On the small-time behavior of stochastic logistic models

  • Dung Tien Nguyen FPT University
Keywords: Stochastic logistic model, small-time behavior, predator-prey systems.


In this paper we investigate the small-time behaviors of the solution to  a stochastic logistic model. The obtained results allow us to estimate the number of individuals in the population and can be used to study stochastic prey-predator systems.


L.H. R. Alvarez, L.A. Shepp, Optimal harvesting of stochastically fluctuating populations. J. Math. Biol. 37 (1998), no. 2, 155--177.

N.T. Dung, On delayed logistic equation driven by fractional Brownian motion. J. Comput. Nonlinear Dynam} 7(3), 031005 (Mar 19, 2012) (5 pages).

N.T. Dung, The existence of a positive solution for a generalized delay logistic equation with multifractional noise. Statist. Probab. Lett. 83 (2013), no. 4, 1240--1246.

G. Hu, K. Wang, On stochastic logistic equation with Markovian switching and white noise. Osaka J. Math. 48 (2011), no. 4, 959--986.

D. Jiang, N. Shi, Ningzhong. A note on nonautonomous logistic equation with random perturbation. J. Math. Anal. Appl. 303 (2005), no. 1, 164--172.

N. Kazamaki, Continuous exponential martingales and BMO. Lecture Notes in Mathematics, 1579. Springer-Verlag, Berlin, 1994.

P.E. Kloeden, E. Platen, Numerical solution of stochastic differential equations. Applications of Mathematics (New York), 23. Springer-Verlag, Berlin, 1992.

S. Li, X. Zhang, Dynamics of a stochastic non-autonomous predator-prey system with Beddington-DeAngelis functional response. Adv. Difference Equ. 2013, 2013:19, 20 pp.

M. Liu, K. Wang, On a stochastic logistic equation with impulsive perturbations. Comput. Math. Appl. 63 (2012), no. 5, 871--886.

M. Liu, M. Deng, B. Du, Analysis of a stochastic logistic model with diffusion. Appl. Math. Comput. 266 (2015), 169--182.

R.M. May, Stability in randomly fluctuating versus deterministic environments, The American Naturalist, Vol. 107, No. 957, 1973, pp. 621-650.

I. Nourdin, G. Peccati, G. Reinert, Stein's method and stochastic analysis of Rademacher functionals. Electron. J. Probab. 15 (2010), no. 55, 1703--1742.

X. Sun, Y.Wang, Stability analysis of a stochastic logistic model with nonlinear diffusion term. Appl. Math. Model. 32 (2008), no. 10, 2067--2075.

How to Cite
Nguyen, D. T. (2017). On the small-time behavior of stochastic logistic models. Statistics, Optimization & Information Computing, 5(3), 234-243. https://doi.org/10.19139/soic.v5i3.291
Research Articles