Compensatory versus overcompensatory dynamics in density-dependent Leslie models

Journal of Difference Equations and Applications

Volumn 10, Issue 13-15, 2004, Pages 1251-1265

  Kulenović, Mustafa R S ^a   Yakubu, Abdul Aziz ^b  

^a University of Rhode Island   (United States)

^b HOWARD UNIVERSITY   (United States)

Author keywords

Age structure; Allee effect; Compensatory dynamics; Density dependent Leslie models; Multiple attractors; Overcompensatory dynamics

Indexed keywords

EID: 8744233203     PISSN: 10236198     EISSN: None     Source Type: Journal    
DOI: 10.1080/10236190410001652711     Document Type: Article

References (36)

1. J. C. Alexander, J. A. Yorke, Z. You and I. Kan, Riddled Basins, Intern. J. Bifurc. Chaos, 2(4) (1992), 795-813.
2. M. Begon, J. L. Harper and C. R. Townsend, Ecology: Individuals, Populations and Communities, Blackwell Science Ltd, Osney Mead, Oxford, 1996.
3. J. Best, V. Pasour, N. Tisch and C. Castillo-Chavez, Delayed density dependence and the dynamic consequences of dispersal between patches, Preprint, 2001.
4. F. Brauer and C. Castillo-Chavez, Mathematical models in population biology and epidemiology Texts in Applied Mathematics 40, Springer Verlag, New York, 2001.
5. C. Castillo-Chavez and A. A. Yakubu, Dispersal, disease and life-History evolution, Math. Biosc., 173 (2001), 35-53.
6. C. Castillo-Chavez and A. A. Yakubu, Intraspecific competition, dispersal and disease dynamics in discrete-time patchy environments, In: Carlos Castillo-Chavez with Sally Blower, Pauline van den Driessche, Denise Kirschner and Abdul-Aziz Yakubu, eds, Mathematical Approaches For Emerging and Reemerging Infectious Diseases: An Introduction to Models, Methods and Theory, Springer-Verlag, New York, 2002.
7. H. Caswell, Matrix Population Models: Construction, Analysis, and Interpretation, Second Edition, Sinauer Associates, Inc. 2001.
8. S. N. Elaydi, An Introduction to Difference Equations, Springer-Verlag, New York, 1996.
9. S. N. Elaydi, Discrete Chaos, Chapman & Hill/CRC, Boca Raton, FL, 2002.
10. J. Franke and A. A. Yakubu, Population exclusion in a one-hump discrete pioneer-climax competitive system, J. Math. Biol., 32 (1994), 771-787.
11. C. Grebogi, E. Ott and J. A. Yorke, Chaos, strange attractors, and fractal basin boundaries in nonlinear dynamics, Science, 228 (1987), 632-638.
12. J. Guckenheimer, G. Oster and A. Ipaktchi, The dynamics of density dependent population models, J. Math. Biol., 4 (1977), 101-147.
13. I. Hanski, J. Poyry, T. Pakkala and M. Kuussaari, Multiple equilibria in metapopulation dynamics, Nature, 377 (1995), 618-621.
14. M. P. Hassell, The dynamics of competition and predation, Studies in Biol. 72, The Camelot Press Ltd. 1976.
15. M. P. Hassell, J. H. Lawton and R. M. May, Patterns of dynamical behavior in single species populations, J. Anim. Ecol., 45 (1976), 471-486.
16. A. Hastings, Complex interactions between dispersal and dynamics: Lessons from coupled logistic equations, Ecology, 75 (1993), 1362-1372.
17. S. M. Henson, R. F. Constantino, J. M. Gushing, B. Dennis and R. A. Desharnais, Multiple attractors, saddles, and population dynamics in periodic habitats, Bull. Math. Biol., 61 (1999), 1121-1149.
18. S. M. Henson and J. M. Cushing, Hierarchical models of intraspecific competition: scramble versus contest, J. Math. Biol., 34 (1996), 755-772.
19. I. Kan, Open sets of diffeomorphisms having two attractors, each with an everywhere dense basin, Bull. AMS, 31(1) (1994), 68-74.
20. V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993.
21. M. R. S. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations, Chapman & Hill/CRC, Boca Raton, FL, 2001.
22. M. Kuussaari, I. Saccheri, M. Camara and I. Hanski, Allee effect and population dynamics in the Glanville fritillary butterfly, Oikos, 82 (1998), 384-392.
23. A. L. Lloyd, The coupled logistic map: A simple model for the effects of spatial heterogeneity on population dynamics, J. Theor. Biol., 173 (1995), 217-230.
24. R. M. May and G. F. Oster, Bifurcations and dynamic complexity in simple ecological models, Am. Nat., 110 (1976), 573-579.
25. R. M. May, Simple mathematical models with very complicated dynamics, Nature, 261 (1977), 459-469.
26. R. M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, 1974.
27. R. M. May, M. P. Hassell, R. M. Anderson and D. W. Tonkyn, Density dependence in host-parasitoid models, J. Anim. Ecol., 50 (1981), 855-865.
28. A. J. Nicholson, Compensatory reactions of populations to stresses, and their evolutionary significance, Aust. J. Zool., 2 (1954), 1-65.
29. W. E. Ricker, Stock and recruitment, J. Fisheries Res. Board Canada, II(5) (1954), 559-623.
30. Mickens, Ronald E., Difference Equations. Theory and Applications, Second edition, Van Nostrand Reinhold Co., New York, 1990.
31. Mickens, Ronald E., Difference Equations, Van Nostrand Reinhold Co., New York-London, 1987.
32. I. Scheuring, Allee effect increases the dynamical stability of populations, J. Theor. Biol., 199 (1999), 407-414.
33. A. A. Yakubu, Discrete-time metapopulation dynamics and unidirectional dispersal, J. Differ. Eqns Appl., 9(7) (2003), 633-653.
34. A. A. Yakubu, Multiple attractors in juvenile-adult single species models, J. Differ. Eqns Appl., 9 (2003), 1083-1098.
35. A. A. Yakubu and C. Castillo-Chavez, Interplay between local dynamics and dispersal in discrete-time metapopulation models, J. Theor. Biol., 218 (2002), 273-288.
36. P. Yodzis, Introduction to Theoretical Ecology, Harper & Row, Publishers, New York, 1989.