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

Sun, Gui‐Quan; Jin, Zhen; Li, Li; Liu, Quan‐Xing

doi:10.1007/s10867-009-9139-y

Cited by 58 publications

(23 citation statements)

References 62 publications

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“…It has been observed in the literature that the effect of color noise on the dynamic behavior of spatial predator-prey models [42,43], especially spatial patterns, had been not well understood despite their potential ecological reality and intrinsic theoretical interest. These structures may, in fact, correspond to the real ecosystem.…”

Section: Discussionmentioning

confidence: 99%

Pattern dynamics of a spatial predator–prey model with noise

Jin

2011

Nonlinear Dyn

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A spatial predator-prey model with colored noise is investigated in this paper. We find that the number of the spotted pattern is increased as the noise intensity is increased. When the noise intensity and temporal correlation are in appropriate levels, the model exhibits phase transition from spotted to stripe pattern. Moreover, we show the number of the spotted and stripe pattern, with respect to both noise intensity and temporal correlation. These studies raise important questions on the role of noise in the pattern formation of the populations, which may well explain some data obtained in the ecosystems.

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Section: Discussionmentioning

confidence: 99%

Pattern dynamics of a spatial predator–prey model with noise

Jin

2011

Nonlinear Dyn

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“…By solving the linear equations (9) and (10) we find and then use the backward transformation (8) to obtain the following formal solution:…”

Section: Main Modelmentioning

confidence: 99%

“…On the other hand, the environments in models and laboratories are much less complex than ecological environments, and thus vegetation systems can be modeled as open systems in which the interaction with the environment is noisy [6,7]. Stochasticity can give rise to counterintuitive behaviors such as stochastic resonance, noise-enhanced stability, noisedelayed extinction, and noise-induced pattern formation [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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

Jian-zhong

2014

Discrete Dynamics in Nature and Society

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The growth of vegetation is undeniably subject to random fluctuations arising from environmental variability and internal effects due to periodic forcing. To address these issues, we investigated a spatial version of a vegetation model including seasonal rainfall, noise, and diffusion. By numerical simulations, we found that noise can induce the pattern transition from stationary pattern to other patterns. More specifically, when noise intensity is small, patch invasion is induced. As noise intensity further increases, chaotic patterns emerge. For the system with noise and seasonal rainfall, it exhibits frequency-locking phenomena. Patterns transition may be a warning signal for the onset of desertification and thus the obtained results may provide some measures to protect vegetation, such as reducing random factors or changing irrigation on vegetation.

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“…The manifestation of noise-induced ordered phases, patterns and traveling waves have been witnessed in various physical, chemical, biological and artificial setups (for a comprehensive review see (Sagués et al, 2007)). Along these lines several groups devoted plenty of attention to the impact of noise in spatially extended ecologically relevant models (Li and Jin, 2012;Liu et al, 2008;Mobilia et al, 2007;Sun et al, 2009a;Wang et al, 2011b). Apart from random fluctuations, ecological parameters are exposed to seasonal variations such as changes in climate or photoperiods as well (Steffen et al, 1997).…”

Section: Introductionmentioning

confidence: 99%