Positive periodic solutions of discrete three-level food-chain model of Holling type II

Applied Mathematics and Computation

Volumn 180, Issue 1, 2006, Pages 353-365

  Sun, Y G ^a   Saker, S H ^b  

^a QUFU NORMAL UNIVERSITY   (China)

^b Mansoura University   (Egypt)

Author keywords

Difference equations; Food chain model; Periodic

Indexed keywords

MATHEMATICAL MODELS; NUMERICAL METHODS; THEOREM PROVING; TIME VARYING SYSTEMS;

CONTINUATION THEOREM; FOOD-CHAIN MODELS;

DIFFERENTIAL EQUATIONS;

EID: 33748293096     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.12.015     Document Type: Article

References (18)

1. Azar C., Holmberg J., and Lindgren K. Stability analysis of harvesting in a predator-prey model. J. Theor. Biol. 174 (1995) 13-19
2. Elabbasy E.M., and Saker S.H. Dynamics of a class of non-autonomous systems of two non-interacting preys with common predator. J. Appl. Math. Comput. 17 (2005) 195-215
3. Elabbasy E.M., and Saker S.H. Periodic solutions and oscillation of discrete nonlinear delay population dynamics model with external force. IMA J. Appl. Math. (2005) 1-15
4. Bhattachaya D.K., and Karan S. Pest management of two non-interacting pests in presence of common predator. J. Appl. Math. Comput. 13 (2003) 301-322
5. Kumar S., Sirvastava S.K., and Chingakham P. Hopf bifurcation and stability analysis in a harvested one-predator-two-prey model. Appl. Math. Comput. 126 (2002) 107-118
6. Liu P., and Gopalsamy K. Global stability and chaos in a population model with piecewise constant arguments. Appl. Math. Comput. 101 (1999) 63-88
7. Gaines R.E., and Mawhin J.L. Coincidence Degree and Nonlinear Differential Equations (1977), Springer, Berlin
8. Fan M., and Wang K. Periodic solutions of a discrete time non-autonomous ratio-dependent predator-prey system. Math. Comput. Model. 35 (2002) 951-961
9. Holling C.S. The components of predation as revealed by a study of small mammal predation of the European pine sawfly. Can. Entomol. 91 (1959) 293-320
10. Holling C.S. Some characteristics of simple types of predation and parasitism. Can. Entomol. 91 (1959) 385-398
11. Holling C.S. The functional response of predators to prey density and its role in mimiery and population regulation. Mem. Entomol. Soc. Can. 45 (1963) 3-60
12. S.H. Saker, Existence of positive periodic solutions of discrete model for the interaction of demand and supply, Nonlinear Funct. Anal. Appl., in press.
13. Saker S.H., and Agarwal S. Oscillation and global attractivity in a nonlinear delay periodic model of population dynamics. Appl. Anal. 81 (2002) 787-799
14. Saker S.H., and Agarwal S. Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics. Comput. Math. Appl. 44 (2002) 623-632
15. Saker S.H., and Agarwal S. Oscillation and global attractivity in a periodic Nicholson's blowflies model. Math. Comput. Model. 35 (2002) 719-731
16. S.H. Saker, S. Agarwal, Oscillation and global attractivity of a periodic survival red blood cells model, J. Dyn. Continuous, Discrete Impulsive Syst. Ser. B: Appl. Algorithms, in press.
17. Yan J., and Feng Q. Global attractivity and oscillation in a nonlinear delay equation. Nonlinear Anal. 43 (2001) 101-108
18. Zhang R.Y., Wang Z.C., Chen Y., and Wu J. Periodic solutions of a single species discrete population model with periodic harvest/stock. Comput. Math. Appl. 39 (2000) 77-90