Anomalous Random Neural Networks: a Special Renewal Process

TL;DR

This paper introduces an anomalous semi-Markovian random neural network model with arbitrary waiting times, analyzing its dynamics and memory effects through renewal processes and master equations.

Contribution

It presents a novel anomalous neural network model incorporating arbitrary waiting times and derives its master equation, highlighting fractional memory effects.

Findings

Fractional memory effects observed in power-law waiting times

Master equations derived for potential evolution

Closed network rate equations introduced

Abstract

In this paper we propose an open anomalous semi-Markovian random neural networks model with negative and positive signals with arbitrary random waiting times. We investigate the signal flow process in the anomalous random neural networks based on renewal process, and obtain the corresponding master equation for time evolution of the probability of the potential of the neurons. As examples, we discuss the special cases of exponential waiting times and power law ones, and find the fractional memory effect of the probability of the system state on its history evolution. Besides, the closed random neural networks model is introduced and the corresponding rate equation is given.