Mean-square almost periodic solution for impulsive stochastic Nicholson’s blowflies model with delays. (English) Zbl 1273.92048

Summary: A class of impulsive stochastic Nicholson’s blowflies model is investigated by applying Cauchy matrix. Under proper conditions, the existence and exponential stability of square-mean almost periodic solutions for the model with multiple nonlinear harvesting terms and delays. Moreover, an example is provided to illustrate the effectiveness of the results.


92D25 Population dynamics (general)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
Full Text: DOI


[1] Tudor, C.; Tudor, M., Pseudo almost periodic solutions of some stochastic differential eqations, J. Math. Rep., 51, 305-314 (1999) · Zbl 1019.60058
[2] Bezandrt, P.; Diagana, T., Existence of almsot periodic solutions to some stochastic differential equations, Appl. Anal., 117, 1-10 (2007)
[3] Fu, M. M.; Liu, Z. X., Square-mean almsot automorphic solutions for some stochastic differential equations, Proc. Amer. Math. Soc., 138, 3689-3701 (2010) · Zbl 1202.60109
[4] He, M. X.; Chen, F. D.; Li, Z., Almost periodic solution of an impulse differential equation model of plankton allelopathy, Nonlinear Anal., 11, 2296-2301 (2010) · Zbl 1200.34050
[5] Ahmad, Shair; Stamov, Gani Tr., On almost periodic processes in impulsive competitive systems with delay and impulsive perturbations, Nonlinear Anal. RWA, 10, 2857-2863 (2009) · Zbl 1170.45004
[6] Ahmad, Shair; Stamov, Gani Tr., Almost periodic solutions of N-dimensional impulsive competitive systems, Nonlinear Anal. RWA, 10, 1846-1853 (2009) · Zbl 1162.34349
[7] Samoilenko, A. M.; Perestyuk, N. A., Differential Equations with Impulse Effect (1995), World Scientific: World Scientific Singapore · Zbl 0837.34003
[8] Zhou, H.; Zhou, Z. F.; Wang, Q., Positive almost periodic solution for a class of Lasota-Wazewska model with infinite delays, Appl. Math. Comput., 218, 4501-4506 (2011) · Zbl 1277.34104
[9] Liu, Z. J., Positive periodic solutions for delay multispecies Logrithmic population model, J. Eng. Math., 19, 4, 11-16 (2002), (in Chinese) · Zbl 1041.34059
[10] Ahmad, Shair; Stamova, Ivanka M., Asymptotic stability of competitive systems with delays and impulsive perturbations, J. Math. Anal. Appl., 334, 686-700 (2007) · Zbl 1153.34044
[11] Ahmad, S.; Stamova, I. M., Asymptotic stability of an N-dimensional impulsive competitive system, Nonlinear Anal. RWA, 8, 654-663 (2007) · Zbl 1152.34342
[12] Huang, H.; Yang, Q., Existence and exponential stability of almost solution for stochastic celluar neural networks with delays, Chaos Solitions Fract., 42, 773-780 (2009) · Zbl 1198.60024
[13] Berezansky, L.; Braverman, E.; Idels, L., Nicholson’s blowflies differential equations revisited: main results and open problems, Appl. Math. Modell., 34, 1405-1417 (2010) · Zbl 1193.34149
[14] Yang, M., Exponential convergence for a class of Nicholsons blowflies model with multiple time-varying delays, Nonlinear Anal. RWA, 12, 2245-2251 (2011) · Zbl 1220.34106
[15] Alzabut, J. O., Almost periodic solutions for an impulsive delay Nicholsons blowflies model, J. Comput. Appl. Math., 234, 233-239 (2010) · Zbl 1196.34095
[16] Chen, W.; Liu, B., Positive almost periodic solution for a class of Nicholson’s blowflies model with multiple time-varying delays, J. Comput. Appl. Math., 235, 2090-2097 (2011) · Zbl 1207.92042
[17] Wang, W.; Wang, L.; Chen, W., Existence and exponential stability of positive almost periodic solution for Nicholson-type delay systems, Nonlinear Anal. RWA, 12, 1938-1949 (2011) · Zbl 1232.34111
[18] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore, NJ, London · Zbl 0719.34002
[19] Stamov, G. T., On the existence of almost periodic solutions for the impulsive Lasota-Wazewska model, Appl. Math. Lett., 22, 516-520 (2009) · Zbl 1179.34093
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.