Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation |
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Authors: | Daqing Jiang Ningzhong Shi Xiaoyue Li |
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Institution: | School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin, PR China |
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Abstract: | This paper discusses a randomized non-autonomous logistic equation , where B(t) is a 1-dimensional standard Brownian motion. In D.Q. Jiang, N.Z. Shi, A note on non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl. 303 (2005) 164-172], the authors show that E1/N(t)] has a unique positive T-periodic solution E1/Np(t)] provided a(t), b(t) and α(t) are continuous T-periodic functions, a(t)>0, b(t)>0 and . We show that this equation is stochastically permanent and the solution Np(t) is globally attractive provided a(t), b(t) and α(t) are continuous T-periodic functions, a(t)>0, b(t)>0 and mint∈0,T]a(t)>maxt∈0,T]α2(t). By the way, the similar results of a generalized non-autonomous logistic equation with random perturbation are yielded. |
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Keywords: | Global stability Stochastic permanence Randomized logistic equation Periodic solution Itô 's formula |
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