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Pseudo almost periodic solutions for a Nicholson’s blowflies model with mortality term. (English) Zbl 1414.39009

Summary: This article is concerned with a discrete Nicholson’s blowflies model, which involvesa nonlinear density-dependent mortality term. By using fixed point theorem and Lyapunov functional method, we obtain the existence and locally exponential stability of pseudo almost periodic solutions for the addressed Nicholson’s blowflies model. In addition, an example is given to illustrate our results.

MSC:

39A24 Almost periodic solutions of difference equations
39A60 Applications of difference equations

References:

[1] J. O. Alzabut, Almost periodic solutions for an impulsive delay Nicholson’s blowflies model, Journal of Computational and Applied Mathematics 234 (2010), no. 1, 233-239. · Zbl 1196.34095
[2] J. O. Alzabut, Y. Bolat, T. Abdeljawad, Almost periodic dynamics of a discrete Nicholson’s blowflies model involving a linear harvesting term, Advances in Difference Equations 2012, 2012:158. · Zbl 1377.39025
[3] J. O. Alzabut, Existence and exponential convergence of almost periodic solutions for a discrete Nicholson’s blowflies model with nonlinear harvesting term, Mathematical Sciences Letters 2 (2013), no. 3, 201-207.
[4] L. Berezansky, E. Braverman, L. Idels, Nicholson’s blowflies differential equations revisited: Main results and open problems, Applied Mathematical Modelling 34 (2010), no. 6, 1405-1417. · Zbl 1193.34149
[5] W. Chen, L. Wang, Positive periodic solutions of Nicholson-type delay systems with nonlinear density-dependent mortality terms, Abstract and Applied Analysis 2012, Art. ID 843178, 13 pp. · Zbl 1260.34149
[6] F. Chérif, Pseudo almost periodic solution of Nicholson’s blowflies model with mixed delays, Applied Mathematical Modelling 39 (2015), no. 17, 5152-5163. · Zbl 1443.92010
[7] C. Corduneanu, Almost periodic functions, 2nd edition, Chelsea Publishing Company, New York, 1989. · Zbl 0672.42008
[8] H.-S. Ding, J.-D. Fu, G. M. N’Guérékata, Positive almost periodic type solutions to a class of nonlinear difference equations, Electronic Journal of Qualitative Theory of Differential Equations 25 (2011), 1-16. · Zbl 1340.39026
[9] H.-S. Ding, J. J. Nieto, A new approach for positive almost periodic solutions to a class of Nicholson’s blowflies model, Journal of Computational and Applied Mathematics 253 (2013), 249-254. · Zbl 1288.92017
[10] H.-S. Ding, J. O. Alzabut, Existence of positive almost periodic solution for a Nicholson’s blowflies model, Electronic Journal of Differential Equations 2015 (2015), no. 180, 1-6. · Zbl 1328.34063
[11] H.-S. Ding, M.-X. Ji, G. M. N’Guérékata, J. Nonl. Evol. Equ. Appl. 2018 (2018) 1-10 · Zbl 1414.39009
[12] L. Duan, L. H. Huang, Pseudo almost periodic dynamics of delay Nicholson’s blowflies model with a linear harvesting term, Mathematical Methods in the Applied Sciences 38 (2015), no. 6, 1178-1189. · Zbl 1309.34073
[13] W. S. Gurney, S. P. Blythe, R. M. Nisbet, Nicholson’s blowflies revisited, Nature 287 (1980), 17-21.
[14] M.-X. Ji, H.-S. Ding, Pseudo almost periodic solutions for a discrete Nicholson’s blowflies model (preprint).
[15] B. Liu, The existence and uniqueness of positive periodic solutions of Nicholson-type delay systems, Nonlinear Analysis: Real World Applications 12 (2011), no. 6, 3145-3151. · Zbl 1231.34119
[16] B. Liu, W. Chen, Positive almost periodic solutions for a class of Nicholson’s blowflies model with multiple time-varying delays, Journal of Computational and Applied Mathematics 235 (2011), no. 8, 2090-2097. · Zbl 1207.92042
[17] B. Liu, Almost periodic solutions for a delayed Nicholson’s blowflies model with a nonlinear density-dependent mortality term, Advances in Difference Equations 2014, 2014:72. · Zbl 1417.92138
[18] Q.-L. Liu, H.-S. Ding, Existence of positive almost periodic solutions for a Nicholson’s blowflies model, Electronic Journal of Differential Equations 2013 (2013), no. 56, 1-9. · Zbl 1293.34106
[19] F. Long, Positive almost periodic solution for a class of Nicholson’s blowflies model with a linear harvesting term, Nonlinear Analysis: Real World Applications 13 (2012), no. 2, 686-693. · Zbl 1238.34131
[20] Y.-L. Xu, Existence and global exponential stability of positive almost periodic solutions for a delayed Nicholson’s blowflies model, Journal of the Korean Mathematical Society 51 (2014), no. 3, 473-493. · Zbl 1307.34112
[21] C. Zhang, Almost periodic type functions and ergodicity, Kluwer Academic/Science Press, Beijing, 2003. · Zbl 1068.34001
[22] Q. Zhou, The positive periodic solution for Nicholson-type delay system with linear harvesting terms, Applied Mathematical Modelling 37 (2013), no. 8, 5581-5590. · Zbl 1274.34209
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