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Positive recurrent of stochastic coral reefs model

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  • Huang, Zaitang

Abstract

In this work, we discuss permanence and ergodicity of a stochastic coral reefs model. One of the distinctive features of our results is that our results enables characterization of the support of a unique invariant probability measure by Lie groups and geometric control theory. It is proved that the densities either converges to an invariant density or converges weakly to a singular measure.

Suggested Citation

  • Huang, Zaitang, 2017. "Positive recurrent of stochastic coral reefs model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 751-761.
    • Handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:751-761
    DOI: 10.1016/j.physa.2017.05.073
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    References listed on IDEAS

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    1. Rudnicki, Ryszard, 2003. "Long-time behaviour of a stochastic prey-predator model," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 93-107, November.
    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.
    3. Jiang, Daqing & Liu, Qun & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed & Xia, Peiyan, 2017. "Dynamics of a stochastic HIV-1 infection model with logistic growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 706-717.
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    Cited by:

    1. Huang, Zaitang & Cao, Junfei & Long, Guangqin, 2018. "Long-time behavior of stochastic multimolecular reaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 331-344.

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