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<p>The paper is concerned with the asymptotic behavior of solutions for a very broad family of systems of functional differential equations with infinite distributed delays in the linear and nonlinear terms. Criteria for the asymptotic convergence to zero of all solutions, as well as for their exponential decay to zero are established. The main results are applied to treat very general Hopfield-type models with infinite distributed delays, both in the leakage terms and in the nonlinear terms, deducing new sufficient conditions for their global asymptotic and global exponential stabilities. Our results largely generalize and enhance previous criteria in recent literature.</p>

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Global stability for functional differential equations with infinite delay and applications to Hopfield-type neural networks

  • 期刊论文

  • 发表日期：

    2026年2月6日

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  • Teresa Faria,
  • José J. Oliveira

摘要

The paper is concerned with the asymptotic behavior of solutions for a very broad family of systems of functional differential equations with infinite distributed delays in the linear and nonlinear terms. Criteria for the asymptotic convergence to zero of all solutions, as well as for their exponential decay to zero are established. The main results are applied to treat very general Hopfield-type models with infinite distributed delays, both in the leakage terms and in the nonlinear terms, deducing new sufficient conditions for their global asymptotic and global exponential stabilities. Our results largely generalize and enhance previous criteria in recent literature.