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Noise-induced bistability and noise-enhanced stability of a stochastic model for resource production–consumption under crowding effect and sigmoidal consumption pattern

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  • Yu, Xingwang
  • Ma, Yuanlin

Abstract

A resource production–consumption model with crowding effect and sigmoidal consumption pattern, subject to cross-correlated multiplicative and additive noises, is proposed in this paper to investigate noise-induced phenomena such as noise-induced bistability and noise-enhanced stability. Firstly, the stationary probability distribution and effective potential function are obtained through an approximate Fokker–Planck equation. Subsequently, P-bifurcation and noise-induced bistability are thoroughly investigated. Finally, the mean first passage time is utilized to calculate the average time for the system escaping from its attraction domain, while further exploring noise-enhanced stability. Our findings demonstrate that noise can induce P-bifurcation, especially bistability, regardless of the presence of bistability in the deterministic counterpart. Furthermore, appropriate noise parameters can cause a shift from an outbreak state to a shortage or depletion state. Additionally, both types of noise enhance the stability of the outbreak state when there is negative cross-correlation; however, for positive cross-correlation, they accelerate the transition from an outbreak state to a shortage or depletion state. The results obtained may offer preliminary or supplementary insights for the formulation of resource management policies.

Suggested Citation

  • Yu, Xingwang & Ma, Yuanlin, 2023. "Noise-induced bistability and noise-enhanced stability of a stochastic model for resource production–consumption under crowding effect and sigmoidal consumption pattern," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010366
    DOI: 10.1016/j.chaos.2023.114135
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    1. Ma, Yuanlin & Ma, Yanjiao & Sun, Haoran & Yu, Xingwang, 2026. "Transitions induced by correlated Gaussian and non-Gaussian noises in a single-species model with Allee effect and aposematism," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
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