Competition in the chemostat: a distributed delay model and its global asymptotic behavior
SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics
Global stability of neural networks with distributed delays
Neural Networks
Linearized oscillation theory for a nonlinear equation with a distributed delay
Mathematical and Computer Modelling: An International Journal
Analysis of a class of distributed delay logistic differential equations
Mathematical and Computer Modelling: An International Journal
Mathematics and Computers in Simulation
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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.