Dissertation/Thesis Abstract

Stability of a stochastic predator prey model
by Nibert, Joel H., Ph.D., University of Southern California, 2012, 63; 3542298
Abstract (Summary)

We consider a stochastic analog of the Lotka-Volterra model for the population dynamics of two interacting species, predator and prey. We investigate the long time behavior of the system, and show that, under certain conditions on the model parameters, asymptotic stability obtains. We provide a novel proof of the existing result of Rudnicki, emphasizing the use of the critical conditions. We split the first quadrant into regions, and through separate analyses, demonstrate that the predator prey process recurs to a compact set. Then a construction of Khasminskii and others provides for the existence of an invariant measure.

Indexing (document details)
Advisor: Baxendale, Peter H.
Commitee: Lototsky, Sergey, Udwadia, Firdaus
School: University of Southern California
Department: Mathematics
School Location: United States -- California
Source: DAI-B 74/03(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: Asymptotic stability, Invariant measure, Lyapunov exponent, Lyapunov function, Predator prey, Stochastic differential equations
Publication Number: 3542298
ISBN: 978-1-267-69938-1
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