IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v486y2017icp751-761.html
   My bibliography  Save this article

Positive recurrent of stochastic coral reefs model

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117305927
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2017.05.073?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simon Levin & Anastasios Xepapadeas, 2021. "On the Coevolution of Economic and Ecological Systems," Annual Review of Resource Economics, Annual Reviews, vol. 13(1), pages 355-377, October.
    2. Jorge H. Maldonado & Rocío del Pilar Moreno-Sánchez & Tatiana G. Zárate & Camila Andrea Barrera, 2013. "Valoración económica del subsistema de Áreas Marinas Protegidas en Colombia: un análisis para formuladores de política desde un enfoque multi-servicios y multi-agentes," Documentos CEDE 11933, Universidad de los Andes, Facultad de Economía, CEDE.
    3. González-Rivero, Manuel & Yakob, Laith & Mumby, Peter J., 2011. "The role of sponge competition on coral reef alternative steady states," Ecological Modelling, Elsevier, vol. 222(11), pages 1847-1853.
    4. Zhao, Xin & Liu, Lidan & Liu, Meng & Fan, Meng, 2024. "Stochastic dynamics of coral reef system with stage-structure for crown-of-thorns starfish," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    5. Reguero, Borja G. & Beck, Michael W. & Schmid, David & Stadtmüller, Daniel & Raepple, Justus & Schüssele, Stefan & Pfliegner, Kerstin, 2020. "Financing coastal resilience by combining nature-based risk reduction with insurance," Ecological Economics, Elsevier, vol. 169(C).
    6. Clancy, Damian & Tanner, Jason E. & McWilliam, Stephen & Spencer, Matthew, 2010. "Quantifying parameter uncertainty in a coral reef model using Metropolis-Coupled Markov Chain Monte Carlo," Ecological Modelling, Elsevier, vol. 221(10), pages 1337-1347.
    7. Lan, Guijie & Chen, Zhewen & Wei, Chunjin & Zhang, Shuwen, 2018. "Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 61-77.
    8. Fu, Xiaoming, 2019. "On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1008-1023.
    9. Guo, Xiaoxia & Zhu, Chunjuan & Ruan, Dehao, 2019. "Dynamic behaviors of a predator–prey model perturbed by a complex type of noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1024-1037.
    10. Renken, Henk & Mumby, Peter J., 2009. "Modelling the dynamics of coral reef macroalgae using a Bayesian belief network approach," Ecological Modelling, Elsevier, vol. 220(9), pages 1305-1314.
    11. Andrew R. Tilman & Elisabeth H. Krueger & Lisa C. McManus & James R. Watson, 2023. "Maintaining human wellbeing as socio-environmental systems undergo regime shifts," Papers 2309.04578, arXiv.org.
    12. Qesmi, Redouane & Hammoumi, Aayah, 2020. "A stochastic delay model of HIV pathogenesis with reactivation of latent reservoirs," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    13. Larsen, Trine C. & Browne, Nicola K. & Erichsen, Anders C. & Tun, Karenne & Todd, Peter A., 2017. "Modelling for management: Coral photo-physiology and growth potential under varying turbidity regimes," Ecological Modelling, Elsevier, vol. 362(C), pages 1-12.
    14. Ji, Chunyan & Jiang, Daqing & Lei, Dongxia, 2019. "Dynamical behavior of a one predator and two independent preys system with stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 649-664.
    15. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    16. Miñarro, Sara & Leins, Johannes & Acevedo-Trejos, Esteban & Fulton, Elizabeth A. & Reuter, Hauke, 2018. "SEAMANCORE: A spatially explicit simulation model for assisting the local MANagement of COral REefs," Ecological Modelling, Elsevier, vol. 384(C), pages 296-307.
    17. Settati, A. & Lahrouz, A. & Zahri, M. & Tridane, A. & El Fatini, M. & El Mahjour, H. & Seaid, M., 2021. "A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    18. Zhang, Tongqian & Xu, Xinna & Wang, Xinzeng, 2023. "Dynamic analysis of a cytokine-enhanced viral infection model with time delays and CTL immune response," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    19. Auad, Guillermo & Blythe, Jonathan & Coffman, Kim & Fath, Brian D., 2018. "A dynamic management framework for socio-ecological system stewardship: A case study for the United States Bureau of Ocean Energy Management," MarXiv nurca, Center for Open Science.
    20. Zhan, Jinxiang & Wei, Yongchang, 2024. "Dynamical behavior of a stochastic non-autonomous distributed delay heroin epidemic model with regime-switching," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:751-761. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.