IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v169y2023ics0960077923001893.html
   My bibliography  Save this article

Impact of correlated Gaussian colored noises on stability and stationary probability density for the randomly forced two-species competitive Gompertz model

Author

Listed:
  • Ma, Yuanlin
  • Yu, Xingwang

Abstract

In this paper, random factors described by correlated Gaussian colored noises are introduced into a two-species competition model with Gompertz growth. Firstly, stochastic stability is studied with the help of singular boundary theory. After that, the stationary probability density of the limiting system is given explicitly and then the extrema of invariant measure are discussed in detail. Finally, the average time of system escaping from the attraction domain is calculated using mean first passage time, and noise enhanced stability is observed. Our results show that random factors are more likely to make the system lose its original stability. Instead, the sample trajectories will stay near the maximum of the stationary probability density for a long time. Importantly, noise intensity and correlation degree are destructive, which can expand the distribution range of population density, weaken the stability of the system, and then easily lead to ecological imbalance. Conversely, the role of correlation time and proper competition between species is constructive and conducive to coexistence.

Suggested Citation

  • Ma, Yuanlin & Yu, Xingwang, 2023. "Impact of correlated Gaussian colored noises on stability and stationary probability density for the randomly forced two-species competitive Gompertz model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
  • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001893
    DOI: 10.1016/j.chaos.2023.113288
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923001893
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2023.113288?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. 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.
    2. Duan, Wei-Long & Lin, Ling, 2021. "Noise and delay enhanced stability in tumor-immune responses to chemotherapy system," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Huang, Dongwei & Wang, Hongli & Feng, Jianfeng & Zhu, Zhi-wen, 2006. "Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1072-1079.
    4. Yuan, Hairui & Meng, Xinzhu, 2022. "Replicator dynamics of the Hawk-Dove game with different stochastic noises in infinite populations," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    5. D. Mei & C. Xie & L. Zhang, 2004. "The stationary properties and the state transition of the tumor cell growth mode," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(1), pages 107-112, September.
    6. G. Augello & D. Valenti & A. L. Pankratov & B. Spagnolo, 2009. "Lifetime of the superconductive state in short and long Josephson junctions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 145-151, July.
    7. Surazhevsky, I.A. & Demin, V.A. & Ilyasov, A.I. & Emelyanov, A.V. & Nikiruy, K.E. & Rylkov, V.V. & Shchanikov, S.A. & Bordanov, I.A. & Gerasimova, S.A. & Guseinov, D.V. & Malekhonova, N.V. & Pavlov, D, 2021. "Noise-assisted persistence and recovery of memory state in a memristive spiking neuromorphic network," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    Full references (including those not matched with items on IDEAS)

    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. Jin, Yanfei & Wang, Haotian & Xu, Pengfei, 2023. "Noise-induced enhancement of stability and resonance in a tri-stable system with time-delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Yuanlin Ma & Xingwang Yu, 2022. "Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises," Mathematics, MDPI, vol. 10(14), pages 1-11, July.
    3. Ping, Zhu, 2023. "Analytical equivalent transformation method for nonlinear stochastic dynamics with multiple noises in high dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    4. Yonkeu, R. Mbakob, 2023. "Stochastic bifurcations induced by Lévy noise in a fractional trirhythmic van der Pol system," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Guo, Yongfeng & Ding, Jiaxin & Mi, Lina, 2024. "Statistical complexity and stochastic resonance of an underdamped bistable periodic potential system excited by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    6. 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.
    7. 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.
    8. Jin, Yanfei & Wang, Heqiang, 2020. "Noise-induced dynamics in a Josephson junction driven by trichotomous noises," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    9. 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.
    10. 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).
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    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:169:y:2023:i:c:s0960077923001893. 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.