Noise-induced bistability and noise-enhanced stability of a stochastic model for resource production–consumption under crowding effect and sigmoidal consumption pattern - Yu, Xingwang; Ma, Yuanlin (Chaos, solitons and fractals, 2023)
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. •A stochastic resource production–consumption model is proposed.•Noise-induced bistability and noise-enhanced stability are discussed.•Noise can induce bistability regardless of the presence of bistability in the deterministic counterpart.•Whether noise enhances or weakens the stability of outbreak state depends on the correlation degree.