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Crossing the Hopf Bifurcation in a Live Predator-Prey System
Abstract
Population biologists have long been interested in the oscillations in population size displayed by many organisms in the field and laboratory. A wide range of deterministic mathematical models predict that these fluctuations can be generated internally by nonlinear interactions among species and, if correct, would provide important insights for understanding and predicting the dynamics of interacting populations. We studied the dynamical behavior of a two-species aquatic laboratory community encompassing the interactions between a demographically structured herbivore population, a primary producer, and a mineral resource, yet still amenable to description and parameterization using a mathematical model. The qualitative dynamical behavior of our experimental system, that is, cycles, equilibria, and extinction, is highly predictable by a simple nonlinear model.
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Cited by
Parameter estimation for differential equations: a generalized smoothing approach
Ramsay, J. O., Hooker, G., Campbell, D., & Cao, J. (2007) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2007.00610.x · Cited by 613
Moon, J.-Y., Lee, U., Blain-Moraes, S., & Mashour, G. A. (2015) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1004225 · Cited by 136
Predator decline leads to decreased stability in a coastal fish community
Britten, G. L., Dowd, M., Minto, C., Ferretti, F., Boero, F., & Lotze, H. K. (2014) · Ecology Letters · doi:10.1111/ele.12354 · Cited by 122
Metadata
- Authors
- Fussmann, G. F., Ellner, S. P., Shertzer, K. W., & Hairston Jr., N. G.
- Venue
- Science
- Published
- 2000-11-17
- Volume
- 290
- Issue
- 5495
- Pages
- 1358-1360
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2000915153
- Cited by
- 439
- References
- 0
- FWCI
- 7.51
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Crossing the Hopf Bifurcation in a Live Predator-Prey System. https://app.cochat.ai/papers/10.1126/science.290.5495.1358
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- Fussmann, G. F., Ellner, S. P., Shertzer, K. W., & Hairston Jr., N. G. (2000). Crossing the Hopf Bifurcation in a Live Predator-Prey System. Science. https://doi.org/10.1126/science.290.5495.1358
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