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In this paper, two types of stochastic mathematical model of ecology , divided into the following three parts. The first chapter , we briefly introduce stochastic differential equations booming overview of the discipline , roughly recalled its research status and achievements , while giving the relevant definitions, theorems , the paper used by the major inequalities and the main results . The second chapter of a class of predator- prey system with random asymptotic properties . Consider the following by environmental noise , wherein the variable coefficient stochastic differential equation a (t), b (t), c (t), d (t), f (t), m (t) are defined in [0, ∞ ) on a bounded positive continuous function . Through moment estimation , and some inequality technique , obtained equation ( 1 ) the existence and uniqueness of positive solutions , stochastic ultimate boundedness and random persistence, generalize previous results . Chapter III study stochastic delay Lotka-Volterra model dx (t) = diag (xl (t), ..., xn (t)) [a Bx (t) Cx (t-τ) dt σx (t) dw (t ) ] ( 2 ) where σ = (σij) nxn. We mainly use the Ito formula and inequality techniques moment estimation obtained equations ( 2 ) and uniqueness of solutions of stochastic ultimate boundedness .
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