IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v85y2016icp98-109.html
   My bibliography  Save this article

Stability in distribution of a stochastic hybrid competitive Lotka–Volterra model with Lévy jumps

Author

Listed:
  • Zhao, Yu
  • Yuan, Sanling

Abstract

Stability in distribution, implying the existence of the invariant probability measure, is an important measure of stochastic hybrid system. However, the effect of Lévy jumps on the stability in distribution is still unclear. In this paper, we consider a n-species competitive Lotka–Volterra model with Lévy jumps under regime-switching. First, we prove the existence of the global positive solution, obtain the upper and lower boundedness. Then, asymptotic stability in distribution as the main result of our paper is derived under some sufficient conditions. Finally, numerical simulations are carried out to support our theoretical results and a brief discussion is given.

Suggested Citation

  • Zhao, Yu & Yuan, Sanling, 2016. "Stability in distribution of a stochastic hybrid competitive Lotka–Volterra model with Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 98-109.
    • Handle: RePEc:eee:chsofr:v:85:y:2016:i:c:p:98-109
    DOI: 10.1016/j.chaos.2016.01.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077916300066
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2016.01.015?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. G. Augello & D. Valenti & B. Spagnolo, 2010. "Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 78(2), pages 225-234, November.
    2. Marten Scheffer & Steve Carpenter & Jonathan A. Foley & Carl Folke & Brian Walker, 2001. "Catastrophic shifts in ecosystems," Nature, Nature, vol. 413(6856), pages 591-596, October.
    3. Yuan, Chenggui & Mao, Xuerong, 2003. "Asymptotic stability in distribution of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 277-291, February.
    4. Brett A. Melbourne & Alan Hastings, 2008. "Extinction risk depends strongly on factors contributing to stochasticity," Nature, Nature, vol. 454(7200), pages 100-103, July.
    5. A. La Cognata & D. Valenti & B. Spagnolo & A. A. Dubkov, 2010. "Two competing species in super-diffusive dynamical regimes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 77(2), pages 273-279, September.
    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. Mi, Li-Na & Guo, Yong-Feng & Zhang, Meng & Zhuo, Xiao-Jing, 2023. "Stochastic resonance in gene transcriptional regulatory system driven by Gaussian noise and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Shao, Yuanfu, 2022. "Global stability of a delayed predator–prey system with fear and Holling-type II functional response in deterministic and stochastic environments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 65-77.
    3. Kuang, Daipeng & Li, Jianli & Gao, Dongdong & Luo, Danfeng, 2024. "Stochastic near-optimal control for a system with Markovian switching and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Li, Lijie & Feng, Yu & Liu, Yongjian, 2016. "Dynamics of the stochastic Lorenz-Haken system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 670-678.

    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. Ian Hodge & William M. Adams, 2016. "Short-Term Projects versus Adaptive Governance: Conflicting Demands in the Management of Ecological Restoration," Land, MDPI, vol. 5(4), pages 1-17, November.
    2. Jenerette, G. Darrel & Lal, Rattan, 2007. "Modeled carbon sequestration variation in a linked erosion–deposition system," Ecological Modelling, Elsevier, vol. 200(1), pages 207-216.
    3. Tong, Jinying & Zhang, Zhenzhong & Bao, Jianhai, 2013. "The stationary distribution of the facultative population model with a degenerate noise," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 655-664.
    4. Jin, Yanfei & Wang, Heqiang, 2020. "Noise-induced dynamics in a Josephson junction driven by trichotomous noises," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    5. Teh, Su Yean & DeAngelis, Donald L. & Sternberg, Leonel da Silveira Lobo & Miralles-Wilhelm, Fernando R. & Smith, Thomas J. & Koh, Hock-Lye, 2008. "A simulation model for projecting changes in salinity concentrations and species dominance in the coastal margin habitats of the Everglades," Ecological Modelling, Elsevier, vol. 213(2), pages 245-256.
    6. Grolleau, Gilles & Ibanez, Lisette & Mzoughi, Naoufel, 2020. "Moral judgment of environmental harm caused by a single versus multiple wrongdoers: A survey experiment," Ecological Economics, Elsevier, vol. 170(C).
    7. Kong, Xiang-Zhen & Jørgensen, Sven Erik & He, Wei & Qin, Ning & Xu, Fu-Liu, 2013. "Predicting the restoration effects by a structural dynamic approach in Lake Chaohu, China," Ecological Modelling, Elsevier, vol. 266(C), pages 73-85.
    8. Paul L. G. Vlek & Asia Khamzina & Hossein Azadi & Anik Bhaduri & Luna Bharati & Ademola Braimoh & Christopher Martius & Terry Sunderland & Fatemeh Taheri, 2017. "Trade-Offs in Multi-Purpose Land Use under Land Degradation," Sustainability, MDPI, vol. 9(12), pages 1-19, November.
    9. Sonia Kéfi & Vishwesha Guttal & William A Brock & Stephen R Carpenter & Aaron M Ellison & Valerie N Livina & David A Seekell & Marten Scheffer & Egbert H van Nes & Vasilis Dakos, 2014. "Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-13, March.
    10. Duncan A. O’Brien & Smita Deb & Gideon Gal & Stephen J. Thackeray & Partha S. Dutta & Shin-ichiro S. Matsuzaki & Linda May & Christopher F. Clements, 2023. "Early warning signals have limited applicability to empirical lake data," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    11. Can Askan Mavi & Nicolas Quérou, 2020. "Common pool resource management and risk perceptions," DEM Discussion Paper Series 20-25, Department of Economics at the University of Luxembourg.
    12. Therese Lindahl & Anne-Sophie Crépin & Caroline Schill, 2016. "Potential Disasters can Turn the Tragedy into Success," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(3), pages 657-676, November.
    13. Mariani, Fabio & Pérez-Barahona, Agustín & Raffin, Natacha, 2010. "Life expectancy and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 798-815, April.
    14. Siewe, M. Siewe & Kenfack, W. Fokou & Kofane, T.C., 2019. "Probabilistic response of an electromagnetic transducer with nonlinear magnetic coupling under bounded noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 26-35.
    15. Eppink, Florian V. & van den Bergh, Jeroen C.J.M., 2007. "Ecological theories and indicators in economic models of biodiversity loss and conservation: A critical review," Ecological Economics, Elsevier, vol. 61(2-3), pages 284-293, March.
    16. Janssen, Marco A. & Anderies, John M. & Walker, Brian H., 2004. "Robust strategies for managing rangelands with multiple stable attractors," Journal of Environmental Economics and Management, Elsevier, vol. 47(1), pages 140-162, January.
    17. Admiraal, Jeroen F. & Wossink, Ada & de Groot, Wouter T. & de Snoo, Geert R., 2013. "More than total economic value: How to combine economic valuation of biodiversity with ecological resilience," Ecological Economics, Elsevier, vol. 89(C), pages 115-122.
    18. H. Klammler & P. S. C. Rao & K. Hatfield, 2018. "Modeling dynamic resilience in coupled technological-social systems subjected to stochastic disturbance regimes," Environment Systems and Decisions, Springer, vol. 38(1), pages 140-159, March.
    19. Mao, Xuerong & Shen, Yi & Yuan, Chenggui, 2008. "Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1385-1406, August.
    20. Tomczak, M.T. & Niiranen, S. & Hjerne, O. & Blenckner, T., 2012. "Ecosystem flow dynamics in the Baltic Proper—Using a multi-trophic dataset as a basis for food–web modelling," Ecological Modelling, Elsevier, vol. 230(C), pages 123-147.

    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:chsofr:v:85:y:2016:i:c:p:98-109. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.