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Impact of noise on bistable ecological systems

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  • Guttal, Vishwesha
  • Jayaprakash, C.

Abstract

The existence and implications of alternative stable states in ecological systems have been studied extensively within deterministic models. In this paper, we study the influence of random fluctuations in environmental parameters (e.g. nutrient input and rainfall) on the behavior of two simple bistable, ecological models with a single dynamical variable. We describe the changes in the bifurcation diagram of the bistable system: we find that the region of bistability is reduced for small amounts of noise while for noise beyond a critical width bistability vanishes completely. In the regime where bistability is eliminated by the noise, the time series of the solution shows that the system can undergo frequent catastrophic regime shifts. We also discuss how some of the results depend on model-specific details. We comment on the robustness of our results to changes in the noise characteristics and the implications for modeling real systems.

Suggested Citation

  • Guttal, Vishwesha & Jayaprakash, C., 2007. "Impact of noise on bistable ecological systems," Ecological Modelling, Elsevier, vol. 201(3), pages 420-428.
    • Handle: RePEc:eee:ecomod:v:201:y:2007:i:3:p:420-428
    DOI: 10.1016/j.ecolmodel.2006.10.005
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    References listed on IDEAS

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    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.
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    7. Zhang, Hongxia & Xu, Wei & Guo, Qin & Han, Ping & Qiao, Yan, 2020. "First escape probability and mean first exit time for a time-delayed ecosystem driven by non-Gaussian colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    8. Bian, Junhao & Ma, Zhiqin & Wang, Chunping & Huang, Tao & Zeng, Chunhua, 2024. "Early warning for spatial ecological system: Fractal dimension and deep learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
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    10. Meng, Qingyan & Wang, Yejuan & Kloeden, Peter E., 2023. "The dynamical behavior of a class of stochastic vegetation models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 341-367.
    11. Mandal, Saroj Kumar & Poria, Swarup, 2023. "A study of Michaelis–Menten type harvesting effects on a population in stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    12. Zeng, Yujie & Liu, Dedi & Guo, Shenglian & Xiong, Lihua & Liu, Pan & Chen, Jie & Yin, Jiabo & Wu, Zhenhui & Zhou, Wan, 2023. "Assessing the effects of water resources allocation on the uncertainty propagation in the water–energy–food–society (WEFS) nexus," Agricultural Water Management, Elsevier, vol. 282(C).

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