The Multicomponent Gause Principle in Models of Biological Communities
- Authors: Razzhevaikin V.N.1
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Affiliations:
- Dorodnitsyn Computing Center, Russian Academy of Sciences
- Issue: Vol 8, No 5 (2018)
- Pages: 421-430
- Section: Article
- URL: https://journals.rcsi.science/2079-0864/article/view/206641
- DOI: https://doi.org/10.1134/S2079086418050067
- ID: 206641
Cite item
Abstract
A refinement is proposed for Gause’s principle of competitive exclusion, which guarantees the disappearance of at least one species in a community with a species number that exceeds the number of resources. Theorems revealing the disappearance of at least n – m components have been developed for a general finite-dimensional system of differential equations that simulates the dynamics of a community with n species in a rough case, i.e., in the absence of a finite number of coincidences defined by relations of the equality type, provided that the Malthusian vector-valued function only assumes values on the hyperplane of the dimension m, which does not contain the origin. It is proposed that the constructed theory can be used for a Lotka–Volterra type system with a Malthusian vector-function, which is a linear combination of the quantities of the available resources.
About the authors
V. N. Razzhevaikin
Dorodnitsyn Computing Center, Russian Academy of Sciences
Author for correspondence.
Email: razzh@mail.ru
Russian Federation, Moscow, 119333