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.
Keywords
Nonlinear systemLimit cycleBounded functionClass (philosophy)MathematicsPopulationLimit (mathematics)Applied mathematicsVolterra equationsCompetition (biology)AmplitudeDynamical systems theoryMathematical and theoretical biologyPopulation modelMathematical analysisStatistical physicsComputer sciencePhysicsEcologyBiology
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Publication Info
- Year
- 1975
- Type
- article
- Volume
- 29
- Issue
- 2
- Pages
- 243-253
- Citations
- 1097
- Access
- Closed
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Cite This
Robert M. May,
Warren J. Leonard
(1975).
Nonlinear Aspects of Competition Between Three Species.
SIAM Journal on Applied Mathematics
, 29
(2)
, 243-253.
https://doi.org/10.1137/0129022
Identifiers
- DOI
- 10.1137/0129022