Oscillation and stability of nonlinear discrete models exhibiting the Allee effect

 Access to full text

 Full (PDF)

1. AGARWAL R. P., Difference Equations and Inequalities, Theory, Methods and Applications, (2nd ed., revised and expanded) Marcel Dekker, New York, 2000. Zbl0952.39001MR1740241
2. AGARWAL R. P.-WONG P. J. Y., Advanced Topics in Difference Equations, Math. Appl. 404, Kluwer Acad. PubL, Dordrecht, 1997. (1997) Zbl0878.39001MR1447437
3. ALLEE W. C., Animal aggregation, Quart. Rev. Biol. 2 (1927), 367-398. (1927) 
4. ALLEE W. C., Animal Aggregation. A Study in General Sociology, Chicago Universitу Press, Chicago, 1933. (1933) 
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. (1994) MR1678657
6. GOPALSAMY K.-LADAS G., On the oscillation and asymptotic behavior of $\dot{N}\left(t\right)=N\left(t\right)[a+bN(t-\tau )-c{N}^2(t-\tau )]$, Quart. Appl. Math. 3 (1990), 433-440. (1990) Zbl0719.34118MR1074958
7. ELAYDI S.-KOCIC V.-LI J., Global stability of nonlinear difference equations, J. Difference Equ. Appl. 2 (1996), 87-96. (1996) MR1375598
8. ERBE L. H.-ZHANG B. G., Oscillation of discrete analogues of delay equations, Differential Integral Equations 2 (1989), 300-309. (1989) Zbl0723.39004MR0983682
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. (1999) Zbl0939.34061MR1698443
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. (1989) MR1010549
11. KUBIACZYK I.-SAKER S. H., Oscillation and global attractivity in a discrete survival red blood cells model, Appl. Math. (To appear). Zbl1057.39002MR2030065
12. KOCIC V. L.-LADAS G., Global Behavior of Nonlinear Differentiall Equations of Higher Order, Kluwer Acadеmic Publishers, Dordrecht, 1993. (1993) MR1247956
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. (1999) MR1675070
14. LEVIN S.-MAY R., A note on difference delay equations, Thеor. Pop. Biol. 9 1976 , 178-187. (1976) Zbl0338.92021MR0504043
15. STAVROULAKIS I. P., Oscillation of delay difference equations, Comput. Math. Appl. 29 (1995), 83-88. (1995) 
16. ZHANG G.-ZHOU Y., Comparison theorems and oscillation criteria for differential equations, J. Math. Anal. Appl. 247 (2000), 397-409. MR1769085