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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 7848793, 15 pages
http://dx.doi.org/10.1155/2016/7848793
Research Article

Dynamics of Stochastic Coral Reefs Model with Multiplicative Nonlinear Noise

Zaitang Huang1,2,3,4

1Yangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning, Guangxi 530023, China
3Key Laboratory of Environment Change and Resources Use in Beibu Gulf, Guangxi Teachers Education University, Nanning, Guangxi 530023, China
4Guangxi Key Laboratory of Earth Surface Processes and Intelligent Simulation, Guangxi Teachers Education University, Nanning, Guangxi 530023, China

Received 26 February 2016; Accepted 16 May 2016

Academic Editor: Elmetwally Elabbasy

Copyright © 2016 Zaitang Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Little seems to be known about the ergodicity of random dynamical systems with multiplicative nonlinear noise. This paper is devoted to discern asymptotic behavior dynamics through the stochastic coral reefs model with multiplicative nonlinear noise. By support theorem and Hörmander theorem, the Markov semigroup corresponding to the solutions is to prove the Foguel alternative. Based on boundary distributions theory, the required conservative operators related to the solutions are further established to ensure the existence a stationary distribution. Meanwhile, the density of the distribution of the solutions either converges to a stationary density or weakly converges to some probability measure.