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<p>In this article, we establish the existence and uniqueness of a global attractor, which is a <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>Q</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(Q,\omega )$</EquationSource> </InlineEquation>-affine periodic solution, for generalized ordinary differential equations (abbreviated, as generalized ODEs) that satisfy a <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>Q</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(Q,\omega )$</EquationSource> </InlineEquation>-affine condition. We apply this result to derive an analogue for measure differential equations that satisfy a zero-average condition and conclude by illustrating our main result with a Hopfield neural network model.</p>

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Global attractivity of affine-periodic solutions for generalized ODEs with application to a Hopfield neural network model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月20日

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  • Claudio A. Gallegos,
  • Jonathan González Ospino,
  • Rogelio Grau

摘要

In this article, we establish the existence and uniqueness of a global attractor, which is a ( Q , ω ) $(Q,\omega )$ -affine periodic solution, for generalized ordinary differential equations (abbreviated, as generalized ODEs) that satisfy a ( Q , ω ) $(Q,\omega )$ -affine condition. We apply this result to derive an analogue for measure differential equations that satisfy a zero-average condition and conclude by illustrating our main result with a Hopfield neural network model.