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Stochastic resonance and noise delayed extinction in a model of two competing species

Author

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  • Valenti, D.
  • Fiasconaro, A.
  • Spagnolo, B.

Abstract

We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka–Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term, which accounts for the environment temperature variation. We find noise-induced periodic oscillations of the species concentrations and stochastic resonance phenomenon. We find also a nonmonotonic behavior of the mean extinction time of one of the two competing species as a function of the additive noise intensity.

Suggested Citation

  • Valenti, D. & Fiasconaro, A. & Spagnolo, B., 2004. "Stochastic resonance and noise delayed extinction in a model of two competing species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(3), pages 477-486.
    • Handle: RePEc:eee:phsmap:v:331:y:2004:i:3:p:477-486
    DOI: 10.1016/j.physa.2003.09.036
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    Citations

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    Cited by:

    1. Wang, Min & Fang, Yuwen & Luo, Yuhui & Yang, Fengzao & Zeng, Chunhua & Duan, Wei-Long, 2019. "Influence of non-Gaussian noise on the coherent feed-forward loop with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 46-55.
    2. Wang, Yi & Cao, Jinde & Sun, Gui-Quan & Li, Jing, 2014. "Effect of time delay on pattern dynamics in a spatial epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 137-148.
    3. 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).
    4. Tian, Rongrong & Wei, Jinlong & Wu, Jiang-Lun, 2021. "On a generalized population dynamics equation with environmental noise," Statistics & Probability Letters, Elsevier, vol. 168(C).
    5. Vladislav Soukhovolsky & Anton Kovalev & Yulia Ivanova & Olga Tarasova, 2023. "Autoregression, First Order Phase Transition, and Stochastic Resonance: A Comparison of Three Models for Forest Insect Outbreaks," Mathematics, MDPI, vol. 11(19), pages 1-19, October.
    6. Chun Zhang & Tao Yang & Shi-Xian Qu, 2021. "Impact of time delays and environmental noise on the extinction of a population dynamics model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-16, November.
    7. Bekoa, D.J. Owono & Kenfack, W. Fokou & Siewe, M. Siewe, 2022. "Dynamics of saline oscillator under sinusoidal and bounded noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    8. Lumi, Neeme & Laas, Katrin & Mankin, Romi, 2015. "Rising relative fluctuation as a warning indicator of discontinuous transitions in symbiotic metapopulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 109-118.
    9. Morozov, Andrew Yu. & Almutairi, Dalal & Petrovskii, Sergei V. & Lai, Ying-Cheng, 2023. "Long transients in discontinuous time-discrete models of population dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    10. Valenti, D. & Tranchina, L. & Brai, M. & Caruso, A. & Cosentino, C. & Spagnolo, B., 2008. "Environmental metal pollution considered as noise: Effects on the spatial distribution of benthic foraminifera in two coastal marine areas of Sicily (Southern Italy)," Ecological Modelling, Elsevier, vol. 213(3), pages 449-462.
    11. Gandhimathi, V.M. & Murali, K. & Rajasekar, S., 2006. "Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1034-1047.
    12. Varughese, M.M. & Fatti, L.P., 2008. "Incorporating environmental stochasticity within a biological population model," Theoretical Population Biology, Elsevier, vol. 74(1), pages 115-129.
    13. Alsulami, Amer & Petrovskii, Sergei, 2023. "A model of mass extinction accounting for the differential evolutionary response of species to a climate change," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    14. Zhu, Ping, 2021. "An equivalent analytical method to deal with cross-correlated exponential type noises in the nonlinear dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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