一类自扩散–交叉扩散离散捕食系统的斑图形成
The Pattern Formation of a Certain Kind of the Self- and Cross-Diffusion Discrete Predator-Prey System
摘要:
通过构建三链耦合映像格子模型，研究了Holling-II型时空离散反应自扩散–交叉扩散捕食系统的时空动力学。在分析并确定该时空离散捕食系统的均匀稳定状态后，对其进行图灵失稳分析，计算出了图灵失稳条件。在图灵失稳基础上进行的数值模拟，展现了空间密度分布斑图的自组织过程，发现捕食者与被捕食者空间密度斑图总会由无规律的随机分布演化出块状、圆盘状以及螺旋波状斑图。
Abstract:
The spatiotemporal dynamics of Holling-II spatiotemporal discrete-time reactive self-diffusion and cross-diffusion predator-prey system was studied by constructing a three-chain coupled map lattice model. After analyzing and determining the homogeneous stable state of the spatio-temporal discrete predator-prey system, the Turing instability was analyzed and the Turing instability conditions were calculated. The numerical simulation on the basis of Turing instability showed the self-organizing process of spatial density distribution patterns, and it was found that the spatial density patterns of predator and prey always evolved into block, disk and spiral wave patterns from random distributions.
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