1. Memristor neurons and their coupling networks based on Edge of Chaos Kernel.
- Author
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Zhou, Wei, Jin, Peipei, Dong, Yujiao, Liang, Yan, and Wang, Guangyi
- Subjects
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ACTION potentials , *BIOLOGICAL neural networks , *NEURONS , *NEURAL circuitry , *HEAT equation , *CONVOLUTIONAL neural networks - Abstract
Chua's theory of local activity shows that local activity is the origin of complexity, and the complexity can only occur on or near the stable locally active domain, referred to as Edge of Chaos (EOC). Very recently, for the voltage-controlled locally active memristors, a new physical concept dubbed "Edge of Chaos Kernel" (EOCK), which consists of a series combination between a negative resistance and a negative inductance and exhibits the EOC phenomenon of being stable yet potentially unstable, was defined and applied to the Hodgkin-Huxley neural circuit model. When an EOCK is coupled to a passive environment, its stability is disrupted, resulting in the emergence of action potentials, chaos and various complex phenomena. This paper proposes the dual version of the EOCK called as R - C EOCK, which consists of the parallel combination between a negative resistance and a negative capacitance. We show that the actual NbO memristor manufactured by NaMLab essentially belongs to a current-controlled locally active memristor which contains a R - C EOCK and gives the signature of its EOCK and EOC. We construct a second-order neuron based on the NbO memristor when connected in parallel with a passive capacitor, and further prove that only memristors endowed with an EOCK can generate action potential. On this basis, we construct a minimum cellular neural network with only 7 components based on two NbO memristor neurons and a passive coupling resistor, in which neuromorphic behaviors of static and dynamic pattern formation may emerge if and only if the single neuron has an EOCK and is poised on the EOC. The analysis in this paper explains the dynamic mechanism of Smale's paradox, in which two mathematically dead neurons coupled by a passive environment may become alive, under the same or different input current excitation, which are more in line with the actual biological neural networks. • Brains need memristors blessed with an Edge of Chaos Kernel (EOCK), the crown jewel of emerging complexity. This paper extended the concept of EOCK of the voltage-controlled memristors to the generic current-controlled memristors through Chua's theories. • Based on the actual S-type NbO memristor, an intrinsic current-controlled memristor, we constructed a second-order NbO memristive neuron circuit by connecting a passive capacitance in parallel with the memristor, and further verified that it can generate action potentials such as damping spiking, periodic spiking, and self-sustained oscillation, if and only if the memristor is endowed with an EOCK. • Furthermore, this paper constructed the simplest fourth-order memristive cellular neural network (CNN) with only 7 components, containing two twinborn NbO memristive neurons with a passive resistor, from which we found that when both neurons are in the resting state and possess an EOCK, the appropriate coupling resistances can make the CNN produce a surprising oscillation phenomenon known as the inexplicable Smale's paradox, while the NbO neurons become "alive". These findings not only reveal the mechanism of the above Smale's paradox in a basic memristive CNN (which can be considered as reaction diffusion equations), but also explain the static and dynamic pattern formation of the memristive CNNs, which can provide a theoretical basis for the design and analysis of the CNNs. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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