Approximating the stability region of a neural network with a general distribution of delays

• Published in: Neural networks Vol. 23; no. 10; pp. 1187 - 1201
• Main Authors: Jessop, R., Campbell, S.A.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-12-2010; Elsevier
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Computer science; control theory; systems; Computer Simulation; Connectionism. Neural networks; Control system analysis; Control theory. Systems; Delay differential equations; Delay independent stability; Discrete delay; Distributed delay; Exact sciences and technology; Linear stability; Neural Networks (Computer); Neurons - physiology; Linear stability; Delay independent stability; Delay differential equations; Distributed delay; Discrete delay; Delay independent system; Differential equation; Delay system; Stability region; Neural network; Delay equation; Equilibrium point; Gamma distribution; Uniform distribution; Characteristic equation; Cumulant
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2010.06.009

We investigate the linear stability of a neural network with distributed delay, where the neurons are identical. We examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. We determine a mean delay and distribution independent stability region. We then illustrate a way of improving on this conservative result by approximating the true region of stability when the actual distribution is not known, but some moments or cumulants of the distribution are known. Finally, we compare the approximate stability regions with the stability regions in the case of the uniform and gamma distributions. We show that the approximations improve as more moments or cumulants are used, and that the approximations using cumulants give better results than the ones using moments.