Stochastic sensitivity analysis of noise-induced transitions in a predator-prey model with environmental toxins

Dongmei Wu; Hao Wang; Sanling Yuan; Dongmei Wu; Hao Wang; Sanling Yuan

doi:10.3934/mbe.2019104

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 2141-2153. doi: 10.3934/mbe.2019104

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Stochastic sensitivity analysis of noise-induced transitions in a predator-prey model with environmental toxins

1.
College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China
2.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Received: 24 September 2018 Accepted: 19 October 2018 Published: 12 March 2019

Huang et al. ^[1] recently developed a toxin-dependent predator-prey model and analyzed its global dynamics. Their results showed that environmental toxins may influence both predators and prey and induce bistable situation, and intermediate toxin concentrations may affect predators disproportionately through biomagnification. Environmental noises can change the dynamical behaviors of the toxin-based predator-prey model. In this paper, by formulating a stochastically forced predator-prey model with environmental toxins, we study the dynamical phenomenon of noise-induced transitions from coexistence to prey-only extirpation in the bistable zone. Numerical simulations based on the technique of stochastic sensitivity functions are provided for constructing the confidence ellipse and estimating the threshold value of the noise intensity of state switching. Meanwhile, we construct the confidence band and study the configurational arrangement of the stochastic cycle.
- predator-prey model,
- environmental toxins,
- stochastic sensitivity,
- noise-induced transitions,
- confidence domain
Citation: Dongmei Wu, Hao Wang, Sanling Yuan. Stochastic sensitivity analysis of noise-induced transitions in a predator-prey model with environmental toxins[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2141-2153. doi: 10.3934/mbe.2019104

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Abstract

Huang et al. ^[1] recently developed a toxin-dependent predator-prey model and analyzed its global dynamics. Their results showed that environmental toxins may influence both predators and prey and induce bistable situation, and intermediate toxin concentrations may affect predators disproportionately through biomagnification. Environmental noises can change the dynamical behaviors of the toxin-based predator-prey model. In this paper, by formulating a stochastically forced predator-prey model with environmental toxins, we study the dynamical phenomenon of noise-induced transitions from coexistence to prey-only extirpation in the bistable zone. Numerical simulations based on the technique of stochastic sensitivity functions are provided for constructing the confidence ellipse and estimating the threshold value of the noise intensity of state switching. Meanwhile, we construct the confidence band and study the configurational arrangement of the stochastic cycle.

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