1975/09/01 by Robert M. May, Warren J. Leonard · 6 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Amplitude #Applied mathematics #Biology #Bounded function #Class (philosophy) #Competition (biology) #Computer science #Dynamical systems theory #Ecology #Evolution and Genetic Dynamics #Limit (mathematics) #Limit cycle #Mathematical Biology Tumor Growth #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematical and theoretical biology #Mathematics #Nonlinear system #Physics #Population #Population model #Statistical physics #Volterra equations
paper · doi:10.1137/0129022
crossref issued 1975/09/01 · crossref published 1975/09/01 · crossref published-print 1975/09/01 · openalex publication_date 1975/09/01 · crossref created 2005/02/23 · crossref deposited 2023/05/02 · openalex created_date 2025/10/10 · crossref indexed 2026/08/01 · openalex updated_date 2026/08/01
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.