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In this paper, a stochastic delay Lotka-Volterra model with Hurst exponent H being in (0, 1/2) is established. Sufficient conditions of asymptotic stability are obtained for stochastic delay Lotka-Volterra model with fractional Brownian motion. The analyses are conducted by using Itô formula, elementary inequality, Borel-Cantelli lemma, derived for stability purposes.
This paper considers the stabilization and destabilization by a Brownian noise perturbation that preserves the equilibrium of the ordinary differential equation x'(t) = f(x(t)). In an extension of earlier work, we lift the restriction that f obeys a global linear bound, and show that when f is locally Lipschitz, a function g can always be found so that the noise perturbation g(X(t)) dB(t) either stabilizes...
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