Noise- and delay-induced regime shifts in an ecological system of vegetation

Abstract

In this paper, the stationary probability distribution (SPD) and mean first passage time (MFPT) in a vegetation model with time delay are investigated, where the vegetation dynamics is assumed to be disturbed by both intrinsic and extrinsic noises. The impacts of the intrinsic noise strength α, extrinsic noise strength D, time delay τ and cross-correlation strength q between two noises on the SPD and MFPT of the regime shifts between the sustainable vegetation and barren states are discussed, respectively. Our main results are as follows. (i) The increase of α will cause regime shifts from the barren state to the sustainable vegetation state, while the increase of D or τ will cause regime shifts from the sustainable vegetation state to the barren state. (ii) The MFPT as a function of the noise intensities (i.e., α and D) exhibits one maximum value in the case of q < 0.0, and the maximum MFPT shows the characteristic of the noise enhanced stability of the sustainable vegetation biomass. (iii) However, for the case of q 0.0, the increase of α or D causes a decrease of the MFPT, i.e., the noises can enhance the probability of regime shifts to the barren state. (iv) Although the cross-correlation between two noises is positive (q > 0.0), the presence of time delay can also cause the existence of extrinsic noise enhanced stability.

Stochastic ecological kinetics of regime shifts in a time‐delayed lake eutrophication ecosystem

“…), catastrophic regime shifts in vegetation ecosystems (Zeng and Wang , Zeng et al. ), delayed feedback as a mean of control of noise‐induced motion (Janson et al. ), and noise‐ and delay‐enhanced stability in a chemical reaction system (Yang et al.…”

Delays-based protein switches in a stochastic single-gene network

“…Amit et al [31] consider only a single (additive) noise, but real systems are simultaneously disturbed by multiplicative and additive noises. In some situations, both noises may have a common origin and thus are not independent; physically this would mean that the noises are of the same origin [32][33][34][35][36][37]. Presently, the effects of cross-correlations between additive and multiplicative noises, either on a stationary state or on dynamics of the bistable potential system, have been widely studied [38][39][40][41][42][43].…”

Noises-induced regime shifts and -enhanced stability under a model of lake approaching eutrophication

“…Practically, in many physical as well as biological systems, the presence of the correlation between two noises plays a significant role in the dynamics. Indeed, the presence of correlation can causes: stochastic resonance (Tessone et al, 2000;Jia et al, 2000), noise enhanced stability (Zeng et al, 2009;Zeng and Wang, 2010), multiple current reversals , fluctuations-induced switch (Liu and Jia, 2004;Zhang et al, 2011;Ghosh et al, 2012), noise-and delay-induced regime shifts (Zeng et al, 2013), and emergent and divergent resilience (Srinivasan and Kumar, 2015).…”