Basins of Attraction: Population Dynamics with Two Stable 4-cycles

Authors

Shandelle M. Henson, Andrews UniversityFollow
R. F. Costantino, University of Rhode Island
Robert A. Desharnais, California State University, Los Angeles
J. M. Cushing, The University of Arizona
Brian Dennis, University of Idaho

Document Type

Article

Publication Date

8-24-2002

Abstract

We use the concepts of composite maps, basins of attraction, basin switching, and saddle fly-by's to make the ecological hypothesis of the existence of multiple attractors more accessible to experimental scrutiny. Specifically, in a periodically forced insect population growth model we identify multiple attractors, namely, two locally stable 4-cycles. Using the model-predicted basins of attraction, we examine data time series from a Tribolium experiment for evidence of the multiple attractors. We conclude that the multiple attractor hypothesis together with demographic stochasticity accounts for the experimental observations.

Journal Title

Oikos

Volume

98

Issue

1

First Page

17

Last Page

24

DOI

https://doi.org/10.1034/j.1600-0706.2002.980102.x

First Department

Mathematics

Recommended Citation

Henson, Shandelle M.; Costantino, R. F.; Desharnais, Robert A.; Cushing, J. M.; and Dennis, Brian, "Basins of Attraction: Population Dynamics with Two Stable 4-cycles" (2002). Faculty Publications. 2172.
https://digitalcommons.andrews.edu/pubs/2172