Positive Almost Periodic Solutions for Neural Multi-Delay Logarithmic Population Model

In this paper, by applying Mawhin-s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result.

• Zhouhong Li

• Almost periodic solution
• Multi-delay
• Logarithmic population model
• Coincidence degree.

[1] S.Lu, W. Ge,Existence of positive periodic solutions for neutral logarithmic
pop- ulation model with multiple delays. J. Comput. Appl. Math. 166(2), 371-383 (2004).
[2] Y. Luo, Z. Luo,Existence of positive periodic solutions for neutral multidelay
log- arithmic population model. Appl. Math. Comput. 216, 1310-1315 (2010)
[3] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations
of Population Dynamics, Kluwer Acad. Publ., 1992.
[4] M. Kot, Elements of Mathematical Ecology, Cambr. Univ. Press, 2001.
[5] Y. Kuang, Delay Differential Equations With Applications in Population
Dynamics, Academic Press, Inc., 1993.
[6] J. Alzabuta, G. Stamovb,E. Sermutlu, Positive almost periodic solutions
for a delay logarithmic population model.Math. and Comput. Model.,53(12), 161-167(2011).
[7] Q. Wang,H. Zhang, Y. Wang, Existence and stability of positive almost
periodic solutions and periodic solutions for a logarithmicpopulation
model. Nonlinear Anal: Theory, Methods and Appl.,72(12), 4384-
4389(2010).
[8] Gaines R, Mawhin J. Coincidence degree and nonlinear differential
equations. Berlin: Springer Verlag; 1977.
[9] Y. Xie, X. Li, Almost periodic solutions of single population model with
hereditary effects, Appl. Math. Comp. 203,690-697(2008).
[10] C. He, Almost Periodic Differential Equations, Higher Education Publishing
House, Beijing, 1992 (in Chinese).