Oscillation of continuous and discrete diffusive delay Nicholson's blowflies models

Applied Mathematics and Computation

Volumn 167, Issue 1, 2005, Pages 179-197

  Saker, S H ^a  

^a Mansoura University   (Egypt)

Author keywords

Nicholson's blowflies model; Nonlinear delay partial differential and difference equations; Oscillation

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENCE EQUATIONS; MATHEMATICAL MODELS; OSCILLATIONS;

FIRST ORDER CHARACTER; NICHOLSON'S BLOWFLIES MODELS; POSITIVE STEADY STATE;

BOUNDARY CONDITIONS;

EID: 24944511236     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.06.083     Document Type: Article

References (38)

1. R.P. Agarwal, S.R. Grace, and D. O'Regan Oscillation Theory for Difference and Functional Differential Equation 2000 Kluwer Academic Publishers Drodrecht
2. C.D. Ahlabrandt, and A.C. Peterson Discrete Hamiltonian Systems: Difference Equations, Continued Fractions 1996 Kluwer Academic Publishers Drodrchet
3. A. Ardito, and P. Riccard Existence and regularity for linear delay partial differential equations Nonlinear Anal. 4 1980 411 414
4. S.S. Cheng, and G. Zhang Existence criteria for positive solutions of a nonlinear difference inequality Annal. Poln. Math. LXXIII 3 2000 197 220
5. A. Friedman Partial Differential Equations of Parabolic Type 1964 Printic-Hall Englewood Cliffs, NJ
6. W.S. Gurney, S.P. Blythe, and R.M. Nisbet Nicholson's blowflies revisited Nature 287 1980 17 21
7. I. Györi, and G. Ladas Oscillation Theory of Delay Differential Equations with Applications 1991 Clarendon Press Oxford
8. I. Györi, and S.I. Trofimchuk On the existence of rapidly oscillatory solutions in the Nicholson Blowflies equation Nonlinear Anal. 48 2002 1033 1042
9. G. Karakostas, Ch.G. Philos, and Y.G. Sficas Stable steady state of some population models J. Dynam. Diff. Eqns. 4 1992 161 190
10. W.G. Kelley, and A.C. Peterson Difference Equations; An Introduction with Applications 1991 Academic Press New York
11. V.L. Kocic, and G. Ladas Oscillation and global attractivity in a discrete model of Nicholson's blowflies Applicable Anal. 38 1990 21 31
12. V.L. Kocic, and G. Ladas Global Behavior of Nonlinear Difference Equations of Higher Order 1993 Kluwer Academic Publishers Dordrecht
13. K. Kreith, and G. Ladas Allowable delays for positive diffusion processes Hiroshima Math. J. 15 1985 437 443
14. I. Kubiaczyk, and S.H. Saker Kamenev-type oscillation criteria for hyeperbolic nonlinear delay difference equations Demonstratio Math. 36 1 2003 113 122
15. I. Kubiaczyk, and S.H. Saker Oscillation theorems for discrete nonlinear delay wave equations Z. Angew. Math. Mech. 83 12 2003 812 819 (J. Appl. Math. Mech. (ZAMM))
16. M.R.S. Kulenovic, and G. Ladas Linearized oscillation in population dynamics Bull. Math. Biol. 44 1987 615 627
17. M.R.S. Kulenovic, G. Ladas, and Y.S. Sficas Global attractivity in Nicholson's blowflies Applicable Anal. 43 1992 109 124
18. X.P. Li Partial difference equations used in the study of molecular orbits Acta Chimica Sinica 40 1982 688 696 (in Chinese)
19. A.J. Nicholson The self adjusment of population to change Cold Spring Harb. Symp. Quant. Biol. 22 1957 153 173
20. A.J. Nicholson The balance of animal population J. Animal Ecol. 2 1993 132 178
21. S.H. Saker, Oscillation of parabolic neutral delay difference equations, Bull. Korean Math. Soc., in press.
22. S.H. Saker Oscillation of parabolic neutral delay difference equations with several positive and negative coefficients Appl. Math. Comput. 143 1 2003 173 186
23. S.H. Saker Kamenev-type oscillation criteria for hyperbolic nonlinear neutral delay difference equations Nonlinear Studies 10 3 2003 221 236
24. S.H. Saker, and S. Agarwal Oscillation and global attractivity in a periodic Nicholson's Blowflies model Math. Comput. Modell. 35 2002 719 731
25. S.H. Saker, and B.G. Zhang Oscillation in a discrete partial Nichlson's Blowflies model Math. Comput. Modell. 36 2002 1021 1026
26. S.H. Saker, and S. Agarwal Oscillation and global attractivity in nonlinear delay periodic model of population dynamics Applicable Anal. 81 2002 787 799
27. S.H. Saker, and S. Agarwal Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics Comput. Math. Appl. 44 2002 623 632
28. S.H. Saker, and P.J.Y. Wong Nonexistence of unbounded nonoscillatory solutions of nonlinear perturbed partial difference equations J. Concr. Applicable Math. 1 1 2003 87 99
29. H. Smith, Monotone Dynamical Systems, AMS Surveys and Monographs Providence, Hode Island, 1995.
30. J.W.H. So, and J.S. Yu On the stability and uniform persistence of a discrete model of Nicholson's blowflies J. Math. Anal. Appl. 193 1995 233 244
31. D.M. Thomas, and F.W. Robbins Analysis of nonatunomous Nicholosn blowfly model Physica A 273 1999 198 211
32. C.C. Travis, and G.F. Webb Existence and stability for partial functional differential equations Trans. Amer. Math. Soc. 200 1974 359 418
33. J. Turo Generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in the Schauder canonic form Ann. Polon. Math. 50 1989 157 183
34. V.S. Vladimirov Equations of Mathematical Physics 1981 Nauka Moscow
35. J.H. Wu Theory and Applications of Partial Functional Differential Equations 1996 Springer New York
36. Y. Yamada On a certain class of semilinear Voltera diffusion equations J. Math. Anal. Appl. 88 1982 433 451
37. B.G. Zhang Oscillation of delay partial difference equations Prog. Natural Sci. 11 2001 321 330
38. B.G. Zhang, and S.H. Saker Oscillation in a discrete partial delay survival red blood cells model Math. Comput. Modell. 37 2003 659 664