×

Almost periodic solutions of single population model with hereditary effects. (English) Zbl 1166.34327

The present paper is concerned with almost periodic solutions of a single population model. The approach is to use the coincidence degree theory. The reviewer thinks that the authors should show some details on the compactness in order to use the coincidence degree theory.

MSC:

34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
92D25 Population dynamics (general)
47N20 Applications of operator theory to differential and integral equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Besicovitch, A. S., Almost Periodic Functions (1954), Dover Publications: Dover Publications New York · Zbl 0065.07102
[2] Chen, B. S.; Liu, Y. Q., On the stable periodic solutions of single sepias molds with hereditary effects, Math. Appl., 1, 42-46 (1999) · Zbl 0948.34047
[3] Chen, F.; Shi, J., Periodicity in a logistic type system with several delays, Comput. Math. Appl., 48, 35-44 (2004) · Zbl 1061.34050
[4] Chen, F.; Xie, X.; Chen, X., Permanence and global attractivity of a delayed periodic logistic equation, Appl. Math. Comput., 177, 118-127 (2006) · Zbl 1101.34058
[5] Chen, Y., Periodic solutions of a delayed periodic logistic equation, Appl. Math. Lett., 16, 1047-1051 (2003) · Zbl 1118.34327
[6] Fan, M.; Wang, K., Periodic solutions of single population model with hereditary effects, Math. Appl., 2, 58-61 (2000) · Zbl 1008.92028
[7] Freedman, H. I.; Xia, H., Periodic solutions of single species models with delay, differential equations, dynamical systems and control science, Lecture Notes Pure Appl. Math., 152, 55-74 (1994) · Zbl 0794.34056
[8] Fujimoto, H., Dynamical behaviours for population growth equations with hereditary effects, Nonlinear Anal. TMA, 5, 549-558 (1998) · Zbl 0887.34071
[9] Gaines, R. E.; Mawhin, J. L., Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag: Springer-Verlag New York · Zbl 0326.34021
[10] Gopalsamy, K., Stability and Oscillations in Delay differential Equations of Population Dynamics (1992), Kluwer Academic: Kluwer Academic Boston · Zbl 0752.34039
[11] Hale, J. K., Ordinary Differential Equations (1980), R.E. Krierger Pub. Co.: R.E. Krierger Pub. Co. New York · Zbl 0186.40901
[12] He, C. Y., Almost Periodic and Differential Equations (1992), High Education Press: High Education Press Beijing
[13] Kuang, Y., Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press: Academic Press Boston · Zbl 0777.34002
[14] Lenhart, S. M.; Travis, C. C., Global stability of a biological model with time delay, Proc. Am. Math. Soc., 96, 75-78 (1986) · Zbl 0602.34044
[15] Li, Y.; Kuang, Y., Periodic solutions of periodic delay Lotka-Volerra equations and systems, J. Math. Anal. Appl., 255, 260-280 (2001) · Zbl 1024.34062
[16] Lisenna, B., Global attractivity in nonautonomous logistic equations with delay, Nonlinear Anal.: Real World Appl., 9, 53-63 (2008) · Zbl 1139.34052
[17] Meng, X. Z.; Chen, L. S., Periodic solution and almost periodic solution for a nonautonomous Lotka-Volterra dispersal system with infinite delay, J. Math. Anal. Appl., 339, 125-145 (2008) · Zbl 1141.34043
[18] Meng, X.; Xu, W.; Chen, L., Profitless delays for a nonautonomous Lotka-Volterra predator-prey almost periodic system with dispersion, Appl. Math. Comput., 188, 365-378 (2007) · Zbl 1113.92070
[19] Seifert, G., On a delay-differential equation for single species population variations, Nonlinear Anal., 9, 1051-1059 (1987) · Zbl 0629.92019
[20] Wang, C. Z.; Shi, J., Positive almost periodic solutions of a class of Lotka-Volterra type competitive system with delays and feedback controls, Appl. Math. Comput., 193, 240-252 (2007) · Zbl 1193.34146
[21] Xia, Y.; Cao, J.; Huang, Z., Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses, Chaos Solitons Fract., 34, 1599-1607 (2007) · Zbl 1152.34343
[22] Zhang, L. J.; Si, L. G., Existence and exponential stability of almost periodic solution for BAM neural networks with variable coefficients and delays, Appl. Math. Comput., 194, 215-223 (2008) · Zbl 1193.34158
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.