Abstract
This study is about getting some conditions that guarantee the existence and uniqueness of the pseudo almost automorphic (PAA) solutions of Nicholson’s blowflies with time-varying delays. Some adequate conditions have been obtained for the existence, uniqueness global exponential stability of the PAA solutions of the Nicholson’s blowflies, which we dealt with using some differential equation inequalities, the PAA theory, and the Banach Fixed Point Theorem. Besides, an example is given to demonstrate the accuracy of the conditions of our main results.
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Nicholson, A.J.: An outline of the dynamics of animal populations. Aust. J. Zool. 2(1), 9–65 (1954)
Gurney, W.S.C., Blythe, S.P., Nisbet, R.M.: Nicholson’s blowflies revisited. Nature 287, 17–21 (1980)
Chen, Y.: Periodic solutions of delayed periodic Nicholson’s blowflies models. Can. Appl. Math. Q. 11(1), 23–28 (2003)
Gyori, I., Trofimchuk, S.: On the existence of rapidly oscillatory solutions in the Nicholson blowflies equation. Nonlinear Anal. 48(7), 1033–1042 (2002)
Liu, B., Tunç, C.: Pseudo almost periodic solutions for a class of nonlinear Duffing system with a deviating argument. J. Appl. Math. Comput. 49(1–2), 233–242 (2015)
Li, J.: Global attractivity in Nicholson’s blowflies. Appl. Math. J. Chin. Univ. Ser. B 11(4), 425–434 (1996)
Zhou, H., Wang, J., Zhou, Z.: Positive almost periodic solutions for impulsive Nicholson’s blowflies model with multiple linear harvesting terms. Math. Models Appl. Sci. 36(4), 456–461 (2013)
Xiao, T.J., Liang, J., Zhang, J.: Pseudo-almost automorphic solutions to semilinear differential equations in Banach spaces. Semigroup Forum 76, 518–524 (2008)
Aouiti, C., M’hamdi, M.S., Touati, A.: Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process. Lett. 45(1), 121–140 (2017)
Liu, B.: Almost periodic solutions for a delayed Nicholson’s blowflies model with a nonlinear density-dependent mortality term. Adv. Differ. Equ. 72, 16 (2014)
Xiong, W.: New results on positive pseudo-almost periodic solutions for a delayed Nicholson’s blowflies model. Nonlinear Dyn. 85(1), 563–571 (2016)
Chérif, F.: Pseudo almost periodic solution of Nicholson’s blowflies model with mixed delays. Appl. Math. Model. 39(17), 5152–5163 (2015)
Duan, L., Huang, L.: Pseudo almost periodic dynamics of delay Nicholson’s blowflies model with a linear harvesting term. Math. Methods Appl. Sci. 38(6), 1178–1189 (2015)
Bochner, S.: Continuous mappings of almost automorphic and almost periodic functions. Proc. Natl. Acad. 52, 907–910 (1964)
Diagana, T.: Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces. Springer, Berlin (2013)
Aouiti, C., Dridi, F., Kong, F.: Pseudo almost automorphic solutions of hematopoiesis model with mixed delays. Comput. Appl. Math. 39(2), 87 (2020)
Xiao, T.J., Zhu, X.X., Liang, J.: Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications. Nonlinear Anal. 70(11), 4079–4085 (2009)
Yazgan, R., Tunç, C.: On the almost periodic solutions of fuzzy cellular neural networks of high order with multiple time lags. Int. J. Math. Comput. Sci. 1, 183–198 (2020)
Yazgan, R., Tunç, C.: On the weighted pseudo almost periodic solutions of Nicholson’s blowflies equation. Appl. Appl. Math. 14(2), 875–889 (2019)
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Yazgan, R. An Analyses on the Pseudo Almost Automorphic Solutions of a Biological Model. Acta Appl Math 179, 1 (2022). https://doi.org/10.1007/s10440-022-00488-9
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DOI: https://doi.org/10.1007/s10440-022-00488-9
Keywords
- Banach fixed point theorem
- Global exponential stability
- Nicholson’s blowflies
- Pseudo almost automorphic