Title: Global exponential stability result for complex valued hysteretic neuron model

Authors: G. Padmavathi; P.V. Siva Kumar; Shahnaz Bathul

Addresses: Department of Mathematics, JNTUH College of Engineering, Kukatpally, Hyderabad-72, Andhra Pradesh, India; CR Rao AIMSCS, University of Hyderabad Campus, P.O. Central University, Hyderabad-500 046, Andhra Pradesh, India ' CSE Department, VNR VJIET, Bachupally, Nizampet (S.O), Hyderabad-090, Andhra Pradesh, India ' Department of Mathematics, JNTUH College of Engineering, Kukatpally, Hyderabad-72, Andhra Pradesh, India

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.

Keywords: discretisation; hysteretic neural networks; activation dynamics; mathematical modelling; artificial neural networks; ANNs; hysteresis; neural delay; differential equations; global dynamics.

DOI: 10.1504/IJMISSP.2013.052869

International Journal of Machine Intelligence and Sensory Signal Processing, 2013 Vol.1 No.1, pp.23 - 45

Received: 21 Mar 2012
Accepted: 30 Apr 2012
Published online: 19 Jul 2014 *