Stationary distribution and pathwise estimation of n-species mutualism system with stochastic perturbation


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.


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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


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