| Title:
|
Oscillation and stability of nonlinear discrete models exhibiting the Allee effect (English) |
| Author:
|
Elabbasy, Elmetwally M. |
| Author:
|
Saker, Samir H. |
| Author:
|
El-Metwally, Hamdy |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
[243]-258 |
| . |
| Category:
|
math |
| . |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| MSC:
|
39A12 |
| MSC:
|
92D25 |
| idZBL:
|
Zbl 1150.39005 |
| idMR:
|
MR2357822 |
| . |
| Date available:
|
2009-09-25T14:38:17Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136952 |
| . |
| Reference:
|
[1] AGARWAL R. P.: Difference Equations and Inequalities, Theory, Methods and Applications.(2nd ed., revised and expanded) Marcel Dekker, New York, 2000. Zbl 0952.39001, MR 1740241 |
| Reference:
|
[2] AGARWAL R. P.-WONG P. J. Y.: Advanced Topics in Difference Equations.Math. Appl. 404, Kluwer Acad. PubL, Dordrecht, 1997. Zbl 0878.39001, MR 1447437 |
| Reference:
|
[3] ALLEE W. C.: Animal aggregation.Quart. Rev. Biol. 2 (1927), 367-398. |
| Reference:
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[4] ALLEE W. C.: Animal Aggregation. A Study in General Sociology.Chicago Universitу Press, Chicago, 1933. |
| Reference:
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[5] CHEN M.-P.-YU J. S.: Oscillation of delay difference equations with variable coefficients.In: Proceeding of the First International Conference on Difference Equations (S. N. Elaуdi et al., eds), Gordon and Breach, New York, 1994 pp. 105-114. MR 1678657 |
| Reference:
|
[6] GOPALSAMY K.-LADAS G.: On the oscillation and asymptotic behavior of $\dot N(t)=N(t)[a+bN(t-\tau)-cN\sp 2(t-\tau)]$.Quart. Appl. Math. 3 (1990), 433-440. Zbl 0719.34118, MR 1074958 |
| Reference:
|
[7] ELAYDI S.-KOCIC V.-LI J.: Global stability of nonlinear difference equations.J. Difference Equ. Appl. 2 (1996), 87-96. MR 1375598 |
| Reference:
|
[8] ERBE L. H.-ZHANG B. G.: Oscillation of discrete analogues of delay equations.Differential Integral Equations 2 (1989), 300-309. Zbl 0723.39004, MR 0983682 |
| Reference:
|
[9] ELABBASY E. M.-SAKER S. H.-SAIF K.: Oscillation of nonlinear delay differential equations with application to models exhibiting the Allee effect.Far East J. Math. Sci. 1 (1999), 603-620. Zbl 0939.34061, MR 1698443 |
| Reference:
|
[10] LADAS G.-PHILOS C. H.-SFICAS Y.: Sharp condition for the oscillation of delay difference equations.J. Appl. Math. Simul. 2 (1989), 101-111. MR 1010549 |
| Reference:
|
[11] KUBIACZYK I.-SAKER S. H.: Oscillation and global attractivity in a discrete survival red blood cells model.Appl. Math. (To appear). Zbl 1057.39002, MR 2030065 |
| Reference:
|
[12] KOCIC V. L.-LADAS G.: Global Behavior of Nonlinear Differentiall Equations of Higher Order.Kluwer Acadеmic Publishers, Dordrecht, 1993. MR 1247956 |
| Reference:
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[13] LIU P.-GOPALSAMY K.: Global stability and chaos in a population modul with piece wise constant arguments.Appl. Math. Comput. 101 (1999), 63-88. MR 1675070 |
| Reference:
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[14] LEVIN S.-MAY R.: A note on difference delay equations.Thеor. Pop. Biol. 9 1976 , 178-187. Zbl 0338.92021, MR 0504043 |
| Reference:
|
[15] STAVROULAKIS I. P.: Oscillation of delay difference equations.Comput. Math. Appl. 29 (1995), 83-88. |
| Reference:
|
[16] ZHANG G.-ZHOU Y.: Comparison theorems and oscillation criteria for differential equations.J. Math. Anal. Appl. 247 (2000), 397-409. MR 1769085 |
| . |
