A stochastic analysis of the spatially extended May–Leonard model
A stochastic analysis of the spatially extended May–Leonard model
复制标题
空间扩展 May-Leonard 模型的随机分析
DOI：
10.1088/1751-8121/aa87a8
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
U. Täuber
中科院分区：
文献类型：
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作者：
Shannon R. Serrao;U. Täuber
对周期性竞争种群的May-Leonard模型的数值研究显示了螺旋形的自发空间结构。在这种空间扩展的随机种群动力学模型中，需要得到一个简单的粗粒度演化方程来描述时空格局的形成。相应的确定性系统上的扩展早期的工作，我们推导出复杂的金斯堡-朗道方程的有效表示的完全随机动力学的这种范式模型的循环优势附近的Hopf分岔，并在三个物种共存制度的小波动。内部的随机反应噪声占通过Doi-Peliti相干状态路径积分形式主义，并随后映射到三个耦合的非线性Langevin方程。这种分析提供了对模型参数的约束，允许时间尺度分离，从而进一步减少到只有两个粗粒度的慢自由度。
Numerical studies of the May–Leonard model for cyclically competing species exhibit spontaneous spatial structures in the form of spirals. It is desirable to obtain a simple coarse-grained evolution equation describing spatio-temporal pattern formation in such spatially extended stochastic population dynamics models. Extending earlier work on the corresponding deterministic system, we derive the complex Ginzburg–Landau equation as the effective representation of the fully stochastic dynamics of this paradigmatic model for cyclic dominance near its Hopf bifurcation, and for small fluctuations in the three-species coexistence regime. The internal stochastic reaction noise is accounted for through the Doi–Peliti coherent-state path integral formalism, and subsequent mapping to three coupled non-linear Langevin equations. This analysis provides constraints on the model parameters that allow time scale separation and in consequence a further reduction to just two coarse-grained slow degrees of freedom.
DOI：
10.1088/1742-5468/2016/11/113402
发表时间：
2016-08
期刊：
Journal of Statistical Mechanics: Theory and Experiment
影响因子：
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作者：
Darka Labavi'c;H. Meyer-Ortmanns
通讯作者：
Darka Labavi'c;H. Meyer-Ortmanns