On Gopalsamy and Liu's conjecture for global stability in a population model

Journal of Computational and Applied Mathematics

Volumn 181, Issue 1, 2005, Pages 70-82

  Muroya, Yoshiaki ^a   Kato, Yoshiko ^a  

^a WASEDA UNIVERSITY   (Japan)

Author keywords

Asymptotic stability; Global asymptotic stability; Logistic equation with a piecewise constant delay

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; THEOREM PROVING;

GLOBAL ASYMPTOTIC STABILITY; LOGISTIC EQUATION; LYAPUNOV FUNCTION;

ASYMPTOTIC STABILITY;

EID: 19444380036     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.11.017     Document Type: Article

References (13)

1. A. Dohtani Occurrence of chaos in higher dimensional discrete time systems SIAM J. Appl. Math. 52 1992 1707-1721
2. M.E. Fisher B.S. Goh Stability results for delayed-recruitment models in population dynamics J. Math. Biol. 19 1984 147-156
3. K. Gopalsamy Stability and Oscillations in Delay Differential Equations of Population Dynamics 1992 Kluwer Academic Publishers Dortrecht
4. K. Gopalsamy P. Liu Persistence and global stability in a population model J. Math. Anal. Appl. 224 1998 59-80
5. J. Guckenheimer G. Oster A. Ipaktchi The dynamics of density dependent population models J. Math. Biol. 4 1977 101-147
6. P. Liu K. Gopalsamy Global stability and chaos in a population model with piecewise constant arguments Appl. Math. Comput. 101 1999 63-88
7. R.M. May Biological populations obeying difference equations: Stable points, stable cycles and chaos J. Theoret. Biol. 51 1975 511-524
8. R.M. May G.F. Oster Bifurcations and dynamic complexity in simple ecological models Amer. Natur. 110 1976 573-599
9. H. Matsunaga T. Hara S. Sakata Global attractivity for a logistic equation with piecewise constant argument Nonlinear Differential Equations Appl. 8 2001 45-52
10. Y. Muroya Persistence, contractivity and global stability in logistic equations with piecewise constant delays J. Math. Anal. Appl. 270 2002 602-635
11. 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
12. G. Seifelt, On an interval map associated with delay logistic equation with discontinuous delays, in: S. Busenberg, M. Martelli (Eds.), Delay Differential Equations and Dynamical Systems, Lecture Notes in Mathematics, vol. 1475, Springer, Berlin, New York, 1991.
13. G. Seifert Certain systems with piecewise constant feedback controls with a time delay Differential Integral Equations 4 1993 937-947