Existence and stability of stationary solutions to spatially extended autocatalytic and hypercyclic systems under global regulation and with nonlinear growth rates

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dc.creatorBratus', Alexander S.
dc.creatorPosvyanskii, Vladimir P.
dc.creatorNovozhilov, Artem S.
dc.date2009-01-22
dc.date.accessioned2026-07-07T12:33:38Z
dc.date.available2026-07-07T12:33:38Z
dc.descriptionAnalytical analysis of spatially extended autocatalytic and hypercyclic systems is presented. It is shown that spatially explicit systems in the form of reaction-diffusion equations with global regulation possess the same major qualitative features as the corresponding local models. In particular, using the introduced notion of the stability in the mean integral sense we prove the competitive exclusion principle for the autocatalytic system and the permanence for the hypercycle system. Existence and stability of stationary solutions are studied. For some parameter values it is proved that stable spatially non-uniform solutions appear.
dc.description31 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/0901.3556
dc.identifierhttp://arxiv.org/abs/0901.3556
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217198
dc.subjectPopulations and Evolution
dc.titleExistence and stability of stationary solutions to spatially extended autocatalytic and hypercyclic systems under global regulation and with nonlinear growth rates
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