Global stability in discrete population models with delayed-density dependence

Mathematical Biosciences

Volumn 199, Issue 1, 2006, Pages 26-37

  Liz, Eduardo ^a   Tkachenko, Victor ^b   Trofimchuk, Sergei ^c  

^a UNIVERSITY OF VIGO   (Spain)

^b INSTITUTE OF MATHEMATICS   (Ukraine)

^c UNIVERSIDAD DE TALCA   (Chile)

Author keywords

Conjecture of Levin and May; Delay differential equations; Difference equations; Global stability; Population models; Yorke condition

Indexed keywords

DIFFERENCE EQUATIONS; DISCRETE TIME CONTROL SYSTEMS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

CONJECTURE OF LEVIN AND MAY; DELAY DIFFERENTIAL EQUATIONS; GLOBAL STABILITY; POPULATION MODELS; YORKE CONDITION;

ASYMPTOTIC STABILITY;

DENSITY DEPENDENCE; POPULATION MODELING; STABILITY ANALYSIS;

ARTICLE; GLOBAL CHANGE; MATHEMATICAL COMPUTING; NEGATIVE FEEDBACK; POPULATION MODEL; POPULATION RESEARCH;

ALGORITHMS; ANIMALS; MODELS, BIOLOGICAL; POPULATION DENSITY; POPULATION DYNAMICS; POPULATION GROWTH;

EID: 30144432115     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2005.03.016     Document Type: Article

References (25)

1. K.L. Cooke, and J. Wiener A survey of differential equations with piecewise continuous argument Lecture Notes in Mathematics vol. 1475 1991 Springer Berlin 1
2. P. Cull, and J. Chaffee Stability in discrete population models Am. Inst. Phys. Conf. Proc. 517 2000 263
3. H.A. El-Morshedy, and E. Liz Convergence to equilibria in discrete population models J. Differ. Equat. Appl. 11 2005 117
4. L.H. Erbe, H. Xia, and J.S. Yu Global stability of a linear nonautonomous delay difference equation J. Differ. Equat. Appl. 1 1995 151
5. T. Faria, E. Liz, J.J. Oliveira, and S. Trofimchuk On a generalized Yorke condition for scalar delayed population models Discrete Contin. Dyn. Syst. 12 2005 481
6. I. Gyori, and S. Trofimchuk Global attractivity and persistence in a discrete population model J. Differ. Equat. Appl. 6 2000 647
7. W.S.C. Gurney, and R.M. Nisbet Ecological Dynamics 1998 Oxford University
8. W.S.C. Gurney, S.P. Blythe, and R.M. Nisbet Nicholson's blowflies revisited Nature 287 1980 17
9. J.K. Hale, and S.M. Verduyn Lunel Introduction to functional differential equations Applied Mathematical Sciences 1993 Springer
10. V.L. Kocić, and G. Ladas Global attractivity in nonlinear delay difference equations Proc. Am. Math. Soc. 115 1992 1083
11. V.L. Kocić, and G. Ladas Global behavior of nonlinear difference equations of higher order with applications Mathematics and its Applications vol. 256 1993 Kluwer Academic Publishers Group Dordrecht
12. Y. Kuang Delay Differential Equations with Applications in Population Dynamics 1993 Academic Press
13. S.A. Levin, and R.M. May A note on difference delay equations Theor. Populat. Biol. 9 1976 178
14. E. Liz Four theorems and one conjecture on the global asymptotic stability of delay differential equations M. Delgado The First 60 Years of Nonlinear Analysis of Jean Mawhin 2004 World Scientific Singapore 117
15. E. Liz, M. Pinto, G. Robledo, V. Tkachenko, and S. Trofimchuk Wright type delay differential equations with negative Schwarzian Discrete Contin. Dyn. Syst. 9 2003 309
16. E. Liz, V. Tkachenko, and S. Trofimchuk A global stability criterion for scalar functional differential equations SIAM J. Math. Anal. 35 2003 596
17. E. Liz, V. Tkachenko, and S. Trofimchuk Yorke and Wright 3/2-stability theorems from a unified point of view Discrete Contin. Dyn. Syst. Suppl. 2003 580
18. H. Matsunaga, T. Hara, and S. Sakata Global attractivity for a nonlinear difference equation with variable delay Comput. Math. Appl. 41 2001 543
19. J.D. Murray Mathematical Biology 1993 Springer
20. E.C. Pielou Population and Community Ecology 1974 Gordon and Breach New York
21. H.L. Smith Monotone dynamical systems An Introduction to the Theory of Competitive and Cooperative systems 1995 AMS Providence, RI
22. H.R. Thieme Mathematics in Population Biology 2003 Princeton University
23. V. Tkachenko, and S. Trofimchuk Global stability in difference equations satisfying the generalized Yorke condition J. Math. Anal. Appl. 303 2005 173
24. P. Turchin Rarity of density dependence or population regulation with lags Nature 344 1990 660
25. P. Turchin Complex Population Dynamics 2003 Princeton University