Global stability and chaos in a population model with piecewise constant arguments

Applied Mathematics and Computation

Volumn 101, Issue 1, 1999, Pages 63-88

  Liu, Pingzhou ^a   Gopalsamy, K ^a  

^a FLINDERS UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008291269     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(98)00037-X     Document Type: Article

References (23)

1. K.L. Cooke, W. Huang, in: A.M. Fink et al. (Eds.), A Theorem of George Seifert and an Equation with State-dependent Delay, Delay and Diffierential Equations, World Scientific, Ames, Iowa, 1991.
2. S. Elaydi, Global stability of difference equations, in: V. Lakshmikantham (Ed.), Proc. 1st World Congress of Nonlinear Analysis, Kluwer Academic Publishers, Florida, 1992.
3. M.E. Fisher, B.S. Goh, Stability results for delayed-recruitment mocels in population dynamics, J. Math. Biol. 19 (1984) 147-156.
4. K. Gopalsamy, Stability and Oscillation in Delay Differential Equations of Population Dynamics, Kluwer Academic Publishers, Dordrecht, 1992.
5. K. Gopalsamy, P. Liu, Persistence and global stability in a population model, J. Math. Anal. Appl. (in press).
6. J. Guckenheimer, G. Oster, A. Ipaktchi, The dynamics of density dependent population models, J. Math. Biol. 4 (1977) 101-147.
7. D. Gulick, Encounters with Chaos, McGraw Hill, New York, 1992.
8. I. Györi, G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Oxford University Press, Oxford, 1991.
9. J.K. Hale, H. Koçak, Dynamics and Bifurcations, Springer, New York, 1991.
10. A.F. Ivanov, A.N. Sharkovsky, Oscillations in singular perturbed delay equations, in: C. Jones et al. (Eds.), Dynamics Reported New Series, vol. 1, Springer, Berlin, 1991.
11. V.L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
12. T-Y. Li, J.A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (10) (1975) 985-992.
13. P. Liu, Stability of Nonlinear Discrete Systems with Applications to Population Dynamics, Ph.D. Thesis, 1997.
14. S.M. Lenhart, C.C. Travis, Global stability of a biological model with time delay, Proc. Amer. Math. Soc. 96 (1986) 75-78.
15. R.M. May, Biological populations obeying difference equations: Stable points, stable cycles and chaos, J. Theoret. Biol. 51 (1975) 511-524.
16. R.M. May, G.F. Oster, Bifurcations and dynamics complexity in simple ecological models, Amer. Nat. 110 (1976) 573-599.
17. D.O. Norris, E. Soewono, Period doubling and chaotic behaviour of solutions to y′(t) = μy(t)[1 - y(δ[t + α/δ])], Appl. Anal. 40 (1991) 181-188.
18. G. Seifert, On a delay-differential equation for single specie population variations, Nonlinear Analysis, TMA, 11 (9) (1987) 1051-1059.
19. G. Seifert, Oscillation of solution of a population with delay, in: V. Lashmikantham (Ed.), Nonlinear Analysis and Applications, Lecture Notes in Pure and Appl. Math., vol. 109, Marcel Dekker, 1987, pp. 549-554.
20. G. Seifert, Oscillatory solutions for certain delay-differential equations, Proc. Amer. Math. Soc. 104 (1988) 553-557.
21. G. Seifert, On a interval map associated with a delay logistic equation with discontinuous delays, delay a differential equations and Dynamical systems, in: S. Busenberg, M. Martelli (Eds.), Lecture Notes in Mathematics, vol. 1475, Springer, Berlin, 1991.
22. D. Singer, Stable orbits and bifurcation of maps of the interval, SIAM J. Appl. Math. 35 (1978) 260-267.
23. J.W.H. So, J.S. Yu, Global stability in a logistic equation with piecewise constant arguments, Hokkaido Math. J. 24 (1995) 269-286.