Nonlinear Aspects of Competition Between Three Species
SIAM Journal on Applied Mathematics1975Vol. 29(2), pp. 243–253
Citations Over TimeTop 10% of 1975 papers
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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