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

  • Weiwei Qi [1] ; Yongkun Li [2]
    1. [1] Nanjing Forestry University

      Nanjing Forestry University

      China

    2. [2] Nanjing University of Science and Technology

      Nanjing University of Science and Technology

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 2, 2026
  • Idioma: inglés
  • Enlaces
  • Resumen

    • 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.

  • Referencias bibliográficas
    • 1. Rihan, F.A.: Delay Differential Equations and Applications to Biology. Springer, Singapore (2021)
    • 2. Araz, S.I., Boulaaras, S.: Fractional modelling of gradual incorporation of infected prey into the predator-prey system with consideration...
    • 3. Zhou, H., Alzabut, J., Rezapour, S., Samei, M.E.: Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy...
    • 4. Adimy, M., Crauste, F., Ruan, S.: Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases....
    • 5. Adimy, M., Crauste, F., Ruan, S.: Periodic oscillations in leukopoiesis models with two delays. J. Theor. Biol. 242(2), 288–299 (2006)
    • 6. Huang, C., Liu, B.: Exponential stability of a diffusive Nicholson’s blowflies equation accompanying multiple time-varying delays. Appl....
    • 7. Huang, C., Liu, B., Yang, H., Cao, J.: Positive almost periodicity on SICNNs incorporating mixed delays and D operator. Nonlinear Anal....
    • 8. Ding, H.S., Liu, Q.L., Nieto, J.J.: Existence of positive almost periodic solutions to a class of hematopoiesis model. Appl. Math. Model....
    • 9. Araz, S.I.: Seasonality of Ricker mutualism model employing rate indicator with almost periodic function. J. Appl. Anal. Comput. 16(1),...
    • 10. Huang, C., Ding, X., Wang, Q.: Positive periodic stability to a neutral Nicholson’s blowflies model. Qual. Theor. Dyn. Syst. 24(140),...
    • 11. Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, New York (1988)
    • 12. Ding, H.S., Xiao, T.J., Liang, J.: Existence of positive almost automorphic solutions to nonlinear delay integral equations. Nonlinear...
    • 13. Zhang, X., Liu, L., Wu, Y.: New fixed point theorems for the sum of two mixed monotone operators of Meir-Keeler type and their applications...
    • 14. Selvam, A., Sabarinathan, S., Noeiaghdam, S., Govindan, V.: Fractional Fourier transform and Ulam stability of fractional differential...
    • 15. Selvam, A., Sabarinathan, S., Selvan, A.P.: Mittag-Leffler-Hyers-Ulam stability for first- and secondorder nonlinear differential equations...
    • 16. Jian, W.-G., Ding, H.-S.: Tauberian theorems on R+ and applications. Proc. Amer. Math. Soc. 152(11), 4745–4757 (2024)
    • 17. Ding, H.-S., Jian, W.-G., Van Minh, N., N’Guérékata, G.M.: Kadets type and Loomis type theorems for asymptotically almost periodic functions....
    • 18. Tu, K., Xue, Y., Zhang, X.: A new approach based on system solutions for passivity analysis of discretetime memristor-based neural networks...
    • 19. Yao, Z., Alzabut, J., Jana, D.: Dynamics of the almost periodic discrete mackey-glass model. Mathematics 6(12), 333 (2018)
    • 20. Hilger, S.: Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten. PhD thesis, Universität Würzburg (1988)
    • 21. Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston (2001)
    • 22. Benevieri, P., Mesquita, J.G., Pereira, A.: Global bifurcation results for nonlinear dynamic equations on time scales. J. Differ. Equations...
    • 23. Yeni, G.: Modeling of HIV, SIR and SIS epidemics on time scales and oscillation theory. PhD thesis, Missouri University of Science and...
    • 24. Yeni, G., Akin, E., Vaidya, N.K.: Time scale theory on stability of explicit and implicit discrete epidemic models: Applications to swine...
    • 25. Georgiev, S.G., Zennir, K.: Differential Equations: Projector Analysis on Time Scales. Walter de Gruyter GmbH, Berlin/Boston (2024)
    • 26. Martynyuk, A.A.: Stability Theory for Dynamic Equations on Time Scales. Birkhäuser, Switzerland (2016)
    • 27. DaCunha, J.J.: Lyapunov stability and Floquet theory for nonautonomous linear dynamic systems on time scales. PhD thesis, Baylor University...
    • 28. Bohner, M., Cuchta, T., Streipert, S.: Delay dynamic equations on isolated time scales and the relevance of one-periodic coefficients....
    • 29. Agrawal, D., Abbas, S.: Existence of periodic solutions for a class of dynamic equations with multiple time varying delays on time scales....
    • 30. Li, Y., Wang, C.: Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales. Abstr. Appl....
    • 31. Wang, C., Tan, Y., Agarwal, R.P.: Almost periodic fractional fuzzy dynamic equations on timescales: A survey. Math. Meth. Appl. Sci. 47(4),...
    • 32. Wang, S., Li, M., Piao, D.: The boundedness of almost-periodic oscillators with asymmetric potentials via normal form theorem. J. Differential...
    • 33. Almagro, P., Boguñá, M., Serrano, M.Á.: Detecting the ultra low dimensionality of real networks. Nat. Commun. 13(1), 6096 (2022)
    • 34. Corduneanu, C.: Almost Periodic Functions, 2nd edn. Chelsea Publishing Company, New York (1989)
    • 35. Bustos, H., Figueroa, P., Pinto, M.: Poincaré-Perron problem for high order differential equations in the class of almost periodic type...
    • 36. Corduneanu, C.: Almost Periodic Oscillations and Waves. Springer, New York (2009)
    • 37. Li, Y., Qi, W., Li, B.: Besicovitch almost periodic solutions to semilinear evolution dynamic equations with varying delay. Qual. Theory...
    • 38. Yuan, J., Liu, L., Wu, Y.: New results on the existence and uniqueness of positive almost periodic solution for the generalized Mackey-Glass...
    • 39. Bell, P.C., Hirvensalo, M.: On injectivity of quantum finite automata. J. Comput. Syst. Sci. 122, 19–33 (2021)
    • 40. Li, Y., Wang, C.: Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time scales. Adv. Differ....
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