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<p>Nonlinear delay differential equations are fundamental in modeling complex dynamics in mathematical biology and ecology, yet the stability of high-dimensional systems with multiple delays and time-varying coefficients remains challenging, particularly under almost periodic behavior beyond the classical Bohr type. This study establishes global exponential stability of Besicovitch almost periodic (BAP) solutions for such systems on time scales by combining time-scale calculus with Besicovitch almost periodicity. Using a fixed-point argument in a tailored Banach space under decay and Lipschitz-type assumptions, we prove the existence and uniqueness of BAP solutions, and derive global exponential stability criteria via Lyapunov-like techniques and time-scale inequalities, explicitly incorporating delays, Lipschitz constants, and graininess. Key advances include extending almost periodicity to the Marcinkiewicz space with trigonometric approximation on time scales, establishing completeness and closure properties of BAP function spaces for the fixed-point framework, and unifying continuous and discrete stability analysis. The approach is validated through a one-dimensional hematopoiesis model and a two-dimensional leukopoiesis model with dual delays under BAP forcing. Numerical simulations on continuous and almost periodic time scales demonstrate convergence to a unique globally stable solution under irregular perturbations, offering a unified framework for systems with broad forcing types beyond Bohr almost periodicity.</p>

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Global Exponential Stability of Besicovitch Almost Periodic Solution for High-Dimensional Delay Systems on Time Scales

  • 期刊论文

  • 发表日期：

    2026年2月19日

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  • Weiwei Qi,
  • Yongkun Li

摘要

Nonlinear delay differential equations are fundamental in modeling complex dynamics in mathematical biology and ecology, yet the stability of high-dimensional systems with multiple delays and time-varying coefficients remains challenging, particularly under almost periodic behavior beyond the classical Bohr type. This study establishes global exponential stability of Besicovitch almost periodic (BAP) solutions for such systems on time scales by combining time-scale calculus with Besicovitch almost periodicity. Using a fixed-point argument in a tailored Banach space under decay and Lipschitz-type assumptions, we prove the existence and uniqueness of BAP solutions, and derive global exponential stability criteria via Lyapunov-like techniques and time-scale inequalities, explicitly incorporating delays, Lipschitz constants, and graininess. Key advances include extending almost periodicity to the Marcinkiewicz space with trigonometric approximation on time scales, establishing completeness and closure properties of BAP function spaces for the fixed-point framework, and unifying continuous and discrete stability analysis. The approach is validated through a one-dimensional hematopoiesis model and a two-dimensional leukopoiesis model with dual delays under BAP forcing. Numerical simulations on continuous and almost periodic time scales demonstrate convergence to a unique globally stable solution under irregular perturbations, offering a unified framework for systems with broad forcing types beyond Bohr almost periodicity.