Zhang Xiao-Chong, Sun Gui-Quan, Jin Zhen
Department of Mathematics, North University of China, Taiyuan, Shan'xi 030051, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 1):021924. doi: 10.1103/PhysRevE.85.021924. Epub 2012 Feb 28.
In this paper spatial dynamics of the Beddington-DeAngelis predator-prey model is investigated. We analyze the linear stability and obtain the condition of Turing instability of this model. Moreover, we deduce the amplitude equations and determine the stability of different patterns. In Turing space, we found that this model has coexistence of H(0) hexagon patterns and stripe patterns, H(π) hexagon patterns, and H(0) hexagon patterns. To better describe the real ecosystem, we consider the ecosystem as an open system and take the environmental noise into account. It is found that noise can decrease the number of the patterns and make the patterns more regular. What is more, noise can induce two kinds of typical pattern transitions. One is from the H(π) hexagon patterns to the regular stripe patterns, and the other is from the coexistence of H(0) hexagon patterns and stripe patterns to the regular stripe patterns. The obtained results enrich the finding in the Beddington-DeAngelis predator-prey model well.
本文研究了贝丁顿 - 德安吉利斯捕食者 - 猎物模型的空间动力学。我们分析了线性稳定性并得到了该模型的图灵不稳定性条件。此外，我们推导了振幅方程并确定了不同模式的稳定性。在图灵空间中，我们发现该模型存在H(0)六边形模式与条纹模式共存、H(π)六边形模式以及H(0)六边形模式。为了更好地描述真实的生态系统，我们将生态系统视为一个开放系统并考虑环境噪声。研究发现噪声会减少模式数量并使模式更加规则。此外，噪声可引发两种典型的模式转变。一种是从H(π)六边形模式转变为规则条纹模式，另一种是从H(0)六边形模式与条纹模式的共存转变为规则条纹模式。所得结果很好地丰富了贝丁顿 - 德安吉利斯捕食者 - 猎物模型的研究成果。
