On the Equilibrium State Stability of a Neural Network Model

Y. V. Bogomolov

P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia

Abstract: In the paper, a neural network model based on three McCulloch–Pitts adder neurons is considered. Previously, the features of the model dynamics were numerically analyzed and the stability of various dynamic modes of the network with small changes of the current state was studied, including the detection of parameters specific for the chaotic system dynamics. In the paper, the stability problem of the neural network equilibrium states (steady operating mode) is considered for different values of feedback synaptic weight coefficients. An analytic proof of the zero equilibrium state instability for the corresponding dynamic system for all parameter values of the neural network is presented as the main result of the article.

Keywords: neural network, stability.

UDC: 519.876.5 + 517.938

Received: 24.04.2014