Stability of Lotka–Volterra systems

NONLINEAR systems are very often studied in terms of simple mathematical models. The Lotka–Volterra equations provide such a model and have been used to study physical, chemical, ecological and social systems 1 . An important question in the analysis of these equations is the stability of the equili...

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Bibliographic Details
Published in:Nature (London) 1975-01, Vol.257 (5525), p.388-389
Main Authors: TULJAPURKAR, S. D., SEMURA, J. S.
Format: Article
Language:English
Subjects:
Humanities and Social Sciences
letter
multidisciplinary
Science
Science (multidisciplinary)
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Summary:NONLINEAR systems are very often studied in terms of simple mathematical models. The Lotka–Volterra equations provide such a model and have been used to study physical, chemical, ecological and social systems 1 . An important question in the analysis of these equations is the stability of the equilibrium values of the interacting variables. Most work with Lotka–Volterra models has considered only neighbourhood stability against small perturbations away from equilibrium. The question of global stability when large perturbations from equilibrium are involved has only been analysed in a few special cases 2 . We establish here that for the general Lotka–Volterra models local stability ensures global stability (asymptotic stability in the large). This result provides justification for the work that has been and is being done 2,3 on linearised versions of the Lotka–Volterra models.
ISSN:0028-0836
1476-4687
DOI:10.1038/257388a0