A simple population model with qualitatively uncertain dynamics

Journal of Theoretical Biology

Volumn 189, Issue 4, 1997, Pages 399-411

  Neubert, Michael G ^a  

^a WOODS HOLE OCEANOGRAPHIC INSTITUTION   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

POPULATION MODEL; RIDDLED BASIN; UNPREDICTABILITY;

ARTICLE; ECOSYSTEM; POPULATION DYNAMICS; POPULATION MODEL; PRIORITY JOURNAL;

EID: 0031583026     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1997.0258     Document Type: Article

References (41)

1. ALEXANDER, J. C., YORKE, J. A., You, Z. & KAN, I. (1992). Riddled basins. Int. J. Bifurcations Chaos 2, 795-813.
2. ASHWIN, P., BUESCU, J. & STEWART, I. (1994). Bubbling of attractors and synchronisation of chaotic oscillators. Phys. Lett. A 193, 126-139.
3. CLARK, C. W. (1990). Mathematical Bioeconomics. New York: John Wiley & Sons.
4. COSTANTINO, R. F. & DESHARNAIS, R. A. (1991). Population Dynamics and the Tribolium Model: Genetics and Demography. New York: Springer-Verlag.
5. DING, M. & YANG, W. (1996). Observation of intermingled basins in coupled oscillators exhibiting synchronized chaos. Phys. Rev. E 54, 2489-2494.
6. FARMER, J. D. (1985). Sensitive dependence on parametrs in nonlinear dynamics. Phys. Rev. Lett. 55, 351-?.
7. FRANKE, J. E. & YAKUBU, A-A. (1991). Global attractors in competitive systems. Nonlinear Analysis 16, 111-129.
8. FRANKE, J. E. & YAKUBU, A-A. (1992). Mutual exclusion versus coexistence of discrete competitive systems. J. Math. Biol. 30, 161-168.
9. FUNASAKI, E. & KOT, M. (1993). Invasion and chaos in a periodically pulsed mass-action chemostat. Theor. Pop. Biol. 44, 203-224.
10. GREBOGI, C., MCDONALD, S. W., OTT, E. & YORKE, J. A. (1985). Exterior dimension of fat fractals. Phys. Lett. A 110, 1-4.
11. GREBOGI, C., OTT, E. & YORKE, J. A. (1986). Metamorphoses of basin boundaries in nonlinear dynamical systems. Phys. Rev. Lett. 56, 1011-1014.
12. GREBOGI, C., OTT, E. & YORKE, J. A. (1987). Basin boundary metamorphoses: changes in accessible boundary orbits. Physica D 24, 243-262.
13. HEAGY, J. F., CARROLL, T. L. & PECORA, L. M. (1994). Experimental and numerical evidence for riddled basins in coupled chaotic systems. Phys. Rev. Lett. 73, 3528-3531.
14. HASTINGS, A. (1993). Complex interactions between dispersal and dynamics: lessons from coupled logistic equations. Ecology 74, 1362-1372.
15. HASTINGS, A. & POWELL, T. (1991). Chaos in a three-species food chain. Ecology 72, 896-903.
16. KAN, I. (1994). Open sets of diffeomorphisms having two attractors, each with an everywhere dense basin. Bull. Am. Mathe. Soc. 31, 68-74.
17. KAPITANIAK, T. (1995). Experimental observation of riddled behaviour. J. Physics A 28, L63-L66.
18. KOT, M. (1989). Diffusion-driven period-doubling bifurcations. Biosystems 22, 270-287.
19. KOT, M. & SCHAFFER, W. M. (1984). The effects of seasonality on discrete models of population growth. Theor. Pop. Biol. 26, 340-360.
20. KOT, M., SAYLER, G. S. & SCHULTZ, T. W. (1992). Complex dynamics in a model microbial system. Bull. Math. Biol. 54, 619-648.
21. LLOYD, A. L. (1995). The coupled logistic map: a simple model for the effects of spatial heterogeneity on population dynamics. J. theor. Biol. 173, 217-230.
22. LLOYD, A. L. & MAY, R. M. (1996). Spatial heterogeneity in epidemic models. J. theor. Biol. 179, 1-11.
23. MCCANN, K. & YODZIS, P. (1993). Bifurcation structure of a three-species food chain model. Theor. Pop. Biol. 48, 93-125.
24. MAY, R. M. (1977). Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269, 471-477.
25. MAY, R. M. (1980). Nonlinear phenomena in ecology and epidemiology. Ann. New York Acad. Sci. 357, 267-281.
26. MAY, R. M. & OSTER, G. F. (1976). Bifurcations and dynamic complexity in simple ecological models. Am. Natur. 110, 573-599.
27. MILNOR, J. (1985). On the concept of attractor. Comm. Math. Phy. 99, 177-195.
28. NEUBERT, M. G. & KOT, M. (1992). The subcritical collapse of predator populations in discrete-time predator-prey models. Math. Biosci. 110, 45-66.
29. NEYMAN, J., PARK, T. & SCOTT, E. L. (1956). Struggle for existence, the Tribolium model: biological and statistical aspects. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Neyman, J. (ed). pp. 41-79. Berkeley: University of California Press.
30. NISBET, R. M. & ONYIAH, L. C. (1994). Population dynamic consequences of competition within and between age classes. J. Math. Biol. 32, 329-344.
31. NOY-MEIR, I. (1975). Stability of grazing systems: an application of predator-prey graphs. J. Ecol. 63, 459-481.
32. OTT, E. (1993). Chaos in Dynamical Systems. Cambridge: Cambridge University Press.
33. OTT, E., ALEXANDER, J. C., KAN, I., SOMMERER, J. C. & YORKE, J. A. (1994). The transistion to chaotic attractors with riddled basins. Physica D 76, 384-410.
34. OTT, E. & SOMMERER, J. C. (1994). Blowout bifurcations: the occurrence of riddled basins and on-off intermittency. Phys. Lett. A 188, 39-47.
35. PARK, T. (1948). Experimental studies of interspecies competition. I. Competition between populations of the flour beetles, Tribolium confusum Duvall and Tribolium castaneum Herbst. Ecol. Monographs 18, 267-307.
36. PARK, T. (1954). Experimental studies of interspecies competition. II. Temperature, humidity, and competition in two species of Tribolium. Physiol. Zool. 27, 177-238.
37. PARK, T. (1957). Experimental studies of interspecies competition. III. Relation of initial species proportion to competitive outcome in populations of Tribolium. Physiol. Zool. 30, 22-40.
38. PARK, T. (1962). Beetles, competition, and populations. Science 138, 1369-1375.
39. PARMENTER, R. H. & Yu. L. Y. (1994). Riddled behavior of certain synchronized systems. Phys. Lett. A 189, 181-186.
40. PASCUAL, M. (1993). Diffusion-induced chaos in a spatial predator-prey system. Proc. Roy. Soc. Lond. B 251, 1-7.
41. SOMMERER, J. C. & OTT, E. (1993). A physical system with qualitatively uncertain dynamics. Nature 365, 138-140.