Local activity is the capability of a system to amplify infinitesimal fluctuations in energy. Complex phenomena, including the generation of action potentials in neuronal axon membranes, may never emerge in an open system unless some of its constitutive elements operate in a locally active regime. As a result, the recent discovery of solid-state volatile memory devices, which, biased through appropriate DC sources, may enter a local activity domain, and, most importantly, the associated stable yet excitable sub-domain, referred to as edge of chaos, which is where the seed of complexity is actually planted, is of great appeal to the neuromorphic engineering community. This paper applies fundamentals from the theory of local activity to an accurate model of a niobium oxide volatile resistance switching memory to derive the conditions necessary to bias the device in the local activity regime. This allows to partition the entire design parameter space into three domains, where the threshold switch is locally passive (LP), locally active but unstable, and both locally active and stable, respectively. The final part of the article is devoted to point out the extent by which the response of the volatile memristor to quasi-static excitations may differ from its dynamics under DC stress. Reporting experimental measurements, which validate the theoretical predictions, this work clearly demonstrates how invaluable is non-linear system theory for the acquirement of a comprehensive picture of the dynamics of highly non-linear devices, which is an essential prerequisite for a conscious and systematic approach to the design of robust neuromorphic electronics. Given that, as recently proved, the potassium and sodium ion channels in biological axon membranes are locally active memristors, the physical realization of novel artificial neural networks, capable to reproduce the functionalities of the human brain more closely than state-of-the-art purely CMOS hardware architectures, should not leave aside the adoption of resistance switching memories, which, under the appropriate provision of energy, are capable to amplify the small signal, such as the niobium dioxide micro-scale device from NaMLab, chosen as object of theoretical and experimental study in this work.

Department of Electrical Engineering and Computer Sciences University of California Berkeley Berkeley CA United States

Department of Microelectronics Brno University of Technology Brno Czechia

Faculty of Electrical and Computer Engineering Institute of Circuits and Systems Technische Universität Dresden Dresden Germany

Institute für Halbleiter und Mikrosystemtechnik Technische Universität Dresden Dresden Germany

Nano electronic Materials Laboratory gGmbH Dresden Germany

See more in PubMed

Ascoli A., Slesazeck S., Mähne H., Tetzlaff R., Mikolajick T. (2015). Nonlinear dynamics of a locally-active memristor. IEEE Trans. Circuits Syst. I Reg. Pap. 62, 1165–1174. 10.1109/TCSI.2015.2413152 DOI

Ascoli A., Tetzlaff R., Kang S. M., Chua L. O. (2019). Memristor and memristor circuit modelling based on methods of nonlinear system theory, in Springer Lecture Notes on Nonlinear Dynamics in Computational Neuroscience, eds Corinto F., Torcini A. (Springer International Publishing; ), 99–132.

Ascoli A., Tetzlaff R., Kang S. M., Chua L. O. (2020a). Edge of Chaos: The Elan Vital of Complex Phenomena. Available online at: https://cmc-dresden.org/media/edge-of-chaos-the-elan-vital-of-complex-phenomena/

Ascoli A., Tetzlaff R., Kang S. M., Chua L. O. (2020b). Theoretical foundations of memristor cellular nonlinear networks: a DRM2-based method to design memcomputers with dynamic memristors. IEEE Trans. Circuits Syst. I Reg. Pap. 67, 2753–2766. 10.1109/TCSI.2020.2978460 DOI

Ascoli A., Tetzlaff R., Kang S. M., Chua L. O. (2020c). Theoretical foundations of memristor cellular nonlinear networks: stability analysis with dynamic memristors. IEEE Trans. Circuits Syst. I Reg. Pap. 67, 1389–1401. 10.1109/TCSI.2019.2957813 DOI

Ascoli A., Tetzlaff R., Kang S. M., Chua L. O. (2021). System-theoretic methods for designing bio-inspired mem-computing memristor cellular nonlinear networks. J. Front. Nanotechnol. 10.3389/fnano.2021.633026 DOI

Biolek D., Biolek Z., Biolkova V. (2011). Pinched hysteretic loops of ideal memristors, memcapacitors and meminductors must be ‘self-crossing’. Electron. Lett. 47, 1385–1387. 10.1049/el.2011.2913 DOI

Bohaichuk S. M., Kumar S., Pitner G., McClellan C. J., Jeong J., Samant M. G., et al. . (2019). Fast spiking of a Mott VO2-carbon nanotube composite device. Nano Lett. 19, 6751–6755. 10.1021/acs.nanolett.9b01554 PubMed DOI

Burr G. W., Shelby R. M., di Nolfo C., Jang J. W., Shenoy R. S., Narayanan P., et al. . (2015). Experimental demonstration and tolerancing of a large-scale neural network (165000 synapses), using phase-change memory as the synaptic weight element. IEEE Trans. Electron. Devices 62, 3498–3507. 10.1109/IEDM.2014.7047135 DOI

Chicca E., Stefanini F., Bartolozzi C., Indiveri G. (2014). Neuromorphic electronic circuits for building autonomous cognitive systems. Proc. IEEE 102, 1367–1388. 10.1109/JPROC.2014.2313954 DOI

Chua L. O. (1971). Memristor: the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519. 10.1109/TCT.1971.1083337 DOI

Chua L. O. (1987). Linear and Nonlinear Circuits. New York, NY: McGraw-Hill College.

Chua L. O. (1998). CNN: A Paradigm for Complexity. World Scientific Series on Nonlinear Science. Available online at: https://www.worldscientific.com/worldscibooks/10.1142/3801 DOI

Chua L. O. (2005). Local activity is the origin of complexity. Int. J. Bifur. Chaos 15, 3435–3456. 10.1142/S0218127405014337 DOI

Chua L. O. (2011). Resistance switching memories are memristors. Appl. Phys. A 102, 765–783. 10.1007/s00339-011-6264-9 DOI

Chua L. O. (2013). Memristor, Hodgkin Huxley, and Edge of Chaos. Nanotechnology 24:383001. 10.1088/0957-4484/24/38/383001 PubMed DOI

Chua L. O. (2014). If it's pinched, it's a memristor. Semicond. Sci. Technol. 29:42. 10.1088/0268-1242/29/10/104001 DOI

Chua L. O. (2015). Everything you wish to know about memristors but are afraid to ask. Radioengineering 24, 319–368. 10.13164/re.2015.0319 DOI

Chua L. O. (2018). Five non-volatile memristor enigmas solved. Appl. Phys. A 124:563. 10.1007/s00339-018-1971-0 DOI

Chua L. O., Kang S. M. (1976). Memristive devices and systems. Proc. IEEE 64, 209–223. 10.1109/PROC.1976.10092 DOI

Chua L. O., Sbitnev V., Kim H. (2012). Hodgkin-Huxley axon is made of memristors. Int. J. Bifurc. Chaos 22:1230011. 10.1142/S021812741230011X DOI

Corinto F., Forti M., Chua L. (2020). Nonlinear Circuits and Systems With Memristors, Nonlinear Dynamics and Analogue Computing via the Flux-Charge Analysis Method. Springer Verlag. Available online at: https://www.springer.com/gp/book/9783030556501

Demirkol A. S., Ascoli A., Messaris I., Tetzlaff R. (2021). Analytical investigation of pattern formation in an M-CNN with locally active NbOx memristors, in IEEE International Symposium of Circuits and Systems (ISCAS).

Di Ventra M., Traversa F. L. (2018). Perspective: memcomputing: Leveraging memory and physics to compute efficiently. J. Appl. Phys. 123:180901. 10.1063/1.5026506 DOI

Dogaru R., Chua L. (1998). Edge of chaos and local activity domain of FitzHugh-Nagumo equation. Int. J. Bifur. Chaos 8, 211–257. 10.1142/S0218127498000152 DOI

Fuller E. J., Keene S. T., Melianas A., Wang Z., Agarwal S., Li Y., et al. . (2019). Parallel programming of an ionic floating-gate memory array for scalable neuromorphic computing. Science 364, 570–574. 10.1126/science.aaw5581 PubMed DOI

Garay B. (2017). A remark on local activity and passivity. Int. J. Bifur. Chaos 27:1750057. 10.1142/S0218127417500572 DOI

Gibson G. A., Musunuru S., Zhang J., Vandenberghe K., Lee J., Hsieh C. C., et al. . (2016). An accurate locally active memristor model for S-type negative differential resistance in NbOx. Appl. Phys. Lett. 108:023505. 10.1063/1.4939913 DOI

Global Foundries Ltd. (2018). Global Foundries Announcement, 28th August 2018. Available online at: https://spectrum.ieee.org/nanoclast/semiconductors/devices/globalfoundries-halts-7nm-chip-development.

Hodgkin A. L., Huxley A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544. 10.1113/jphysiol.1952.sp004764 PubMed DOI PMC

Ielmini D., Waser R. (2016). Resistive Switching: From Fundamentals of Nanoionic Redox Processes to Memristive Device Applications, 1st Edn. Wiley-VCH. Available online at: https://www.wiley.com/en-us/Resistive+Switching%3A+From+Fundamentals+of+Nanoionic+Redox+Processes+to+Memristive+Device+Applications-p-9783527334179

Ielmini D., Wong H. S. P. (2018). In-memory computing with resistive switching devices. Nat. Electron. 1, 333–343. 10.1038/s41928-018-0092-2 DOI

Indiveri G., Linares-Barranco B., Legenstein R., Deligeorgis G., Prodromakis T. (2013). Integration of nanoscale memristor synapses in neuromorphic computing architectures. Nanotechnology 24:384010. 10.1088/0957-4484/24/38/384010 PubMed DOI

Kumar S., Strachan J. P., Williams R. S. (2017). Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing. Nature 548, 318–321. 10.1038/nature23307 PubMed DOI

Mähne H., Wylezich H., Slesazeck S., Mikolajick T., Vesely J., Klemm V., et al. . (2013). Room temperature fabricated NbOx/Nb2O5 memory switching device with threshold switching effect, in Proceedings of the 5th IEEE International Memory Workshop (IMW), 174–177. Available online at: https://ieeexplore.ieee.org/abstract/document/6582127

Mainzer K., Chua L. O. (2013). Local Activity Principle. Imperial College Press. Available online at: https://www.worldscientific.com/worldscibooks/10.1142/p882 DOI

Mikolajick T., Salinga M., Kund M., Kever T. (2009). Nonvolatile memory concepts based on resistive switching in inorganic materials. Adv. Eng. Mater. 11, 235–240. 10.1002/adem.200800294 DOI

Min L., Chen G. (2004). Local activity of the Van der Pol CNN. Int. J. Bifur. Chaos 7, 2211–2222. 10.1142/S0218127404010552 DOI

Moore G. E. (1965). Cramming more components onto integrated circuits. Electronics 38, 114–117.

Pickett M. D., Medeiros-Ribeiro G., Williams R. S. (2013). A scalable neuristor built with Mott memristors. Nat. Mater. 12, 114–117. 10.1038/nmat3510 PubMed DOI

Pickett M. D., Williams R. S. (2012). Sub-100 fJ and sub-nanosecond thermally driven threshold switching in niobium oxide crosspoint nanodevices. Nanotechnology 23:215202. 10.1088/0957-4484/23/21/215202 PubMed DOI

Pickett M. D., Williams R. S. (2013). Phase transitions enable computational universality in neuristor-based cellular automata. Nanotechnology 24:384002. 10.1088/0957-4484/24/38/384002 PubMed DOI

Serb A., Corna A., George R., Khiat A., Rocchi F., Reato M., et al. . (2020). Memristive synapses connect brain and silicon spiking neurons. Sci. Rep. 10:2590. 10.1038/s41598-020-58831-9 PubMed DOI PMC

Slesazeck S., Ascoli A., Mähne H., Tetzlaff R., Mikolajick T. (2014). Unfolding the threshold switching behavior of a memristor, in Proceedings of the International IEEE Workshop on NDES, eds Mladenov V. M., Ivanov P. C. (Springer International Publishing Switzerland; ), 156–164. Available online at: https://link.springer.com/chapter/10.1007/978-3-319-08672-9_20 DOI

Slesazeck S., Herzig M., Mikolajick T., Ascoli A., Weiher M., Tetzlaff R. (2016). Analysis of Vth variability in NbOx-based threshold switches, in IEEE Nonvolatile Memory Technology Symposium (NVMTS). Available online at: https://ieeexplore.ieee.org/abstract/document/7781515

Slesazeck S., Mähne H., Wylezich H., Wachowiak A., Radhakrishnan J., Ascoli A., et al. . (2015). Physical model of threshold switching in NbO2 based memristors. J. R. Soc. Chem. 5, 102318–102322. 10.1039/C5RA19300A DOI

Tetzlaff R., Ascoli A., Messaris I., Chua L. O. (2020). Theoretical foundations of memristor cellular nonlinear networks: memcomputing with bistable-like memristors. IEEE Trans. Circuits Syst. I Reg. Pap. 67, 502–515. 10.1109/TCSI.2019.2940909 DOI

Tzouvadaki I., Jolly P., Lu X., Ingebrandt S., de Micheli G., Estrela P., et al. . (2016). Label-free ultrasensitive memristive aptasensor. Nano Lett. 16, 4472–4476. 10.1021/acs.nanolett.6b01648 PubMed DOI

Tzouvadaki I., Stathopoulos S., Abbey T., Michalas L., Prodromakis T. (2020). Monitoring PSA levels as chemical state-variables in metal-oxide memristors. Sci. Rep. 10:15281. 10.1038/s41598-020-71962-3 PubMed DOI PMC

Weiher M., Herzig M., Tetzlaff R., Ascoli A., Mikolajick T., Slesazeck S. (2019). Pattern formation with local active S-type NbOx memristors. IEEE Trans. Circuits Syst. I Reg. Pap. 66, 2627–2638. 10.1109/TCSI.2019.2894218 DOI

Weiher M., Herzig M., Tetzlaff R., Ascoli A., Mikolajick T., Slesazeck S. (2021). Improved vertex coloring with NbOx memristor based oscillatory networks. IEEE Trans. Circuits Syst. I Reg. Pap. 10.1109/TCSI.2021.3061973 DOI

Williams R. S. (2017). What's next? [The end of Moore's law]. IEEE Comput. Sci. Eng. 19, 7–13. 10.1109/MCSE.2017.31 DOI

Wylezich H., Mähne H., Rensberg J., Ronning C., Zahn P., Slesazeck S., et al. . (2014). Local ion irradiation induced resistive threshold and memory switching in films. ACS Appl. Mater. Interfaces 6, 17474–17480. 10.1021/am5021149 PubMed DOI

Xia Q., Yang J. J. (2019). Memristive crossbar arrays for brain-inspired computing. Nat. Mater. 18, 309–323. 10.1038/s41563-019-0291-x PubMed DOI

Yi W., Tsang K. K., Lam S. K., Bai X., Crowell J. A., Flores E. A. (2018). Biological plausibility and stochasticity in scalable VO2 active memristor neurons. Nat. Commun. 9, 1–10. 10.1038/s41467-018-07052-w PubMed DOI PMC

Zhang X., Wu Z., Chua L. (2020). Hearts are poised near the edge of chaos. Int. J. Bifurc. Chaos 30:2030023. 10.1142/S0218127420300232 DOI

Zidan M. A., Fahmy H. A. H., Hussain M. M., Salama K. N. (2013). Memristor-based memory: the sneak paths problem and solutions. Microelectron. J. 44, 176–183. 10.1016/j.mejo.2012.10.001 DOI

Zidan M. A., Strachan J. P., Lu W. D. (2018). The future of electronics based on memristive systems. Nat. Electron. 1, 22–29. 10.1038/s41928-017-0006-8 DOI