Negative Differential Resistance Effects in Memristors at the Origin of Complex Phenomena in Biological and Nano-electronic Systems

As established by the second law of thermodynamics, complex phenomena may not emerge in isolated systems. On the other hand, if a system is allowed to interact with the environment, it may undergo complex dynamics, provided some of its constitutive units, stabilized in suitable bias points by appropriate energy sources, are capable to boost the local signals, entering a significant operating regime called Local Activity [1,2]. Moreover, if the bias points of these small-signal amplifiers are asymptotically stable, the system is said to be
poised on the Edge of Chaos [3], which is known as Local Activity Pearl, since complex, and sometimes counterintuitive, phenomena originate in this subset of the Local Activity domain. The Edge of Chaos extends the second law of thermodynamics to open systems, allowing to explain the mechanisms underlying the emergence of complexity in physical systems from
fields as diverse as biology, ecology, physics, chemistry, electronics, as well as economics, and sociology. This new physics principle provides answers to various open questions, which animated the scientific community for decades. To name but a couple of examples, which will be analyzed over the course of this seminar, through its robust theoretical foundations, one may unveil the secrets behind the origin of all-or-none spikes in neuronal axons from our brain
[4] and heart [5], a fascinating topic, which has been puzzling scientists for 60 years since the 1952 seminal work from Hodgkin and Huxley [6], and resolve the mystery, which mesmerized luminaries as prestigious as Alan Turing [7], Ilya Prigogine [8], and Stephen Smale [9] over the past century, and lies behind the emergence of symmetry-breaking instabilities, leading to static and dynamic pattern formation, in homogeneous media consisting of identical diffusively-coupled cells, which would be silent on their own. Last but not least, the Local
Activity and Edge of Chaos theory allows to leverage Negative Differential Resistance effects in certain memristor physical nano-scale realizations, exhibiting similar behaviors as the ion channels inside biological axon membranes [10], for the development of a systematic approach to bio-inspired circuit design [11,12,13].  

 

Bibliography:
[1] L.O. Chua, “Local activity is the origin of complexity”, Int. J. Bifurc. Chaos, vol. 15, no. 11, pp. 3435-3456, 2005
[2] K. Mainzer, and L.O. Chua, “The Local Activity Principle”, Imperial College Press, 2013, ISBN-13: 978-1908977090
[3] L.O. Chua, A. Ascoli, and R. Tetzlaff, “Edge of Chaos: The Elan Vital of Complex Phenomena,” available on the 26th of March 2021 at https://cmc-dresden.org/media/edge-of-chaos-the-elan-vitalof- complex-phenomena/ (password upon request), created in Nov. 2020
[4] L.O. Chua, V. Sbitnev, and H. Kim, “Neurons are poised near the Edge of Chaos”, vol. 22, vol. 4, 1250098 (49pp.), 2012
[5] X. Zhang, Z. Wu, and L.O. Chua, “Hearts are poised near the Edge of Chaos,” Int. J. Bifurc. Chaos, vol. 30, no. 9, 2030023(78pp.), 2020
[6] A.L. Hodgkin, and A.F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve”, J. Physiol., vol. 117, no. 4, pp. 500-544, 1952
[7] A.M. Turing, “The Chemical Basis of Morphogenesis”, Philosophical Transactions of the Royal Society of London, Series B, Biological Sciences, vol. 237, no. 641, pp. 37-72, 1952
[8] I. Prigogine, and G. Nicolis, "On Symmetry-Breaking Instabilities in Dissipative Systems”, J. Chem. Phys., vol. 46, no. 9, pp. 3542-3550, 1967
[9] S. Smale, “A Mathematical Model of Two Cells via Turing’s Equation”, Lectures in Applied Mathematics, American Mathematical Society, vol. 6, pp. 15-26, 1974
[10] L.O. Chua, V. Sbitnev, and H. Kim, “Hodgkin-Huxley axon is made of memristors”, Int. J. Bifurc. Chaos, vol. 22, no. 3, 1230011(48pp.), 2012
[11] A. Ascoli, A.S. Demirkol, R. Tetzlaff, S. Slesazeck, T. Milolajick, and L.O. Chua, “On Local Activity and Edge of Chaos in a NaMLab Memristor”, Frontiers in Neuroscience, 2021, DOI: 10.3389/fnins.2021.651452
[12] M. Weiher, M. Herzig, R. Tetzlaff, A. Ascoli, T. Mikolajick, and S. Slesazeck, “Pattern formation with local active S-type NbOx memristors,” IEEE Trans. on Circuits and Systems–I: Regular Papers, vol. 66, no. 7, pp. 2627-2638, 2019, DOI: 10.1109/TCSI.2019.2894218
[13] M. Weiher, M. Herzig, R. Tetzlaff, A. Ascoli, T. Mikolajick, and S. Slesazeck, “Improved Vertex Coloring With NbOx Memristor-Based Oscillatory Networks”, IEEE Trans. Circuits and Systems-I: Regular Papers, 2021, DOI: 10.1109/TCSI.2021.3061973 

Short Biography:
Alon Ascoli (IEEE member) received a Ph.D. Degree in Electronic Engineering from University College Dublin in 2006. From 2006 to 2009 he worked as RFIC analog engineer at CSR Sweden AB. From 2009 to 2012 he was Research Assistant in the Department of Electronics and Telecommunications at Politecnico di Torino. Since 2018 he is Scientific Collaborator with the Department of Microelectronics, Brno University of Technology, Brno, Czech Republic. Since 2012 he is Scientific Collaborator in the Faculty of Electrical and Computer Engineering, Technische Universität Dresden, where he is currently pursuing a Habilitation in Fundamentals of Electrical Engineering. His research interests lie in the area of nonlinear circuits and systems, networks of oscillators, Cellular Nonlinear Networks and memristors. Dr. Ascoli was honored with the International Journal of Circuit Theory and its Applications (IJCTA) 2007 Best Paper Award. He is the President of the Cellular Nanoscale Networks and Array Computing Technical Committee (CNNAC-TC) since May 2019. In April 2017 he was conferred the habilitation title as Associate Professor in Electrical Circuit Theory from the Italian Ministry of Education. Since 2014 he is Management Committee Substitute for Germany in then COST Action IC1401 MemoCIS “Memristors – Devices, Models, Circuits, Systems, and Applications”. He has been Program Chair and Special Session Chair for the 15th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA) in 2016. He is the Technical Program Chair for the International Conference on Memristive Materials, Devices, and Systems (MEMRISYS) 2019.