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.
|Advisor:||Baxendale, Peter H.|
|Commitee:||Lototsky, Sergey, Udwadia, Firdaus|
|School:||University of Southern California|
|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|
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