Stationary distribution and pathwise estimation of n-species mutualism system with stochastic perturbation
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Authors
Weiwei Fang
- School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, P. R. China.
Qixing Han
- School of Mathematics, Changchun Normal University, Changchun 130032, P. R. China.
Xiangdan Wen
- Department of Mathematics, Yanbian University, Yanji 133002, P. R. China.
Qiuyue Li
- Department of Foundation Courses, Aviation University of Airforce, Changchun 130012, P. R. China.
Abstract
In this paper, we develop a new stochastic mutualism population model
\[dx_i(t)=x_i(t)\left[\left(r_i+ \sum^n_{j=1}a_{ij}x_j(t)\right)dt + \sigma_i\sigma x_i(t)dB_i(t)\right], \qquad i=1,2,...,n.\]
By constructing suitable Lyapunov functions, we show the system has a stationary distribution. We also
discuss the pathwise behaviour of the solution. The conclusions of this paper is very powerful since they
are independent both of the system parameters and of the initial value. It is also independent of the noise
intensity as long as the noise intensity \(\sigma_i^2 > 0\). Computer simulations are used to illustrated our results.
Share and Cite
ISRP Style
Weiwei Fang, Qixing Han, Xiangdan Wen, Qiuyue Li, Stationary distribution and pathwise estimation of n-species mutualism system with stochastic perturbation, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 4, 1936--1943
AMA Style
Fang Weiwei, Han Qixing, Wen Xiangdan, Li Qiuyue, Stationary distribution and pathwise estimation of n-species mutualism system with stochastic perturbation. J. Nonlinear Sci. Appl. (2016); 9(4):1936--1943
Chicago/Turabian Style
Fang, Weiwei, Han, Qixing, Wen, Xiangdan, Li, Qiuyue. "Stationary distribution and pathwise estimation of n-species mutualism system with stochastic perturbation." Journal of Nonlinear Sciences and Applications, 9, no. 4 (2016): 1936--1943
Keywords
- Mutualism model
- Itô's formula
- stationary distribution
- ergodicity
- pathwise estimation.
MSC
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