf. Inspected PDF indices 0/printed 507, 2/509, and 4/511 for the charge–flux element and charge-/flux-controlled response forms; no physical ideal-device realization is inferred. [^ref-a8a638341ce3]: Dmitri B. Strukov, Gregory S. Snider, Duncan R. Stewart, and R. Stanley Williams, “The missing memristor found,” Nature 453:80–83 (2008). Author-hosted journal PDF: https://www.ece.ucsb.edu/~strukov/papers/2008/Nature2008.pdf. Inspected PDF indices 0–2/printed 80–82, distinguishing the moving-boundary equations, Fig. 3(a–c) simulations, and Fig. 3(d) experimental comparison attributed to the paper's earlier ref. 21. Read affected material with the 2009 corrigendum; no all-instance ideality claim is adopted. [^ref-584b3011d23d]: Dmitri B. Strukov and colleagues (2009). “Erratum, The missing memristor found.” Nature 459:1154. https://doi.org/10.1038/nature08166. The publisher HTML labels it Erratum; the original PDF prints Corrigendum. Corrects affected Fig. 2a right-hand resistance and a window-function formula; reports that published simulations used the corrected formulas. [^ref-99056f939844]: I. Valov and colleagues, “Nanobatteries in redox-based resistive switches require extension of memristor theory,” Nature Communications 4:1771 (2013). https://www.nature.com/articles/ncomms2784. Abstract and Introduction inspected for the observed nonzero-crossing redox-cell behavior and proposed electromotive-force extension. [^ref-462e90de5acb]: Massimiliano Di Ventra and Yuriy V. Pershin, “On the physical properties of memristive, memcapacitive, and meminductive systems,” arXiv:1302.7063 (2013). https://arxiv.org/abs/1302.7063. Author theory on response boundaries; no universal physical-device claim is inferred.
[^ref-3f46af413f22]: Leon O. Chua and Sung Mo Kang, “Memristive Devices and Systems,” University of California, Berkeley, Electronics Research Laboratory Memorandum ERL-M515, 15 April 1975, original report PDF, especially printed pp. 1–4 (definition and Examples 1–2), 5–6 (Property 1), 7–8 (Property 3), and 10–11 (Property 6). https://www2.eecs.berkeley.edu/Pubs/TechRpts/1975/Archive/ERL-m-515.pdf. [^ref-3e70f35028e9]: Massimiliano Di Ventra, Yuriy V. Pershin, and Leon O. Chua, “Circuit Elements with Memory: Memristors, Memcapacitors and Meminductors,” arXiv:0901.3682v1, 23 January 2009, inspected six-page author manuscript, especially PDF pp. 2, 3, and 5. https://diventra.physics.ucsd.edu/Memdevicespub.pdf. The paper's nearby TiO2 ideal-model assertion is not adopted as physical ideality evidence here. [^ref-4d46a290599e]: Yuriy V. Pershin and Massimiliano Di Ventra, “A Simple Test for Ideal Memristors,” arXiv:1806.07360v2, revised 26 September 2018, inspected abstract only. https://arxiv.org/abs/1806.07360v2.