The cost of materials to make one M-device. The cost is estimated according to common suppliers on the market.
Abstract
Memristors are finding widespread applications in neuromorphic circuits due to their unique resistance memory effect. Nonvolatile memristors are used for implementing artificial synapses and volatile ones for spiking neurons. An important example of the latter is the memristive neurons based on Mott insulators. However, fabricating and understanding volatile memristors based on Mott materials remains a difficult challenge, which hinders their adoption. In recent years, we have been developing an alternative approach based on a novel volatile device that is trivially made with a thyristor and a resistor. These two ordinary out-of-the-shelf conventional electronic components make our memristive device trivial to implement, widely available, reliable and extremely affordable. The key nontrivial insight was to recognize that it exhibits a memristive current-voltage characteristic qualitatively identical to that of Mott insulators. Here, we introduce in detail our device and show how it can be used to implement spiking neurons. We discuss the example of a bursting-neuron circuit model, which exhibits spiking behaviors in remarkable agreement to some observed in biological bursting neurons of mammals. The simplicity and low cost of our neuromorphic hardware makes it an ideal platform for implementing electroceutical medical devices for neuropathologies like epilepsy and Parkinson's disease.
Keywords
- spiking neuron
- neuronal networks
- artificial intelligence
- bursting
- thyristor
1. Introduction
Since the theory of memristors was proposed in the 1970s [1, 2], these devices have been regarded as the fourth fundamental circuit element and have attracted much attention. However, that theory has also provoked some debate [3]. Besides that debate, the physical phenomenon of a resistance, whose value depends on the past history of the current that has circulated thought it, is well established. The potential technological interest has been the initial driver for the massively increasing number of publications that are produced [4]. Memristors have been already applied in various areas, such as resistive random access memories (ReRAM), in-memory computing (IMC), and neuromorphic hardware [5, 6, 7, 8]. The application in neuromorphic technology has gained particularly widespread attention in the AI. This is motivated by the possibility of using memristive arrays to process massive data at extremely low power consumption [9, 10, 11].
Neuromorphic computing is a computational approach inspired by the structure and function of the neural network of human brain [12, 13]. The basic components of neural networks are neurons that are interconnected by synapses [14, 15]. The former can be viewed as computational units that use the information that is stored in the latter. Hence, there is intimate physical proximity between CPU and memory, which is in drastic contrast with the traditional von Neumann computer architecture. In neuromorphic hardware, nonvolatile memristors are usually used to implement the functions of synapses [16, 17, 18, 19], while volatile memristors are used to implement the artificial neurons [20, 21, 22, 23]. One of the most prominent types of materials that are adopted for fabricating memristors are transition metal oxides [24]. Some of the most popular nonvolatile resistive switching compounds are TiO2, HfO2, and Ta2O5, which are finding their way into large crossbar arrays [25]. On the other hand, volatile compounds for neuristors are NbO2 [26] and specially vanadates [24], such as VO2 [27], V2O3 [28], and V3O5 [29]. However, a major challenge that the implementation of this type of neuromorphic devices still faces is their lack of reliability and systematic reproducibility of their characteristics [20, 24, 30]. This issue is significantly more severe for the neuristors, that is, the electronic spiking neurons, which are based on Mott quantum materials. The key property of the so-called Mott insulators that allows them to implement spiking neurons is that they exhibit a spectacular insulator-to-metal transition as function of temperature. In essence, upon application of short and intense voltage pulses, the Mott insulator accumulates the effect of the electric stress until, suddenly, its resistance collapses. As it does, a surge of current flows though the device. That surge is assimilated to the emission of an action potential [31]. We should also mention that another aspect that complicates the situation further is that the theoretical description of Mott materials is also challenging [32]. This is even more so when the materials are pushed away from equilibrium, under the action of strong electric pulsing. Therefore, to provide qualitative understanding of the physics, phenomenological descriptions are a useful [23]. Thus, despite much current effort, the implementation of reliable Mott insulator devices for realizing artificial spiking neurons remains a significant problem of material science.
In this context, in this book chapter, we describe our recent efforts to propose a new volatile memristive device that permits a practical, simple, affordable, and reliable implementation of an electronic spiking neuron [33, 34, 35]. Our device is composed of inexpensive out-of-the-shelf components, namely, a thyristor and a resistor, which will be referred to as the “M-device” in the following (M for Marcelo). The key insight that enables this breakthrough was to realize that the thyristor has an I-V characteristic that closely resembles that of Mott insulator materials, such as VO2, NbO2, and GaTa4Se8 [21, 26, 36, 37]. However, the thyristor is a three-terminal device, while the Mott devices only one. Hence, a second key insight was to realize that analogy with the Mott I-V characteristics can be made complete by simply connecting the gate and anode terminals of the thyristor with a resistance. In Figure 1 below, we show the qualitative agreement between the I-V characteristics of NbO2 and our M-device.
![](/media/chapter/a043Y00000yuj5oQAA/a093Y00001g6EvXQAU/media/F1.png)
Figure 1.
(a) The current-voltage curves of two NbO2 crosspoint devices [reproduced from [
To fully demonstrate this full qualitative agreement between the Mott and the M-device behaviors, we show in the Figure 2 below that both systems when connected in parallel with a capacitor produce the same type of periodic oscillations which resemble the periodic neuronal tonic spiking.
![](/media/chapter/a043Y00000yuj5oQAA/a093Y00001g6EvXQAU/media/F2.png)
Figure 2.
(a) Time dependence of the current through the V3O5 Mott device [reproduced from [
In the present work, we shall describe in detail how our M-device volatile memristor is a simple solution that allows us to build reliable artificial neuron circuits in a very cost-effective and straightforward manner. We shall first describe a basic memristive spiking neuron (MSN) and then extend it to implement a memristive spiking bursting neuron (MSBN) with more complex dynamical behaviors. We shall explore the full parameter space on the MSBN, obtaining a phase diagram of neuronal behaviors. Surprisingly, the phase diagram exploration allowed us to discover various qualitatively different spiking modes that bear striking similarities with those observed in real bursting neurons, rendering unexpected biological relevance to our neuron circuit model. This suggests exciting direction for future developments, such as the implementation of electroceuticals for the medical treatment of neurodegenerative diseases, such as Parkinson’s [38] and epilepsy.
Since the thyristor is a conventional electronic device, one may also extend the memristive circuit to the realm of very-large-scale-integrated CMOS circuits (VLSI) [39]. This enables the fabrication of massive numbers of spiking neurons and adopt it as a platform of large artificial neural networks for Artificial Intelligence applications.
2. The memristive device based on the thyristor
The thyristor, also known as the Silicon-Controlled Rectifier (SCR), is a conventional semiconductor current control device invented in the 1950s [40]. It is composed of p-type and n-type materials arranged in a p-n-p-n four-layer structure. Figure 3(a) and (b) show the schematic and circuit symbol of the thyristor, which has three terminals: Anode, Cathode, and Gate (A, K, G).
![](/media/chapter/a043Y00000yuj5oQAA/a093Y00001g6EvXQAU/media/F3.png)
Figure 3.
(a) Schematic of the thyristor with p-n-p-n four-layer structure, and the changes of the width of the depletion layer at the J2 junction under different external conditions. (b) Circuit symbol of the thyristor. (c) Schematic of the M-device, consists of one thyristor and one resistor connecting the anode and gate of the thyristor. (d) Characteristic I-V of a thyristor in forward bias. Initially, the thyristor is in the high-resistance sate as there is a depletion layer in the inverse junction J2. The gate current (or applied voltage) controls the threshold switch-on value. Note that the I-V displays a negative differential resistance, which is key for the excitability of the memristive neuron device. In addition, there is also hysteresis, which is crucial to produce the
The working principle of a thyristor can be most simply described as a diode with a threshold. A diode is a p-n junction that exhibits low resistance in the forward direction (say, p to n for positive bias) but experiences a significantly high resistance (low conductance) when subjected to a reverse voltage bias. Therefore, a positively biased thyristor can be regarded as two p-n junctions in direct (J1 and J3 in Figure 3(a)), and one in inverse (J2). Therefore, when a forward voltage is applied between Anode and Cathode, and no external voltage applied to the Gate, J1, and J3 would be able to conduct. However, J2 being reverse-biased creates a large depletion region that is difficult for carriers to overcome (Figure 3(a)). Thus, the thyristor is at a very low conductance state. By applying bias to the Gate, the electrons/holes forming the depletion region can be removed so that the depletion layer becomes thinner (Figure 3(a)). Thus, there are in principle two ways to switch on the device, one by applying sufficient positive bias so that a current is forced through the depletion region (as in an inverse bias breakdown of a diode) or by injecting current into the gate. Indeed, when the Gate current (or voltage) reaches a sufficiently high level, the depletion layer becomes “flooded,” and the device switches to the high conductive state. These two phenomena are intertwined, so we can think of a threshold AK voltage that is controlled by the GK current (see Figure 3(d)).
Based on this property of the thyristor, a key insight is that one may connect the Gate directly to the Anode through a resistor
![](/media/chapter/a043Y00000yuj5oQAA/a093Y00001g6EvXQAU/media/F4.png)
Figure 4.
(a) The measured I-V characteristics of the M-device with different
Another key property worth noting of the M-device characteristics is the hysteresis, which originates in the “holding” current of the thyristor. Once the thyristor is at a high conductance state, a large current density is flowing through the formerly depleted region. Hence, even the
These mechanisms enable the memristive characteristic of the M-device even with different
In addition, from the engineering point of view, the threshold voltage (
As the thyristor and resistor are both stable, inexpensive, and out-of-the-shelf electronic components, they make the M-device a reliable and cost-effective volatile memristive device. The cost of building an M-device is much less than 1 $, as listed in Table 1.
Component | Brand | Manufacturer part number | Cost |
---|---|---|---|
Thyristor | STMicroelectronics | P0118MA 2AL3 | ∼0.3 $ |
Resistor | Nova | CBR-14 | <0.1 $ |
Table 1.
3. The memristive spiking neuron model
In this section, we describe the implementation of an analog spiking neuron model exploiting the volatile memristive properties of the M-device. We shall first introduce a basic circuit configuration that implements a leaky-integrate-and-fire model neuron. We shall then extend the basic model to implement a bursting neuron with rich dynamic characteristics. An important point to make is that while a mathematical model is defined by a set of equations, the present neuron models are defined by their hardware implementation. In other words,
A typical biological neuron is schematically represented in Figure 5(a). The neuron receives input current signals through the dendrites and generates electric action potential pulses (spikes) that travel down the axon and generate the output to other (downstream) neurons. A molecular-level mechanism of the spiking neuron can be roughly described by looking at the membrane of the neuron cell depicted in Figure 5(b). The cell body of the neuron is surrounded by a membrane, which is a lipid bilayer containing various types of embedded protein structures [42]. The lipid bilayer membrane is an excellent insulator, preventing the free flow of ions (such as sodium and potassium ions) between the two sides of the cell membrane. However, there are also proteins that form many ion channels across the cell membrane to actively transport or passively allow the passage of ions under certain conditions. Therefore, from a functional perspective, the lipid bilayer can be represented as a capacitor
![](/media/chapter/a043Y00000yuj5oQAA/a093Y00001g6EvXQAU/media/F5.png)
Figure 5.
Schematic of (a) a biological neuron, (b) its membrane structure with lipid bilayer and ion channels, and (c) an equivalent circuit of the integrate-and-fire model, where we only show one conductance channel for simplicity.
The very simplified working principle of such a system can be described as an Integrate-and-Fire (IF) neuron model, as shown in the Figure 5(c). The input currents to the neuron, the charges (ions in the biological case), are first “integrated” in the membrane capacitor
where
In an innovative hardware implementation that is receiving significant attention, a type of quantum materials called Mott insulators is used to implement the nonlinearity required in a voltage-gated channels [20, 21]. The key insight in the present approach is, as demonstrated in Section 2, that the M-devices exhibit I-V characteristics that are analogous to those of Mott insulators, particularly in terms of their volatile history-dependent conductivity or memristance. Therefore, M-devices exhibit the key feature required to implement the conductance channels of Eqs. (1) and (2) above. Moreover, in contrast to the Mott materials that remain a challenge to reliably fabricate and to theoretically understand, our M-device is solely implemented in inexpensive conventional off-the-shelf electronic components.
Figure 6(a) shows the circuit implementation (i.e., definition) of a Memristive Spiking Neuron (MSN). As can be seen in Figure 6(c), the basic MSN circuit realizes a (Leaky) Integrate-and-Fire neuron model. In this model,
![](/media/chapter/a043Y00000yuj5oQAA/a093Y00001g6EvXQAU/media/F6.png)
Figure 6.
(a) Schematic of the Memristive spiking neuron (MSN) circuit based on the M-device. (b) a typical spike generated by the MSN, and the corresponding nonlinear conductance changes of the M-device during the spike event [adapted from [
Under the excitation of a constant current
The Integrate-and-Fire behavior is also very intuitively observed when the input is a train of synaptic current pulses, as seen in Figure 6(c). The pulse inputs are (leaky) integrated in the
From this description, one can readily understand that the spike frequency (firing rate) should depend on the input current. For instance, upon the excitation with a constant current
![](/media/chapter/a043Y00000yuj5oQAA/a093Y00001g6EvXQAU/media/F7.png)
Figure 7.
(a) The spiking frequency’s dependence on input current
However, it is worth noting that such a linear relationship between spiking frequency and
The reason for the departure from the linear behavior at
We observe in Figure 7 the good quality of the fit using the expression of the LIF model in Eq. (3). Those data also demonstrate the type 1 excitability of the MSN model, which refers to systems that initiate spiking from zero frequency [15, 45].
As for the deviation from linear behavior at
4. The memristive bursting neuron model
To search for more complex neuronal dynamics, we extended the MSN into a Memristive Spiking Bursting Neuron (MSBN) model by introducing a second time constant in the circuit model. This is inspired by the two-compartment models (Figure 8(a)) from theoretical neuroscience such as Pinsky-Rinzel model [47]. We introduced a second capacitor
![](/media/chapter/a043Y00000yuj5oQAA/a093Y00001g6EvXQAU/media/F8.png)
Figure 8.
(a) Schematic representation of a two-compartment neuron model. (b) Memristive spiking bursting neuron (MSBN) inspired by the two-compartment model. (c) Four neuronal behaviors generated by the MSBN, including tonic spiking, fast spiking, intrinsic bursting type 1 and type 2. (d) the same spiking and bursting traces generated in a biological realistic timescale by tuning the value of
Thus, the MSBN has, in addition to the first time constant in the circuit defined by the
Note that the last equation in this set shares the same form as the dynamic equation for the [Ca]-current in the theoretical model of Bursting neurons [45].
The MSBN has, nevertheless, some differences from those theoretical mathematical models. In those models, the second time constant
An important point to make is that, as mentioned in the previous section, the spiking frequency is a function of
The MSBN is a remarkably compact circuit comprising only five conventional electronic components, yet its emergent dynamics is complex and biomimetic. Notably, as we shall discuss later on, the neuronal behaviors generated by the MSBN are qualitatively similar to those observed in some biological neurons, such as nigral dopamine neurons under the effect of neurotoxins.
5. The phase diagram and connections to neuroscience
To better understand the origin of the various spiking states of the MSBN, we explore the phase diagram of the model. We find convenient to do this in terms of the variables input current
Figure 9 illustrates the full phase diagram. The red, blue, green, and yellow regions represent the location of the four different neuronal behaviors shown above. The gray region stands for the quiescent state, which appears when
![](/media/chapter/a043Y00000yuj5oQAA/a093Y00001g6EvXQAU/media/F9.png)
Figure 9.
Left: Phase diagram of the Memristive spiking bursting neuron circuit, with the two variables being the input current and the time-constant of the soma-compartment
The phase diagram gives us further insights on the mechanism operating in the MSBN neuron model. For example, on the left part of the phase diagram, where
As
We consider the transition from TS to FS as an example to describe the mechanism by which other spiking states emerge. Let us for the moment disregard the influence of
The understanding of the mechanism of IB1 and IB2 is not so straightforward. We have provided a mathematical description of its dynamics elsewhere [49]. Nevertheless, we can qualitatively see that these behaviors are associated to the upper and lower current excitability thresholds, which correspond to
While our MSBN is not a bio-realistic model, it is a striking observation that it is biomimetic. Indeed, we discovered surprising similarities between the spiking modes generated by our circuit and those measured in traces of biological bursting neurons under the action of different neurotoxins that affect their normal spiking behavior. This is shown in Figure 10, where we directly compare MSBN traces to those from biological bursting neurons. In panel (a), we compare the different traces obtained in nigral dopamine neurons, which start from the normal (control) state and then become severely affected by exposure to neurotoxins: first apamin and then apamin+TTX + TEA [38]. These neurotoxins are found to provoke two different sets of pathological spiking behaviors, as shown in the Figure 8(a). Interestingly, all the different spiking behaviors seen in the nigral dopamine neurons can be qualitatively found in our phase diagram, as we show in the figure. It is a very interesting observation that we may then associate a “path” in the phase diagram to the action of neurotoxins. This may have a potentially useful application as a guide for neurologists to understand the origin of pathological spiking behaviors.
![](/media/chapter/a043Y00000yuj5oQAA/a093Y00001g6EvXQAU/media/F10.png)
Figure 10.
The evolutionary paths in phase diagram can reproduce to some extent the evolution of biological neuronal behavior. (a) the central panel shows the successive firing states due to effects of neurotoxins on nigral dopamine neurons [adapted from [
Perhaps even more striking is our second example shown in panel (b). In this case, the biological neurons are another type of bursters: pre-Bötzinger respiratory neurons [51]. In this case, the experiment consisted in rendering the neuron quiescent by application of a neurotoxin. Then, by sole application of input current, the neuron can be reactivated. Upon increasing input current in small steps, it is observed that the neuron emits an increasing number of short spike trains. Eventually, at high enough input current, the trains become a continuous fast spiking. Quite strikingly, we find that this same behavior can be captured by our MSBN. In fact, as shown in the Figure 10(b), we observe how by moving vertically in the phase diagram, that is, solely increasing the input current, the MSBN evolves from the quiescent state through a series of bursting states with increasing number of spike trains, to a final fast spiking, in excellent qualitative agreement with the behavior of the biological pre-Bötzinger neuron [51].
6. Conclusion
In this work, we described in detail a novel volatile memristive electronic component, the M-device, which we synthetize out of two conventional out-of-the-shelf electronic components (a thyristor and a resistor).
The M-device exhibits pinched hysteresis and bears a striking qualitative similarity to the I-V behavior of many Mott insulators, which are quantum materials emerging as candidates for future neurocomputing hardware [20, 21, 24, 26, 37]. Like Mott neurons, our device has extreme simplicity enabling straightforward biomimetic spiking neuron behavior. Unlike Mott neurons, which are still hard to fabricate and function in a consistent and reliable manner, our M-device is extremely reliable and affordable, allowing for very cost-effective implementations. While neurons made out of discrete components present an evident limit to the practical number of neurons that one may envision in a neural network (up to hundreds), they provide a flexibility in circuit design that is unachievable in CMOS VLSI systems, which require long design times and fabrication. In any case, the M-device can be straightforwardly ported to CMOS VLSI technology [39] while carrying along the conceptual simplicity provided by the memristive device.
In recent years, Neuromorphic technology has become a significant application arena for volatile memristors [20, 21, 24, 26, 37]. Based on the M-device, we demonstrated here a simple Memristive Spiking Neuron (MSN) circuit, which provides a physical hardware implementation of the functionality of the popular Leaky Integrate-and-Fire (LIF) model, in fully analogic electronic. This is a concrete realization of the concept “
This simplicity enabled us the full exploration of the phase diagram of neuronal behavior of the MSBN. We made explicit contact with two notable examples of biological bursting neurons: Nigral Dopamine and pre-Bötzinger respiratory. Specifically, we were able to “follow the path” in the phase diagram of their pathological spiking evolution under the action of neurotoxins. These amazing connections may open up the way for potential unprecedented novel approaches to understanding pathological states such as those in Parkinson’s and epilepsy, or even new ways for treating neurodegenerative diseases, though implementations in the field of neuroprosthetics and neuro-implants.
Acknowledgments
We acknowledge support from the French ANR “MoMA” project ANR-19-CE30-0020.
References
- 1.
Chua L. Memristor-the missing circuit element. IEEE Transactions on Circuit Theory. 1971; 18 (5):507-519. DOI: 10.1109/TCT.1971.1083337 - 2.
Chua LO, Kang SM. Memristive devices and systems. Proceedings of the IEEE. 1976; 64 (2):209-223. DOI: 10.1109/PROC.1976.10092 - 3.
Di Ventra M, Pershin YV, Chua LO. Circuit elements with memory: Memristors, memcapacitors, and meminductors. Proceedings of the IEEE. 2009; 97 (10):1717-1724 - 4.
Jeong DS, Kim KM, Kim S, Choi BJ, Hwang CS. Memristors for energy-efficient new computing paradigms. Advanced Electronic Materials. 2016; 2 (9):1600090 - 5.
Zahoor F, Azni Zulkifli TZ, Khanday FA. Resistive random access memory (RRAM): An overview of materials, switching mechanism, performance, multilevel cell (MLC) storage, modeling, and applications. Nanoscale Research Letters. 2020; 15 :1-26 - 6.
Golonzka O, et al. Non-Volatile RRAM embedded into 22FFL FinFET technology. In: 2019 Symposium on VLSI Technology. 2019. pp. T230-T231 - 7.
Mehonic A, Sebastian A, Rajendran B, et al. Memristors—From in-memory computing, deep learning acceleration, and spiking neural networks to the future of neuromorphic and bio-inspired computing. Advanced Intelligent Systems. 2020; 2 (11):2000085 - 8.
Lanza M, Sebastian A, Lu WD, Le Gallo M, Chang MF, Akinwande D, et al. Memristive technologies for data storage, computation, encryption, and radio-frequency communication. Science. 2022; 376 (6597):eabj9979 - 9.
Merolla PA, Arthur JV, Alvarez-Icaza R, Cassidy AS, Sawada J, Akopyan F, et al. A million spiking-neuron integrated circuit with a scalable communication network and interface. Science. 2014; 345 (6197):668-673 - 10.
Marković D, Mizrahi A, Querlioz D, et al. Physics for neuromorphic computing. Nature Reviews Physics. 2020; 2 (9):499-510 - 11.
Thakur CS, Molin JL, Cauwenberghs G, Indiveri G, Kumar K, Qiao N, et al. Large-scale neuromorphic spiking array processors: A quest to mimic the brain. Frontiers in Neuroscience. 2018; 12 :891 - 12.
Mead C. Neuromorphic electronic systems. Proceedings of the IEEE. 1990; 78 (10):1629-1636 - 13.
Ham D, Park H, Hwang S, et al. Neuromorphic electronics based on copying and pasting the brain. Nature Electronics. 2021; 4 :635-644. DOI: 10.1038/s41928-021-00646-1 - 14.
Herz AVM, Gollisch T, Machens CK, et al. Modeling single-neuron dynamics and computations: A balance of detail and abstraction. Science. 2006; 314 (5796):80-85 - 15.
Gerstner W, Kistler WM, Naud R, et al. Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge: Cambridge University Press; 2014 - 16.
Rahimi Azghadi M, Chen YC, Eshraghian JK, Chen J, Lin CY, Amirsoleimani A, et al. Complementary metal-oxide semiconductor and memristive hardware for neuromorphic computing. Advanced Intelligent Systems. 2020; 2 (5):1900189 - 17.
Kim H, Mahmoodi MR, Nili H, Strukov DB. 4K-memristor analog-grade passive crossbar circuit. Nature Communications. 2021; 12 (1):5198 - 18.
Kim SG, Han JS, Kim H, Kim SY, Jang HW. Recent advances in memristive materials for artificial synapses. Advanced Materials Technologies. 2018; 3 (12):1800457 - 19.
Chang YF, Fowler B, Chen YC, Zhou F, Pan CH, Chang TC, et al. Demonstration of synaptic behaviors and resistive switching characterizations by proton exchange reactions in silicon oxide. Scientific Reports. 2016; 6 (1):21268 - 20.
del Valle J, Ramírez JG, Rozenberg MJ, Schuller IK. Challenges in materials and devices for resistive-switching-based neuromorphic computing. Journal of Applied Physics. 2018; 124 (21):211101. DOI: 10.1063/1.5047800 - 21.
Yi W, Tsang KK, Lam SK, Bai X, Crowell JA, Flores EA. Biological plausibility and stochasticity in scalable VO2 active memristor neurons. Nature Communications. 2018; 9 (1):4661 - 22.
Park SO, Jeong H, Park J, Bae J, Choi S. Experimental demonstration of highly reliable dynamic memristor for artificial neuron and neuromorphic computing. Nature Communications. 2022; 13 (1):2888 - 23.
Rocco R, del Valle J, Navarro H, Salev P, Schuller IK, Rozenberg M. Exponential escape rate of filamentary incubation in Mott spiking neurons. Physical Review Applied. 2022; 17 (2):024028 - 24.
Hoffmann A et al. Quantum materials for energy-efficient neuromorphic computing: Opportunities and challenges. APL Materials. 2022; 10 (7):070904 - 25.
Strukov D, Snider G, Stewart D, et al. The missing memristor found. Nature. 2008; 453 :80-83. DOI: 10.1038/nature06932 - 26.
Pickett MD, Medeiros-Ribeiro G, Williams RS. A scalable neuristor built with Mott memristors. Nature Materials. 2013; 12 (2):114-117 - 27.
Del Valle J et al. Subthreshold firing in Mott nanodevices. Nature. 2019; 569 (7756):388-392 - 28.
Del Valle J et al. Spatiotemporal characterization of the field-induced insulator-to-metal transition. Science. 2021; 373 (6557):907-911 - 29.
Adda C et al. Direct observation of the electrically triggered insulator-metal transition in V 3 O 5 far below the transition temperature. Physical Review X. 2022; 12 (1):011025 - 30.
Li Y, Wang Z, Midya R, Xia Q, Yang JJ. Review of memristor devices in neuromorphic computing: Materials sciences and device challenges. Journal of Physics D: Applied Physics. 2018; 51 (50):503002 - 31.
Stoliar P et al. A leaky-integrate-and-fire neuron analog realized with a Mott insulator. Advanced Functional Materials. 2017; 27 (11):1604740 - 32.
Georges A, Kotliar G, Krauth W, Rozenberg MJ. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Reviews of Modern Physics. 1996; 68 (1):13 - 33.
Wu J, Wang K, Schneegans O, Stoliar P, Rozenberg M. Bursting dynamics in a spiking neuron with a memristive voltage-gated channel. Neuromorphic Computing and Engineering. 2023; 3 (4):044008 - 34.
Rozenberg MJ, Schneegans O, Stoliar P. An ultra-compact leaky-integrate-and-fire model for building spiking neural networks. Scientific Reports. 2019; 9 (1):11123 - 35.
Stoliar P, Schneegans O, Rozenberg MJ. Biologically relevant dynamical behaviors realized in an ultra-compact neuron model. Frontiers in Neuroscience. 2020; 14 :421 - 36.
Stoliar P et al. Universal electric-field-driven resistive transition in narrow-gap Mott insulators. Advanced Materials. 2013; 25 (23):3222-3226 - 37.
Janod E, Tranchant J, Corraze B, Querré M, Stoliar P, Rozenberg M, et al. Resistive switching in Mott insulators and correlated systems. Advanced Functional Materials. 2015; 25 (40):6287-6305 - 38.
Rubin JE, Terman D. High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. Journal of Computational Neuroscience. 2004; 16 :211-235 - 39.
Stoliar P, Akita I, Schneegans O, Hioki M, Rozenberg MJ. A spiking neuron implemented in VLSI. Journal of Physics Communications. 2022; 6 (2):021001 - 40.
Sze SM, Li Y, Ng KK. Physics of Semiconductor Devices. New Jersey: John Wiley & Sons; 2021 - 41.
Chua L. If it’s pinched it’sa memristor. Semiconductor Science and Technology. 2014; 29 (10):104001 - 42.
Kandel ER, Schwartz JH, Jessell TM, Siegelbaum S, Hudspeth AJ, Mack S, editors. Principles of Neural Science. Vol. 4. New York: McGraw-Hill; 2000. pp. 1227-1246 - 43.
Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology. 1952; 117 (4):500 - 44.
Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal. 1981; 35 (1):193-213 - 45.
Ermentrout B, Terman DH. Mathematical foundations of neuroscience. New York: Springer; 2010 - 46.
Bianchi D, Marasco A, Limongiello A, Marchetti C, Marie H, Tirozzi B, et al. On the mechanisms underlying the depolarization block in the spiking dynamics of CA1 pyramidal neurons. Journal of Computational Neuroscience. 2012; 33 :207-225 - 47.
Pinsky PF, Rinzel J. Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. Journal of Computational Neuroscience. 1994; 1 :39-60 - 48.
Segev I, Rall W. Excitable dendrites and spines: Earlier theoretical insights elucidate recent direct observations. Trends in Neurosciences. 1998; 21 (11):453-460 - 49.
Fernandez LE, Carpio A, Wu J, Boccaletti S, Rozenberg M, Mindlin GB. A model for an electronic spiking neuron built with a memristive voltage-gated element. Chaos, Solitons and Fractals. 2024; 180 :114555 - 50.
Ping HX, Shepard PD. Apamin-sensitive Ca (2+)-activated K+ channels regulate pacemaker activity in nigral dopamine neurons. Neuroreport. 1996; 7 (3):809-814 - 51.
Butera RJ Jr, Rinzel J, Smith JC. Models of respiratory rhythm generation in the pre-Botzinger complex. I. Bursting pacemaker neurons. Journal of Neurophysiology. 1999; 82 (1):382-397