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Nonlinear Aspects of Competition Between Three Species
Abstract
It is shown that for three competitors, the classic Gause–Lotka–Volterra equations possess a special class of periodic limit cycle solutions, and a general class of solutions in which the system exhibits nonperiodic population oscillations of bounded amplitude but ever increasing cycle time. Biologically, the result is interesting as a caricature of the complexities that nonlinearities can introduce even into the simplest equations of population biology ; mathematically, the model illustrates some novel tactical tricks and dynamical peculiarities for 3-dimensional nonlinear systems.
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Cited by
Pattern formation outside of equilibrium
Cross, M. C., & Hohenberg, P. C. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.851 · Cited by 7,859
Simple mathematical models with very complicated dynamics
May, R. M. (1976) · Nature · doi:10.1038/261459a0 · Cited by 7,001
Self-citationA structural approach for understanding multispecies coexistence
Saavedra, S., Rohr, R. P., Bascompte, J., Godoy, O., Kraft, N. J. B., & Levine, J. M. (2017) · Ecological Monographs · doi:10.1002/ecm.1263 · Cited by 282
Strategy selection in structured populations
Tarnita, C. E., Ohtsuki, H., Antal, T., Fu, F., & Nowak, M. A. (2009) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2009.03.035 · Cited by 281
Multiple strategies in structured populations
Tarnita, C. E., Wage, N., & Nowak, M. A. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1016008108 · Cited by 106
Metadata
- Authors
- May, R. M., & Leonard, W. J.
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 1975-09
- Volume
- 29
- Issue
- 2
- Pages
- 243-253
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W2043691077
- Cited by
- 1,114
- References
- 0
- FWCI
- 13.12
- Type
- journal article
- Language
- en
- Open access
- closed
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- May, R. M., & Leonard, W. J. (1975). Nonlinear Aspects of Competition Between Three Species. SIAM Journal on Applied Mathematics. https://doi.org/10.1137/0129022
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