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Abstract <p> The ordinal structure of the fixed point set of a monotone operator acting in a partiallyordered space is studied. Stability conditions for the fixed point set under changes in themonotone operator are obtained. Based on these results, a boundary value problem and a controlsystem for the differential equation of a neural network—a Hopfield-type model of theelectrical activity of the brain with a continuous and a discontinuous activationfunction—are analyzed.</p>

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Stability of Fixed Points in Ordered Spaces. Applications to Boundary Value Problems for Hopfield-Type Equations of a Neural Network

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • E. S. Zhukovskiy,
  • A. S. Patrina

摘要

Abstract

The ordinal structure of the fixed point set of a monotone operator acting in a partiallyordered space is studied. Stability conditions for the fixed point set under changes in themonotone operator are obtained. Based on these results, a boundary value problem and a controlsystem for the differential equation of a neural network—a Hopfield-type model of theelectrical activity of the brain with a continuous and a discontinuous activationfunction—are analyzed.