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Impact of time delays and environmental noise on the extinction of a population dynamics model

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  • Chun Zhang

    (Shaanxi Normal University)

  • Tao Yang

    (Northwestern Polytechnical University)

  • Shi-Xian Qu

    (Shaanxi Normal University)

Abstract

In this paper, we examine a population model with carrying capacity, time delay, and sources of additive and multiplicative environmental noise. We find that time delay, noise sources and their correlation induce regime shifts and transitions between the population survival state and the extinction state. To explore the transition mechanism between these two states, we analyzed the shift time to extinction, or the delayed extinction time, of populations. The main finding is that the extinction transition time as a function of the noise intensity shows a maximum, indicating the existence of an appropriate noise intensity leading to a maximal delayed extinction. This nonmonotonic behavior, with a maximum, is a signature of the noise-enhanced stability phenomenon, observed in many physical and complex metastable systems. In particular, this maximum increases (or decreases) as the cross-correlation intensity or the delay time in the death process increases. Furthermore, the signal-to-noise ratio as a function of noise intensity shows a maximum, which is a signature of the stochastic resonance phenomenon in the population dynamics model investigated in the presence of time delay and environmental noise. Graphic abstract

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:94:y:2021:i:11:d:10.1140_epjb_s10051-021-00219-3
    DOI: 10.1140/epjb/s10051-021-00219-3
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    References listed on IDEAS

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    1. Davide Valenti & Giorgio Fazio & Bernardo Spagnolo, 2017. "The stabilizing effect of volatility in financial markets," Papers 1708.08695, arXiv.org.
    2. B. Spagnolo & A. Dubkov & N. Agudov, 2004. "Enhancement of stability in randomly switching potential with metastable state," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 40(3), pages 273-281, August.
    3. Deng, Fangyu & Luo, Yuhui & Fang, Yuwen & Yang, Fengzao & Zeng, Chunhua, 2021. "Temperature and friction-induced tunable current reversal, anomalous mobility and diffusions," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    4. Fiasconaro, A & Valenti, D & Spagnolo, B, 2003. "Role of the initial conditions on the enhancement of the escape time in static and fluctuating potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 136-143.
    5. Zhang, Chun & Du, Liping & Wang, Tonghuan & Yang, Tao & Zeng, Chunhua & Wang, Canjun, 2017. "Impact of time delay in a stochastic gene regulation network," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 120-129.
    6. 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.
    7. Ghirlanda, Stefano & Enquist, Magnus & Perc, Matjaž, 2010. "Sustainability of culture-driven population dynamics," Theoretical Population Biology, Elsevier, vol. 77(3), pages 181-188.
    8. Spagnolo, B. & La Barbera, A., 2002. "Role of the noise on the transient dynamics of an ecosystem of interacting species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 114-124.
    9. A. Fiasconaro & A. Ochab-Marcinek & B. Spagnolo & E. Gudowska-Nowak, 2008. "Monitoring noise-resonant effects in cancer growth influenced by external fluctuations and periodic treatment," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 435-442, October.
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