Periodic solutions and oscillation of discrete non-linear delay population dynamics model with external force

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 70, Issue 6, 2005, Pages 753-767

  Elabbasy, E M ^a   Saker, S H ^a  

^a Mansoura University   (Egypt)

Author keywords

Non linear delay difference equations; Oscillation; Periodic solutions; Population dynamics

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; DYNAMICS; EVOLUTIONARY ALGORITHMS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; OSCILLATIONS; THEOREM PROVING;

DELAY POPULATION DYNAMICS; INVARIANT TRANSFORMATION; NON-LINEAR DELAY DIFFERENCE EQUATIONS; PERIODIC SOLUTIONS;

MATHEMATICAL MODELS;

EID: 29544435349     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxh068     Document Type: Article

References (23)

1. Chen, M. -P.&Yu, J. S. (1994) Oscillation of delay difference equations with variable coefficients. Proceeding of the First International Conference on Difference Equations (S. N. Elaydi et al. eds). New York: Gorden and Breach, pp. 105-114.
2. Erbe, L. H.&Zhang, B. G. (1989) Oscillation of discrete analogues of delay equations. Diff. Integ. Eqns., 2, 300-309.
3. Fan, M.&Wang, K. (2002) Periodic solutions of a discrete time non-autonomous ratio-dependent predator prey system. Math. Comput. Model., 35, 951-961.
4. Gaines R. E.&Mawhin, J. L. (1977) Coincidence Degree and Nonlinear Differential Equations. Berlin: Springer.
5. Gyori I., Philos, C. H.&Sficas, Y. (1989) Sharp condition for the oscillation of delay difference equations. J. Appl. Math. Simul., 2, 101-112.
6. Kelley, W. G.&Peterson, A. C. (1991) Difference Equations: An Introduction with Applications. New York: Academic Press.
7. Kuang, Y. (1993) Delay Differential Equations with Applications in Population Dynamics. New York: Academic Press.
8. Kubiaczyk, I.&Saker, S. H. (2003) Oscillation and global attractivity of discrete survival red blood cells model. Appl. Math., 30, 441-449.
9. Kulenovic, M. R. S., Ladas, G.&Sficas, Y. S. (1989) Global attractivity in population dynamics. Comput. Math. Appl., 18, 925-928.
10. Ladas, G.&Qian, C. (1992) Linearized oscillations for nonautonomous delay difference equations. Contem. Math., 129, 115-125.
11. Lalli, B. S.&Zhang, B. G. (1994) On a periodic delay population model. Q. Appl. Math., 52, 35-42.
12. Liu, P.&Gopalsamy, K. (1999) Global stability and chaos in a population model with piecewise constant arguments. Appl. Math. Comput., 101, 63-88.
13. Nazarenko, V. G. (1976) Influence of delay on auto-oscillation in cell populations. Biofisika, 21, 352-356.
14. Nicholson, A. J. (1993) The balance of animal population. J. Anim. Ecol., 2, 132-178.
15. Saker, S. H. (2002) Oscillation of nonlinear neutral difference equations. Int. J. Pure Appl. Math., 1, 459-470.
16. Saker, S. H. (2003) Oscillation and global attractivity in hematopoiesis model with periodic coefficients. Appl. Math. Comput., 142, 477-494.
17. Saker, S. H. (2003) Oscillation and global attractivity in a periodic delay hematopoiesis model. J. Appl. Math. Comput., 13, 287-300.
18. Saker, S. H.&Agarwal, S. (2002a) Oscillation and global attractivity in a nonlinear delay periodic model of population dynamics. Appl. Anal., 81, 787-799.
19. Saker, S. H.&Agarwal, S. (2002b) Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics. Comput. Math. Appl., 44, 623-632.
20. Saker, S. H.&Agarwal, S. (2002c) Oscillation and global attractivity in a periodic Nicholson's blowflies model. Math. Comput. Model., 35, 719-731.
21. Saker, S. H.&Agarwal, S. (in press) Oscillation and global attractivity of a periodic survival red blood cells model. J. Dynam Contin. Discrete Impulsive Syst. Ser. B Appl. Algorithms.
22. Stavroulakis, I. P. (1995) Oscillation of delay difference equations. Comput. Math. Appl., 29, 83-88.
23. Zhang, R. Y., Wang, Z. C., Chen, Y.&Wu, J. (2000) Periodic solutions of a single species discrete population model with periodic harvest/ stock. Comput. Math. Appl., 39, 77-90.