On the small-time behavior of stochastic logistic models

  • Dung Tien Nguyen FPT University
DOI: https://doi.org/10.19139/soic.v5i3.291
Keywords: Stochastic logistic model, small-time behavior, predator-prey systems.

Abstract

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.

References

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.

Published
2017-08-29
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
Issue
Vol 5 No 3 (2017)
Section
Research Articles
Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).