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Zbl 1136.34324
Jiang, Da-Qing; Zhang, Bao-Xue; Wang, De-Hui; Shi, Ning-Zhong
Existence, uniqueness, and global attractivity of positive solutions and MLE of the parameters to the logistic equation with random perturbation. (English)
[J] Sci. China, Ser. A 50, No. 7, 977-986 (2007). ISSN 1006-9283; ISSN 1862-2763/e

Noting that population systems are often subject to environmental noise, the authors consider the random logistic equation $$\dot{N}(t)=(r+\alpha\dot{B}(t))N(t)[1-(N(t)/K)],$$ where $N(0)$ is a random variable satisfying $0<N(0)<K$ and $B(t)$ is a 1-dimensional standard Brownian motion. The existence, uniqueness and global attractivity of positive solutions are investigated, and maximum likelihood estimators of the parameters are found.
[Andrew Dale (Durban)]

MSC 2000:: *34F05 ODE with randomness
60H10 Stochastic ordinary differential equations
34A55 Inverse problems of ODE

Keywords: random logistic equations; existence; uniqueness; global attractivity

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