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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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    4. Amemiya, Takashi & Enomoto, Takatoshi & Rossberg, Axel G. & Yamamoto, Tetsuya & Inamori, Yuhei & Itoh, Kiminori, 2007. "Stability and dynamical behavior in a lake-model and implications for regime shifts in real lakes," Ecological Modelling, Elsevier, vol. 206(1), pages 54-62.
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    6. Vishwesha Guttal & Srinivas Raghavendra & Nikunj Goel & Quentin Hoarau, 2016. "Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk," PLOS ONE, Public Library of Science, vol. 11(1), pages 1-20, January.
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