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.
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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).
[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).
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55117", author = "Zhouhong Li", title = "Positive Almost Periodic Solutions for Neural Multi-Delay Logarithmic Population Model", abstract = "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.
", keywords = "Almost periodic solution, Multi-delay, Logarithmic population model, Coincidence degree.", volume = "6", number = "8", pages = "959-5", }