Persistence and Global Stability in a Population Model

Journal of Mathematical Analysis and Applications

Volumn 224, Issue 1, 1998, Pages 59-80

  Gopalsamy, K ^a   Liu, Pingzhou ^a  

^a FLINDERS UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002393430     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.5984     Document Type: Article

References (19)

1. Agarwal R. P. Difference Equations and Inequalities, Theory, Methods, and Applications. 1992;Dekker, New York.
2. Carvalho L. A. V., Cooke K. L. A nonlinear equation with piecewise continuous argument. Differential Integral Equations. 1:1988;359-367.
3. Cooke K. L., Huang W. A theorem of George Seifert and an equation with state-dependent delay. Fink A. M., Miller K., Kliemann W. Delay and Differential Equation. 1991;World Scientific, Singapore.
4. Cull P. Global stability of population models. Bull. Math. Biol. 43:1981;47-58.
5. Dohtani A. Occurrence of chaos in higher dimensional discrete time systems. SIAM J. Appl. Math. 52:1992;1707-1721.
6. Fisher M. E., Goh B. S. Stability results for delayed-recruitment models in population dynamics. J. Math. Biol. 19:1984;147-156.
7. Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics. 1992;Kluwer Academic, Dordrecht.
8. Guckenheimer J., Oster G., Ipaktchi A. The dynamics of density dependent population models. J. Math. Biol. 4:1977;101-147.
9. Hale J. K., Koçak H. Dynamics and Bifurcations. 1991;Springer-Verlag, New York.
10. Ivanov A. F., Sharkovsky A. N. Oscillations in singularly perturbed delay equations. Jones C. K. R. T., Kirchgraber U., Walther H.-O. Dynamics Reported. 1991;164-224 Springer-Verlag, Berlin.
11. Kocic V. K., Ladas G. Global Behavior of Nonlinear Difference Equations of Higher Order with Applications. 1993;Kluwer Academic, Dordrecht.
12. LaSalle J. P. Stability theory for difference equations. Hale J. K. Studies in Ordinary Differential Equations. 1977;Math. Assoc. of America, Washington.
13. May R. M. Biological populations obeying difference equations: stable points, stable cycles and chaos. J. Theoret. Biol. 51:1975;511-524.
14. May R. M., Oster G. F. Bifurcations and dynamic complexity in simple ecological models. Amer. Natur. 110:1976;573-599.
15. Norris D. O., Soewono E. Period doubling and chaotic behaviour of solutions toytytyt. Appl. Anal. 40:1991;181-188.
16. Sandefur J. T. Discrete Dynamical Systems, Theory and Applications. 1990;Clarendon, Oxford.
17. Seifert G. On an interval map associated with delay logistic equation with discontinuous delays. Busenberg S., Martelli M. Delay Differential Equations and Dynamical Systems. Lecture Notes in Mathematics. 1475:1991;Springer-Verlag, Berlin/New York.
18. Seifert G. Certain systems with piecewise constant feedback controls with time delay. Differential Integral Equations. 6:1993;937-947.
19. Wiener J. Generalized Solution of Functional Differential Equations. 1993;World Scientific, Singapore.