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The positive almost periodic solution for Nicholson-type delay systems with linear harvesting terms. (English) Zbl 1252.34082

Summary: We study the existence and exponential convergence of positive almost periodic solutions for a class of Nicholson-type delay system with linear harvesting terms. Under appropriate conditions, we establish some criteria to ensure that the solutions of this system converge locally exponentially to a positive almost periodic solution. Moreover, we give an example to illustrate our main results.

MSC:

34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
Full Text: DOI

References:

[1] Berezansky, L.; Idels, L.; Troib, L., Global dynamics of Nicholson-type delay systems with applications, Nonlinear Anal. Real World Appl., 12, 1, 436-445 (2011) · Zbl 1208.34120
[2] Wang, W.; Wang, L.; Chen, W., Existence and exponential stability of positive almost periodic solution for Nicholson-type delay systems, Nonlinear Anal. Real World Appl., 12, 4, 1938-1949 (2011) · Zbl 1232.34111
[3] Berezansky, L.; Braverman, E.; Idels, L., Nicholson’s blowflies differential equations revisited: main results and open problems, Appl. Math. Model., 34, 1405-1417 (2010) · Zbl 1193.34149
[4] Fink, A. M., Almost Periodic Differential Equations, Lecture Notes in Mathematics, vol. 377 (1974), Springer: Springer Berlin · Zbl 0325.34039
[5] He, C. Y., Almost Periodic Differential Equation (1992), Higher Education Publishing House: Higher Education Publishing House Beijing, (in Chinese)
[6] Hale, J. K.; Verduyn Lunel, S. M., Introduction to Functional Differential Equations (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0787.34002
[7] Hale, J. K., Ordinary Differential Equations (1980), Krieger: Krieger Malabar, Florida · Zbl 0186.40901
[8] Long, F., Positive Almost Periodic Solution for a Class of Nicholson’s Blowflies Model with a Linear Harvesting Term, Nonlinear Anal. Real World Appl., 13, 686-693 (2012) · Zbl 1238.34131
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