**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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