Global exponential stability result for complex valued hysteretic neuron model

Abstract

A mathematical model of artificial neural networks with hysteresis is formulated using neutral delay differential equations. Hysteresis modifies the systems such that they cannot produce unique output for any given input, rather output is produced based on the past history of the system. Motivated by the applications of complex valued neural networks in artificial neural networks, we studied the global dynamics of complex valued neural network with hysteresis. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the neural delay. In this paper continuous hysteresis neuron model has been used to arrive at the sufficient condition for global exponential stability of a unique equilibrium. The hypothetical insight has been successfully applied and verified using relevant numerical examples.