Tipping time in a stochastic Leslie predator–prey model

Anji Yang, Hao Wang and Sanling Yuan

Chaos, Solitons & Fractals, 2023, vol. 171, issue C

Abstract: Critical transitions are usually accompanied by a decline in ecosystem services and potentially have negative impacts on human economies. Although some early warning signals based on a generic characteristic of local bifurcations, such as variance and autocorrelation, can be used to predict an imminent critical transition, studies have shown that these indicators are ineffective for purely stochastic transitions. In this paper, we propose to use the maximum likelihood state, based on the Fokker–Planck equation, to track the true state of a predator–prey model under noisy fluctuations. Then, we use the maximal likely trajectory to determine tipping times for the most probable transitions from a high biomass state to a low biomass one. Numerical results show that the tipping times of population collapse depend strongly on the noise intensity and the growth rate of predator. We uncover that the enhanced disturbance events promote ecosystem collapse and that an increase in predator growth rate significantly alleviates the influence, which is beneficial to the stability and biodiversity of an ecosystem. Based on this, we define a two-dimensional region, called the Safe Operating Set (SOS) of the population ecosystem. SOS boundary exhibits a trade-off such that increased predator growth rates can compensate to some degree for losses from environmental perturbations. To verify the above conclusions, we fix noise intensity and calculate the quasi-potentials of the corresponding high biomass state for different predator growth rates. We can see that the results for measuring the stability of the high biomass state derived from the perspective of quasi-potential are consistent with the results obtained from the analysis of tipping time.

Keywords: Critical transition; Noise-induced tipping; Maximal likely trajectory; Tipping time; Fokker–Planck equation; Safe operating set (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077923003405
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003405

DOI: 10.1016/j.chaos.2023.113439

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().