The Hodgkin-Huxley model for action potential generation in biological axons is central for understanding the computational capability of the nervous system and emulating its functionality. Owing to the historical success of silicon complementary metal-oxide-semiconductors, spike-based computing is primarily confined to software simulations and specialized analogue metal-oxide-semiconductor field-effect transistor circuits. However, there is interest in constructing physical systems that emulate biological functionality more directly, with the goal of improving efficiency and scale. The neuristor was proposed as an electronic device with properties similar to the Hodgkin-Huxley axon, but previous implementations were not scalable. Here we demonstrate a neuristor built using two nanoscale Mott memristors, dynamical devices that exhibit transient memory and negative differential resistance arising from an insulating-to-conducting phase transition driven by Joule heating. This neuristor exhibits the important neural functions of all-or-nothing spiking with signal gain and diverse periodic spiking, using materials and structures that are amenable to extremely high-density integration with or without silicon transistors.

A scalable neuristor built with Mott memristors

Redox-based nanoionic resistive memory cells are one of the most promising emerging nanodevices for future information technology with applications for memory, logic and neuromorphic computing. Recently, the serendipitous discovery of the link between redox-based nanoionic-resistive memory cells and memristors and memristive devices has further intensified the research in this field. Here we show on both a theoretical and an experimental level that nanoionic-type memristive elements are inherently controlled by non-equilibrium states resulting in a nanobattery. As a result, the memristor theory must be extended to fit the observed non-zero-crossing I-V characteristics. The initial electromotive force of the nanobattery depends on the chemistry and the transport properties of the materials system but can also be introduced during redox-based nanoionic-resistive memory cell operations. The emf has a strong impact on the dynamic behaviour of nanoscale memories, and thus, its control is one of the key factors for future device development and accurate modelling.

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Nanobatteries in redox-based resistive switches require extension of memristor theory

This paper illustrates that for a device to be a memristor it should exhibit three characteristic fingerprints: 1) When driven by a bipolar periodic signal the device must exhibit a “pinched hysteresis loop” in the voltage-current plane, assuming the response is periodic. 2) Starting from some critical frequency, the hysteresis lobe area should decrease monotonically as the excitation frequency increases, and 3) the pinched hysteresis loop should shrink to a single-valued function when the frequency tends to infinity. Examples of memristors exhibiting these three fingerprints, along with non-memristors exhibiting only a subset of these fingerprints are also presented. In addition, two different types of pinched hysteresis loops; the transversal (self-crossing) and the non-transversal (tangential) loops exhibited by memristors are also discussed with its identification criterion.

Three Fingerprints of Memristor

This chapter consists of two parts. Part I gives a circuit-theoretic foundation for the first four elementary nonlinear 2-terminal circuit elements, namely, the resistor, the capacitor, the inductor, and the memristor. Part II consists of a collection of colorful “Vignettes” with carefully articulated text and colorful illustrations of the rudiments of the memristor and its characteristic fingerprints and signatures. It is intended as a self-contained pedagogical primer for beginners who have not heard of memristors before.

If it’s pinched it’s a memristor

A relaxation oscillator incorporating nanoscale niobium dioxide memristors that exhibit both a current- and a temperature-controlled negative differential resistance produces chaotic dynamics that aid biomimetic computing. In recent years, grids of memristor devices, with their synapse-like dynamics and adaptable conductivity, have demonstrated neural-network-type implementations of analogue (non-Boolean) computing. Suhas Kumar et al. now explore the possibility of exploiting chaotic dynamics in highly nonlinear niobium dioxide memristor devices. This idea is inspired by the theory that biological neurons operate in a regime called 'the edge of chaos', which is thought to be key to the ability of the human brain to tackle complex information processing tasks with high efficiency. The authors demonstrate a controllable regime of chaotic self-oscillations in their devices and simulate a memristor grid that can solve a typical computationally hard task—a travelling salesman problem—with higher accuracy and efficiency than an approach that does not incorporate chaotic elements. Building artificial neural networks with chaotic oscillators based on single electronic devices provides an exciting direction for unconventional analogue computing. At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos1 that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains2,3,4,5,6,7. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos2, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems8. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos9,10,11,12, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking5,6,13. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal–insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator14 and observe a tunable range of periodic and chaotic self-oscillations15. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such memristors into the hardware of a Hopfield computing network can greatly improve the efficiency and accuracy of converging to a solution for computationally difficult problems.

Chaotic dynamics in nanoscale NbO 2 Mott memristors for analogue computing

This paper presents a rigorous and comprehensive nonlinear circuit-theoretic foundation for the memristive Hodgkin–Huxley Axon Circuit model. We show that the Hodgkin–Huxley Axon comprises a potass...

Hodgkin–huxley axon is made of memristors

This paper shows the action potential (spikes) generated from the Hodgkin–Huxley equations emerges near the edge of chaos consisting of a tiny subset of the locally active regime of the HH equations. The main result proves that the eigenvalues of the 4 × 4 Jacobian matrix associated with the mathematically intractable system of four nonlinear differential equations are identical to the zeros of a scalar complexity function from complexity theory. Moreover, we show the loci of a pair of complex-conjugate zeros migrate continuously as a function of an externally applied DC current excitation emulating the net synaptic excitation current input to the neuron. In particular, the pair of complex-conjugate zeros move from a subcritical Hopf bifurcation point at low excitation current to a super-critical Hopf bifurcation point at high excitation current. The spikes are generated as the excitation current approaches the vicinity of the edge of chaos, which leads to the onset of the subcritical Hopf bifurcation regime. It follows from this in-depth qualitative analysis that local activity is the origin of spikes.

Neurons are Poised Near the Edge of Chaos

By exploiting the new concepts of CA characteristic functions and their associated attractor time-τ maps, a complete characterization of the long-term time-asymptotic behaviors of all 256 one-dimensional CA rules are achieved via a single "probing" random input signal. In particular, the graphs of the time-1 maps of the 256 CA rules represent, in some sense, the generalized Green's functions for Cellular Automata. The asymptotic dynamical evolution on any CA attractor, or invariant orbit, of 206 (out of 256) CA rules can be predicted precisely, by inspection. In particular, a total of 112 CA rules are shown to obey a generalized Bernoulli στ-shift rule, which involves the shifting of any binary string on an attractor, or invariant orbit, either to the left, or to the right, by up to 3 pixels, and followed possibly by a complementation of the resulting bit string. The most intriguing result reported in this paper is the discovery that the four Turing-universal rules $\fbox{110}$, $\fbox{124}$, $\fbox{137}$...

A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IV: FROM BERNOULLI SHIFT TO 1/f SPECTRUM

We prove rigorously the four cellular automata local rules 110, 124, 137 and 193 have identical dynamic behaviors capable of universal computations. We exploit Felix Klein's remarkable Vierergruppe to partition the 256 local rules studied empirically by Wolfram into 89 global equivalence classes of which only 50 may exhibit complex dynamics. We define a 24-element rotation group which induces 30 local equivalence classes of nonlinear difference equations whose parameters can be mapped into each other among members of the same class.

A nonlinear dynamics perspective of wolfram's new kind of science part iii: predicting the unpredictable

This paper continues our quest to develop a rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. The 18 yet uncharacterized local rules are henceforth partitioned into ten complex Bernoulliστ-shift rules and eight hyper Bernoulliστ-shift rules, the latter including such famous rules $\kern.5pt{\fboxsep2pt\fbox{30}}\kern.5pt\xspace$ and $\kern.5pt{\fboxsep2pt\fbox{110}}\kern.5pt\xspace$. All exhibit a bizarre composite wave dynamics with arbitrarily large Bernoulli velocity σ and Bernoulli return time τ as the length L → ∞. Basin tree diagrams of all ten complex Bernoulli στ-shift rules are exhibited for lengths L = 3, 4, …, 8. Superficial as it may seem, these basin tree diagrams suggest general qualitative properties which have since been proved to be true in general. Two such properties form the main results of this paper; namely, Explicit global state transition formulas are given for local rules $\kern.5pt{\fboxsep2pt\fbox{90}}\kern.5pt\xspace$, $\kern.5pt{\fboxsep...

Valery I. Sbitnev

Papers

Hodgkin–huxley axon is made of memristors

Neurons are Poised Near the Edge of Chaos

A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IV: FROM BERNOULLI SHIFT TO 1/f SPECTRUM

A nonlinear dynamics perspective of wolfram's new kind of science part iii: predicting the unpredictable

a Nonlinear Dynamics Perspective of Wolfram's New Kind of Science Part Vii: Isles of Eden