Almost periodicity of impulsive Hematopoiesis model with infinite delay

Volume 8, Issue 5, pp 856--865 http://dx.doi.org/10.22436/jnsa.008.05.35

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1310 Downloads
• 2087 Views

Authors

Zhijian Yao - Department of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China.

Abstract

This paper is concerned with almost periodicity of impulsive Hematopoiesis model with infinite delay. By employing the decreasing operator fixed point theorem, we obtain suficient conditions for the existence of unique almost periodic positive solution. In addition, the exponential stability is derived by Liapunov functional.

Share and Cite

Keywords

• Impulsive Hematopoiesis model
• infinite delay
• almost periodic solution
• exponential stability
• decreasing operator
• fixed point theorem.

MSC

•  34K14
•  34K20

References

• [1] D. Bainov, P. Simeonov, Impulsive Differential Equation: Periodic Solutions and Applications, Longman Scientific and Technical, Harlow (1993)


• [2] D. Bainov, P. Simeonov , System with Impulse Effect: Stability, Theory and Applications, John Wiley and Sons, New York (1989)


• [3] A. Fink, Almost Periodic Differential Equations, Lecture Notes in Mathematics, Springer, Berlin, (1974),


• [4] X. L. Fu, B. Q. Yan, Y. S. Liu, Introduction to Impulsive Differential System (in Chinese), Science Press, Beijing (2005)


• [5] M. Fan, K. Wang, Global existence of positive periodic solutions of periodic predator-prey system with infinite delays, J. Math. Anal. Appl., 262 (2001), 1-11.


• [6] I. Gyori, G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford (1991)


• [7] K. Gopalsamy, M. R. S. Kulenovic, G. Ladas, Oscillation and global attractivity in models of Hematopoiesis, J. Dynam. Differential Equations, 2 (1990), 117-132.


• [8] D. Guo, Nonlinear Functional Analysis, Shandong Science and Technology Press, Jinan (2001)


• [9] C. Y. He , Almost Periodic Differential Equations, Higher Education Press, Beijing (1992)


• [10] H. F. Huo, W. T. Li, X. Z. Liu, Existence and global attractivity of positive periodic solution of an impulsive delay differential equation, Appl. Anal., 83 (2004), 1279-1290.


• [11] D. Q. Jiang, J. J. Wei , Existence of positive periodic solutions for non-autonomous delay differential equations, Chinese Ann. Math. Ser. A, 20 (1999), 715-720.


• [12] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston (1993)


• [13] G. Karakostas, C. G. Philos, Y. G. Sficas, Stable steady state of some population models, J. Dynam. Differential Equations, 4 (1992), 161-190.


• [14] V. Lakshmikantham, D. Bainov, P. Simeonov, Theory of Impulsive Differential Equations, World Scientific Publishing Co., Teaneck (1989)


• [15] W. T. Li, H. F. Huo , Existence and global attractivity of positive periodic solutions of functional differential equations with impulses, Nonlinear Anal., 59 (2004), 857-877.


• [16] M. C. Mackey, L. Glass, Oscillations and chaos in physiological control systems, Sciences, 197 (1977), 287-289.


• [17] S. H. Saker, Oscillation and global attractivity in Hematopoiesis model with time delay, Appl. Math. Comput., 136 (2003), 241-250.


• [18] S. H. Saker , Oscillation and global attractivity in Hematopoiesis model with periodic coefficients, Appl. Math. Comput., 142 (2003), 477-494.


• [19] A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, River Edge, NJ (1995)


• [20] A. Wan, D. Jiang, X. Xu, A new existence theory for positive periodic solutions to functional differential equations, Comput. Math. Appl., 47 (2004), 1257-1262.


• [21] D. Ye, M. Fan, Periodicity in mutualism systems with impulse, Taiwanese J. Math., 10 (2006), 723-737.


• [22] A. Zaghrout, A. Ammar, M. M. A. Elsheikh, Oscillation and global attractivity in delay equation of population dynamics, Appl. Math. Comput., 77 (1996), 195-204.