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Dynamics of Stochastic Coral Reefs Model with Multiplicative Nonlinear Noise

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  • Zaitang Huang

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.

Suggested Citation

  • Zaitang Huang, 2016. "Dynamics of Stochastic Coral Reefs Model with Multiplicative Nonlinear Noise," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:7848793
    DOI: 10.1155/2016/7848793
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    References listed on IDEAS

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    1. Wang, Hao & Morrison, Wendy & Singh, Abhinav & Weiss, Howard (Howie), 2009. "Modeling inverted biomass pyramids and refuges in ecosystems," Ecological Modelling, Elsevier, vol. 220(11), pages 1376-1382.
    2. Peter J. Mumby & Alan Hastings & Helen J. Edwards, 2007. "Thresholds and the resilience of Caribbean coral reefs," Nature, Nature, vol. 450(7166), pages 98-101, November.
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