Dynamics of two neuron-like generators with memristive connection
Authors: Bolshakov D. I. , Mishchenko M. A. , Belov A. I. , Matrosov V. V. , Mikhaylov A. N. 
Published: May 2024

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].