Dynamics of two neuron-like generators with memristive connection
- Authors: Bolshakov D.I.1, Mishchenko M.A.1, Belov A.I.1, Matrosov V.V.1, Mikhaylov A.N.1
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Affiliations:
- National Research Lobachevsky State University of Nizhny Novgorod
- Issue: Vol 18, No 4 (2023)
- Pages: 790-793
- Section: Conference proceedings
- URL: https://genescells.ru/2313-1829/article/view/623344
- DOI: https://doi.org/10.17816/gc623344
- ID: 623344
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Abstract
At present one of the most urgent tasks of interdisciplinary science is the design and research of neuromorphic devices. Such devices are most often used to create systems for processing various kinds of information with algorithms similar to the data processing algorithms of the human brain or the brain of animals. The development of such neuromorphic electronics will allow computing devices and information processing systems to be built based on new principles and with a high level of parallelism [1].
Neuromorphic devices require the development of electronic components: neurons and synapses.
The paper [2] proposed a phase-locked loop system with a bandpass filter in the control circuit. A more detailed study of the mathematical model of such a system has shown missing equilibrium states corresponding to the synchronization mode of the phase-locked loop system, but there are self-oscillating modes of varying complexity. Self-oscillations observed in such system are similar to spike and burst oscillation of the neuron’s membrane potential.
Hardware implementation [3] of the considered neuron like generator in the form of an electronic device demonstrated the possibility of reproducing the same dynamic modes as in the mathematical model [2].
A fundamental disadvantage of the proposed model [2] and its experimental implementation [3] – the absence of an excitable mode (by excitable we mean a dynamic system with a stable equilibrium state and a periodic pseudoorbit of large amplitude, passing in the vicinity of the equilibrium state), when pulse generation would only respond to external disturbance. At the same time, the vast majority of brain neurons are in the excitable subthreshold mode, and their generation is primarily caused by presence of multiple connection.
One of the tasks of this work was to modification the existing model of the neuron-like generator in order to preserve the known dynamics and add a mode of excited oscillator.
While solving this problem, a modification of the neuron like generator based on the phase-locked loop system with a band-pass filter in the control circuit was proposed and implemented as an electronic circuit. The modification eliminates the basic drawback of the initial model – inability to work in the excitable mode. The new dynamic mode with the absence of self-oscillations was obtained by adding an electronically controlled switch between the low- and high-pass filters in the control loop.
Existence of the excitable mode and the existence of previously known self-oscillating modes of varying complexity was demonstrated experimentally: spike, burst, and chaotic modes was confirmed [4].
Another task in this work was to explore the dynamics of two neuron-like generators with memristive coupling.
A second-order memristor model based on Chua's memristor was used as a model of synaptic connection.
When solving this problem, nonlinear frequency dependences of the conductivity of the memristive element were found. This dependence has the same character for self-oscillating modes of varying complexity: spike and burst.
In addition, it was demonstrated synchronization of two neuron-like generators connected through a memristive element. Synchronization of two coupled neuron-like generators is interim in nature and strongly depends on the current state of the memristive element [5].
Full Text
Currently, one of the most vital goals of interdisciplinary science is the development and investigation of neuromorphic devices. These devices are frequently implemented in the construction of information processing systems that use algorithms closely resembling those used by the brain of humans and animals. The development of neuromorphic electronics enables the construction of computing devices and information processing systems according to new principles and with a high level of parallelism [1].
Neuromorphic devices necessitate the creation of electronic components, specifically neurons and synapses.
The researchers recommend the use of a phase-locked loop system accompanied by a band-pass filter within the control circuit in their research paper [2]. Further mathematical analysis of this system revealed the absence of equilibrium states that correspond to the synchronization mode of the phase-locked loop system. However, self-oscillating modes with varying degrees of complexity exist. Self-oscillations observed in this system resemble the spike and burst oscillation of a neuron’s membrane potential.
Hardware implementation [3] of the neuron-like generator showed that it is possible to replicate identical dynamic modes to those in the mathematical model [2] through an electronic device.
A significant drawback of the proposed model [2] and its experimental implementation [3] is the lack of an excitable mode. By “excitable”, we refer to a dynamic system with a stable equilibrium state and a periodic pseudo-orbit of significant amplitude passing near the equilibrium state. In this mode, pulse generation would respond solely to external disturbance. At the same time, the majority of neurons in the brain are in the subthreshold mode, which renders them excitable, and this generation is primarily due to the presence of multiple connections.
One aim of this study was to modify the current model of the neuron-like generator to maintain its known dynamics while including an excited oscillator mode.
While solving this problem, an electronic circuit was developed that serves as a modified version of the neuron-like generator. Based on the phase-locked loop system with a band-pass filter integrated into its control circuit, this modification effectively addresses the main issue of the previous model, specifically, its incapacity to function in excitable mode. The upgraded device now operates in a new dynamic mode that boasts an absence of self-oscillation, a feature achieved through the addition of an electronically controlled switch between the low- and high-pass filters in the control loop.
Existence of the excitable mode and previously known self-oscillating modes of varying complexity was experimentally demonstrated, confirming spike, burst, and chaotic modes [4].
Another task in this study was to investigate the behavior of two neuron-like oscillators with memristive coupling.
A second-order memristor model based on Chua’s memristor was used as a synaptic connection model.
Nonlinear frequency dependencies of the conductivity of the memristive element were discovered during the problem-solving process. The self-oscillating modes of varying complexity, namely spike and burst, depict identical characteristics of this dependence.
In addition, two neuron-type generators connected by a memristive element were shown to be capable of synchronization. This synchronization between two coupled neuron-like generators is transient and highly reliant on the present condition of the memristive element [5].
ADDITIONAL INFORMATION
Authors’ contribution. All authors made a substantial contribution to the conception of the work, acquisition, analysis, interpretation of data for the work, drafting and revising the work, final approval of the version to be published and agree to be accountable for all aspects of the work.
Funding sources. This study was conducted within the framework of the scientific program of the National Center for Physics and Mathematics, section No. 9 “Artificial Intelligence and Big Data in Technical, Industrial, Natural and Social Systems”.
Competing interests. The authors declare that they have no competing interests.
About the authors
D. I. Bolshakov
National Research Lobachevsky State University of Nizhny Novgorod
Author for correspondence.
Email: denis.bolhakov@gmail.com
Russian Federation, Nizhny Novgorod
M. A. Mishchenko
National Research Lobachevsky State University of Nizhny Novgorod
Email: denis.bolhakov@gmail.com
Russian Federation, Nizhny Novgorod
A. I. Belov
National Research Lobachevsky State University of Nizhny Novgorod
Email: denis.bolhakov@gmail.com
Russian Federation, Nizhny Novgorod
V. V. Matrosov
National Research Lobachevsky State University of Nizhny Novgorod
Email: denis.bolhakov@gmail.com
Russian Federation, Nizhny Novgorod
A. N. Mikhaylov
National Research Lobachevsky State University of Nizhny Novgorod
Email: denis.bolhakov@gmail.com
Russian Federation, Nizhny Novgorod
References
- Wunderlich T, Kungl AF, Müller E, et al. Demonstrating advantages of neuromorphic computation: a pilot study. Front Neurosci. 2019;13:260. doi: 10.3389/fnins.2019.00260
- Shalfeev VD. Investigation of the dynamics of a system of automatic phase control of frequency with a coupling capacitor in the control loop. Radiophysics and Quantum Electronics. 1968;11(3):221–226.
- Mishchenko MA, Bolshakov DI, Matrosov VV. Instrumental implementation of a neuronlike generator with spiking and bursting dynamics based on a phase-locked loop. Technical Physics Letters. 2017;43(7):596–599. doi: 10.1134/S1063785017070100
- Mishchenko MA, Bolshakov DI, Matrosov VV, Sysoev IV. Electronic neuron-like generator with excitable and self-oscillating behavior. 5th Scientific School Dynamics of Complex Networks and their Applications (DCNA); 2021 Sept 13–15; Kaliningrad. 2021. doi: 10.1109/DCNA53427.2021.9587210
- Mishchenko MA, Bolshakov DI, Lukoyanov VI, et al. Inverted spike-rate-dependent plasticity due to charge traps in a metal-oxide memristive device. Journal of Physics D: Applied Physics. 2022;55(39):394002. doi: 10.1088/1361-6463/ac79de
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