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

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.