Wada basins and qualitative unpredictability in ecological models: A graphical interpretation

Ecological Modelling

Volumn 176, Issue 1-2, 2004, Pages 65-74

  Vandermeer, John ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Ecological model; Unpredictability; Wada basins

Indexed keywords

ECOLOGICAL MODELING; GRAPHICAL METHOD; MATHEMATICAL ANALYSIS; MODELING;

EID: 2642523864     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecolmodel.2003.10.028     Document Type: Article

References (21)

1. Alligood, K.T., Sauer, T.D., Yorke, J.A., 1996. Chaos: An Introduction to Dynamical Systems. Springer, Berlin.
2. Bak, P., 1986. The devil's staircase. Phys. Today 39-45.
3. Bohr T., Bak P., Jensen M.H. Transition to chaos by interaction of resonances in dissipative systems. II. Josephson junctions, charge-density waves, and standard maps. Phys. Rev. A. 30:1984;1970-1981
4. Cavalieri, L.F., Koçak, H., 1999. Coexistence of multipule attractors and its consequence for a three species food chain. In: Hawkins, B.A., Howard, V.C. (Eds.), Theoretical Approaches to Biological Control. Cambridge University Press, Cambridge, UK.
5. Cvitanovic P., Gunaratne G.H., Vinson M.J. On the mode-locking universality for critical circle maps. Nonlinearity. 3:1990;873-885
6. Ding M., Yang W. Observation of intermingled basins in coupled oscillators exhibiting synchronized chaos. Phys. Rev. E. 54:1996;2489-2494
7. Hastings A., Hom C.L., Ellner S., Turchin P., Godfray H.C.J. Chaos in ecology: is mother nature a strange attractor? Ann. Rev. Ecol. System. 24:1993;1-33
8. Huisman J., Weissing F.J. Biodiversity of plankton by species oscillations and chaos. Nature. 401:1999;407-410
9. Huisman J., Weissing F.J. Fundamental unpredictability in multispecies competition. Am. Nat. 157:2001;488-494
10. Jensen M.H., Bak P., Bohr T. Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps. Phys. Rev. A. 30:1984;1960-1969
11. Levins R. The strategy of model building in population biology. Am. Scientist. 54:1966;421-431
12. May, R.M., 1973. Stability and complexity in model ecosystems. Monographs in Population Biology, No. 6. Princeton University Press, Princeton, N.J.
13. May R.M. Simple mathematical models with very complicated dynamics. Nature. 261:1976;459-467
14. May R.M. Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature. 269:1977;471-477
15. Neubert M.G. A simple population model with qualitatively uncertain dynamics. J. Theor. Biol. 189:1997;399-411
16. Nusse H.E., Yorke J.A. Basins of attraction. Science. 271:1996;1376-1380
17. Ott E.J., Alexander C., Kan I., Sommerer J.C., Yorke J.A. The transition to chaotic attractors with riddled basins. Phys. D. 76:1994;384-410
18. Sommerer J.C., Ott E. A physical system with qualitatively uncertain dynamics. Nature. 365:1993;138-140
19. Vandermeer J.H. The qualitative behavior of coupled predator prey oscillations as deduced from simple circle maps. Ecol. Model. 73:1994;135-148
20. Vandermeer J.H., Yodzis P. Basin boundary collision as a model of discontinuous change in ecosystems. Ecology. 80:1999;1817-1827
21. Vandermeer J.H., Stone L., Blasius B. Categories of chaos and fractal basin boundaries in a forced Lotka-Volterra model. Chaos, Solitons and Fractals. 12:2001;265-276