Colored-noise-induced Hopf bifurcations in predator-prey communities

Abstract

A broad class of (N+1) -species ratio-dependent predator-prey stochastic models, which consist of one predator population and N prey populations, is considered. The effect of a fluctuating environment on the carrying capacities of prey populations is taken into account as colored noise. In the framework of the mean-field theory, approximate self-consistency equations for prey-populations mean density and for predator-population density are derived (to the first order in the noise variance). In some cases, the mean field exhibits Hopf bifurcations as a function of noise correlation time. The corresponding transitions are found to be reentrant, e.g., the periodic orbit appears above a critical value of the noise correlation time, but disappears again at a higher value of the noise correlation time. The nonmonotonous dependence of the critical control parameter on the noise correlation time is found, and the conditions for the occurrence of Hopf bifurcations are presented. Our results provide a possible scenario for environmental-fluctuations-induced transitions between the oscillatory regime and equilibrium state of population sizes observed in nature.

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

“…In this paper, the problem of the predator-prey dynamical system [4,5,6,7,8] is revisited and the results are presented concerning the noise aspects of the formation of spatial patterns in two dimensions. To our knowledge, the predator-prey dynamics in the absence of noise have been studied extensively using mathematical models.…”

“…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.…”

“…[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. But both models are studied in nonspatial.…”

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

“…The models they employed were ordinary differential equations [15][16][17][18][19] or partial differential equations with logistic growth [20][21][22][23][24][25]. However, it has been observed in the literature that the Allee effect [26][27][28][29][30], especially combined with diffusion of the spatial patterns, had been generally overlooked, despite its potential ecological reality and intrinsic theoretical interest.…”

Propagation of travelling waves in sub-excitable systems driven by noise and periodic forcing

“…Noise can induce transition [1,2], bifurcations [3], and stochastic resonance [4,5,6,7]. Especially, in Ref.…”