Lotka-Volterra Stochastic Population System

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Keshavarz, Fatemeh | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41912 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zohouri Zangeneh, Bijan
Abstract:
We study stochastically perturb the classical Lotka-Volterra model x ̇(t)=diag(x_1 (t),…,x_n (t))[b+Ax(t)] Into the stochastic differential equation dx(t)=diag(x_1 (t),…,x_n (t))[b+Ax(t)dt+σ(t)dw(t)]. The main aim is to study the asymptotic properties of the solution. We will show that if the noise is too large then the population may become extinct with probability one. We find out a sufficient condition for stochastic differential equation such that it has a unique global positive solution. Moreover, we will establish some new asymptotic properties for the moments as well as for the sample paths of the solution. In particular, we discuss ultimate boundedness and extinction in population systems
Keywords:
Extinction ; Ito Formula ; Stochastic Lotka-Volterra Model ; Ultimate Boundness

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