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- Title
Stability of Lotka-Volterra systems.
- Authors
TULJAPURKAR, S. D.; SEMURA, J. S.
- Abstract
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 systems1. 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 cases2. 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 done2,3 on linearised versions of the Lotka-Volterra models.
- Publication
Nature, 1975, Vol 257, Issue 5525, p388
- ISSN
0028-0836
- Publication type
Article
- DOI
10.1038/257388a0