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<p>This paper investigates the existence and global exponential stability of Pseudo <i>S</i>-asymptotically <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-antiperiodic solutions in delayed Cohen–Grossberg neural networks (CGNNs). Motivated by the need to describe oscillatory behaviors with asymptotic convergence, we develop a rigorous analytical framework based on inequality techniques, fixed-point theory, and careful exponential estimates for a scalar convolution kernel. Under local Lipschitz conditions on activation functions, sufficient conditions for existence are established with explicit convergence estimates, while global Lipschitz assumptions guarantee uniqueness and global exponential stability. Two numerical examples implemented in MATLAB validate the theoretical results and illustrate the system’s oscillatory dynamics under different parameter settings. The proposed framework extends existing stability theory for delayed neural networks and provides a foundation for analyzing complex time-dependent neural dynamics.</p>

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Pseudo S-asymptotically \(\omega \)-antiperiodic behavior in delayed Cohen–Grossberg neural networks

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Chaouki Aouiti,
  • Mahjouba Ben Rezek

摘要

This paper investigates the existence and global exponential stability of Pseudo S-asymptotically \(\omega \) ω -antiperiodic solutions in delayed Cohen–Grossberg neural networks (CGNNs). Motivated by the need to describe oscillatory behaviors with asymptotic convergence, we develop a rigorous analytical framework based on inequality techniques, fixed-point theory, and careful exponential estimates for a scalar convolution kernel. Under local Lipschitz conditions on activation functions, sufficient conditions for existence are established with explicit convergence estimates, while global Lipschitz assumptions guarantee uniqueness and global exponential stability. Two numerical examples implemented in MATLAB validate the theoretical results and illustrate the system’s oscillatory dynamics under different parameter settings. The proposed framework extends existing stability theory for delayed neural networks and provides a foundation for analyzing complex time-dependent neural dynamics.