On a heavy-tailed distribution and the stability of an equilibrium in a distributed delay symmetric network

• Published in: Chaos, solitons and fractals solitons and fractals, 2021-11, Vol.152, p.111330, Article 111330
• Main Author: Ncube, Israel
• Format: Article
• Language: English
• Subjects: Equilibrium; Pareto distribution; S-type distributed time delays; Stability; Static neural networks
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2021.111330

•Complete characterisation of the effects of a heavy-tailed distribution on the local stability of an equilibrium in a distributed time delay artificial neural network.•Explicit characterisation of the shape and the scale of a distribution on the local stability stability of an equlibrium.•Characterisation of the interplay between the stability boundary and intrinsic statistical parameters (shape and scale of a distribution). We consider a static artificial neural network model endowed with multiple unbounded S-type distributed time delays. The delay kernels are described by the Pareto distribution, which is a heavy-tailed power-law probability distribution frequently employed in the characterisation of many observable phenomena. We give a characterisation of the effects of the shape and the scale of the Pareto delay distribution on the stability of an equilibrium of the network.