Entropy-statistical approach to phase-locking detection of pulse oscillations: application for the analysis of biosignal synchronization

In this study a new method for analyzing synchronization in oscillator systems is proposed using the example of modeling the dynamics of a circuit of two resistively coupled pulse oscillators. The dynamic characteristic of synchronization is fuzzy entropy (FuzzyEn) calculated a time series composed of the ratios of the number of pulse periods (subharmonic ratio, SHR) during phase-locking intervals. Low entropy values indicate strong synchronization, whereas high entropy values suggest weak synchronization between the two oscillators. This method effectively visualizes synchronized modes of the circuit using entropy maps of synchronization states. Additionally, a classification of synchronization states is proposed based on the dependencies of FuzzyEn on the length of embedding vectors of SHR time series. An extension of this method for analyzing non-relaxation (non-spike) type signals is illustrated using the example of phase-phase coupling rhythms of local field potential of rat hippocampus. The entropy-statistical approach using rational fractions and pulse signal forms makes this method promising for analyzing biosignal synchronization and implementing the algorithm in mobile digital platforms.

A Bio-Inspired Chaos Sensor Based on the Perceptron Neural Network: Concept and Application for Computational Neuro-science

The study presents a bio-inspired chaos sensor based on the perceptron neural network. After training, the sensor on perceptron, having 50 neurons in the hidden layer and 1 neuron at the output, approximates the fuzzy entropy of short time series with high accuracy with a determination coefficient R2 ~ 0.9. The Hindmarsh-Rose spike model was used to generate time series of spike intervals, and datasets for training and testing the perceptron. The selection of the hyperparameters of the perceptron model and the estimation of the sensor accuracy were performed using the K-block cross-validation method. Even for a hidden layer with 1 neuron, the model approximates the fuzzy entropy with good results and the metric R2 ~ 0.5-0.8. In a simplified model with 1 neuron and equal weights in the first layer, the principle of approximation is based on the linear transformation of the average value of the time series into the entropy value. The bio-inspired chaos sensor model based on an ensemble of neurons is able to dynamically track the chaotic behavior of a spiked biosystem and transmit this information to other parts of the bio-system for further processing. The study will be useful for specialists in the field of computational neuroscience.

Oscillator Circuit for Spike Neural Network with Sigmoid Like Activation Function and Firing Rate Coding

The study presents an oscillator circuit for a spike neural network with the possibility of firing rate coding and sigmoid-like activation function. The circuit contains a switching element with an S-shaped current-voltage characteristic and two capacitors; one of the capacitors is shunted by a control resistor. The circuit is characterised by a strong dependence of the frequency of relaxation oscillations on the magnitude of the control resistor. The dependence has a sigmoid-like form and we present an analytical method for dependence calculation. Finally, we describe the concept of the spike neural network architecture with firing rate coding based on the presented circuit for creating neuromorphic devices and artificial intelligence.