Phase-locked states in a spiking neural network model with a context-dependent connectivity
Authors: Makovkin S. Yu. , Kastalsky I. A. 
Published: May 2024

The investigation of nonlinear processes in brain systems based on the oscillatory-wave approach is currently one of the most consequential domains of researching signal generation and processing mechanisms in the brain. These investigations may offer insights into various phenomena, such as the mechanism of associative memory, based on network models of biologically relevant neurons. A neural network architecture is proposed in this paper to solve applied problems, such as signal filtering, processing, and recognition of information images. Mechanisms for incomplete fragments were implemented, enabling the extraction and complete restoration of objects from memory. Each neuron in this neural network comprises a Hodgkin–Huxley biophysical model with a Mainen modification, the dynamics of which most plausibly reproduce the processes in the neural cells of the brain.
In the research on individual neurons, a constant external current with varying amplitudes was applied. The study determined the average periods of self-oscillations and identified parameter values for the Andronov–Hopf bifurcation. In particular, a stable limit cycle is created and destroyed depending on different scenarios when the bias current is increased or decreased. A stable limit cycle arises via the Andronov–Hopf bifurcation and is terminated via the saddle-node bifurcation on the cycle.
The study identified parameter regions whereby two neurons with excitatory and inhibitory synaptic connections synchronize. The neurons were all in self-oscillating mode and exhibited a stable limit cycle in the phase space.
A three-layer neural network was constructed, comprising of a reference neuron, sensory, control, and interneurons. The control and intermediate layer connections are arranged based on the Hebbian learning rule.
Areas of excitation for various types of neurons were found.
Experiments were conducted using the neural network architecture to distinguish binary information patterns encoded through signal phase. Excitatory and inhibitory synaptic connections were employed to encode the images stored in memory. The dynamic patterns are determined through the in-phase or anti-phase mode of phase locking, i.e., phase synchronization relative to the global rhythm. Before reaching the output layer of neurons, the signals are summed on the interneuron layer with the signal of the reference neuron, resulting in the filtering out of a certain information segment (in-phase or anti-phase). The network accurately recognized the patterns after parameter adjustments were made.
Areas of neuron phase synchronization were discovered, enabling control of network activity modes. The confirmation of the viability of phase capture and pattern recognition modes using Hodgkin–Huxley–Mainen neurons was achieved.
In total, as a result of the implementation of the spike neural network modeling project:
1) two-parameter diagrams of regions of neuronal excitation in various modes are calculated;
2) the effect of excitatory and inhibitory coupling in synaptic currents is used to represent the input signal;
3) an abstract mathematical algorithm for calculating the Hebbian matrix has been transferred to the implementation of synaptic currents between layers of neurons;
4) the effect of phase clusters is used to represent the output pattern;
5) the neurons’ topology in the visual-cerebral department served as a working model for recognizing graphic images through the Hopfield network on a spike neural network, using the Hebbian rule.