Existence of positive periodic solutions of nonlinear discrete model exhibiting the Allee effect

Applied Mathematics and Computation

Volumn 168, Issue 2, 2005, Pages 1086-1097

  Sun, Y G ^a   Saker, S H ^b  

^a QUFU NORMAL UNIVERSITY   (China)

^b Mansoura University   (Egypt)

Author keywords

Discrete population model; Nonoscillation; Periodic

Indexed keywords

NONLINEAR EQUATIONS; THEOREM PROVING;

COINCIDENCE DEGREE THEOREM; DISCRETE POPULATION MODELS; NONOSCILLATION; PERIODIC;

MATHEMATICAL MODELS;

EID: 26044472122     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.10.005     Document Type: Article

References (22)

1. W.C. Allee Animal aggregation Quart. Rev. Biol. 2 1927 367 398
2. W.C. Allee Animal aggregation A Study in General Sociology 1933 Chicago University Press Chicago
3. E.M. Elabbasy, S.H. Saker, and K. Saif Oscillation of nonlinear delay differential equations with application to models exhibiting the Allee effect Far East J. Math. Sci. 1 4 1999 603 620
4. S. Elaydi Global stability of nonlinear difference equations J. Diff. Eqn. Appl. 2 1996 87 96
5. M. Fan, and K. Wang Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system Math. Comp. Model. 35 2002 951 961
6. R.E. Gaines, and J.L. Mawhin Coincidence Degree and Nonlinear Differential Equations 1977 Springer Berlin
7. K. Gopalsamy, and G. Ladas On the oscillation and asymptotic behavior of N ̇ (t ) = N (t ) [ a + bN (t - τ ) - cN 2 (t - τ ) ] Quart. Appl. Math. 3 1990 433 440
8. W.G. Kelley, and A.C. Peterson Difference Equations; An Introduction with Applications 1991 Academic Press New York
9. V.L. Kocic, and G. Ladas Global Behavior of Nonlinear Difference Equations of Higher Order 1993 Kluwer Academic Publishers Dordrecht
10. Y. Kuang Delay Differential Equations with Applications in Population Dynamics 1993 Academic Press New York
11. I. Kubiaczyk, and S.H. Saker Oscillation and global attractivity of discrete survival red blood cells model Applicationes Mathematicae 30 2003 441 449
12. G. Ladas, and C. Qian Oscillation and global stability in delay logistic equation Dyn. Syst. Appl. 9 1994 153 162
13. B.S. Lalli, and B.G. Zhang On a periodic delay population model Quart. Appl. Math. 52 1994 35 42
14. P. Liu, and K. Gopalsamy Global stability and chaos in a population model with piecewise constant arguments Appl. Math. Comp. 101 1999 63 88
15. A.J. Nicholson The balance of animal population J. Animal Ecol. 2 1993 132 178
16. S.H. Saker Oscillation and global attractivity in hematopoiesis model with periodic coefficients Appl. Math. Comp. 142 2003 477 494
17. S.H. Saker, and S. Agarwal Oscillation and global attractivity in nonlinear delay periodic model of population dynamics Appl. Anal. 81 2002 787 799
18. S.H. Saker S. Agarwal, Oscillation and global attractivity of a periodic survival red blood cells model, J. Dyn. Continuous, Discrete Impulsive Syst. Series B: Appl. Algorithms, in press.
19. S.H. Saker, and S. Agarwal Oscillation and global attractivity in a periodic Nicholson's Blowflies model Math. Comp. Model. 35 2002 719 731
20. S.H. Saker, and S. Agarwal Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics Comp. Math. Appl. 44 2002 623 632
21. J. Yan, and Q. Feng Global attractivity and oscillation in a nonlinear delay equation Nonlinear Anal. 43 2001 101 108
22. R.Y. Zhang, Z.C. Wang, Y. Chen, and J. Wu Periodic solutions of a single species discrete population model with periodic harvest/stock Comp. Math. Appl. 39 2000 77 90