WSEAS Transactions on Systems and Control

Print ISSN: 1991-8763
E-ISSN: 2224-2856

Volume 12, 2017

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 12, 2017

A Multi-Step Method to Calculate the Equilibrium Point of the Continuous Hopfield Networks: Application to the Max-Stable Problem

AUTHORS: Mohammed El Alaoui, Karim El Moutaouakil, Mohamed Ettaouil

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ABSTRACT: The Continuous Hopfield Networks (CHN) is a neural network tools which can be used to solve many problems like auto-memory and optimization problems. The dynamics of the CHN is described by differential equations system which is hard to solve analytically. That is why, the researchers use the Euler Cauchy method to calculate the CHN equilibrium point. Unfortunately, this method suffers from several problems, especially quality of the decision for a large step, sensibility to the slope function parameters and to the initial conditions. In this work, we use the well-known multi-step numerical method called Adams– Bashforth method, which is strong in terms of stability and performance, to calculate the equilibrium point of the CHN associated with the max stable problem. This method introduces an intermediary step to improve the Euler Cauchy method precision. The experimental results show that the (CHN+Adams-Bashforth) method produce a large max stable sets in comparison with the (CHN+Euler-Cauchy) method.

KEYWORDS: Continuous Hopfield Networks, Euler Cauchy method, Adams–Bashforth method, max-stable problem


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WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 12, 2017, Art. #44, pp. 418-425

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