Colored-noise-induced discontinuous transitions in symbiotic ecosystems

Abstract

A symbiotic ecosystem is studied by means of the Lotka-Volterra stochastic model, using the generalized Verhulst self-regulation. The effect of fluctuating environment on the carrying capacity of a population is taken into account as dichotomous noise. The study is a follow-up of our investigation of symbiotic ecosystems subjected to three-level (trichotomous) noise [Phys. Rev. E 65, 051108 (2002)]]. Relying on the mean-field theory, an exact self-consistency equation for stationary states is derived. In some cases the mean field exhibits hysteresis as a function of noise parameters. It is established that random interactions with the environment can cause discontinuous transitions. The dependence of the critical coupling strengths on the noise parameters is found and illustrated by phase diagrams. Predictions from the mean-field theory are compared with the results of numerical simulations. Our results provide a possible scenario for catastrophic shifts of population sizes observed in nature.

Formation of spatial patterns in an epidemic model with constant removal rate of the infectives

“…In comparison with Refs. [8,21,22,23], here the difference is that we take into account the spatial noise in two dimensions. For the spatial noise we choose the colored noise ξ(x, y; t), which accounts for density fluctuations at point (x, y).…”

“…How- * Electronic address: jinzhn@263.net ever, the essential role of environmental fluctuations has recently been recognized in theoretical ecology. Noiseinduced effects on population dynamics have been subject to intense theoretical investigations [8,18,19,20,21,22,23,24,25,26]. Moreover, ecological investigations suggest that population dynamics is sensitive to noise.…”

“…For former model, the result of the study has shown that the noise induces discontinuous transitions from a stable state to an instable one in Refs. [21,22]. The latter model [8] has shown that the phenomena of colored-noise-induced Hopf bifurcation and corresponding reentrant transitions can appear in ecosystems.…”

Rich Spatiotemporal Dynamics of a Vegetation Model with Noise and Periodic Forcing

“…In (2a) and (2b), the stochastic factors are taken into account as the term ( , ), which is obtained in the continuum limit from the master equation arising from microscopic interaction in the space [23,24] where the typical white noise will emerge. Recently, colored noise and white noise have both been used in describing ecological evolution [25,26]. White noise is the limiting case of colored noise, so we consider the more general case-colored noise in the present paper.…”

The role of noise in a predator–prey model with Allee effect

“…Recently, colored noise and white noise have both been used in describing ecological evolution [42][43][44]. White noise is the limiting case of colored noise, so we consider the more general case of colored noise.…”