无标度网络上的简单反应扩散种群模型
Simple reaction-diffusion population model on scale-free networks
摘要：
本文研究了一个简单的反应扩散种群模型[A. Windus和H. J. Jensen，J. Phys. A：Math. Theor. 40，2287（2007）]的无标度网络。在完全随机扩散的情况下，网络拓扑结构不影响临界死亡率，而异质连通性会导致较小的稳态种群密度和临界种群密度.在修正扩散的情况下，我们得到了较大的临界死亡率和稳定的种群密度，同时得到了较低的临界种群密度，这有利于物种的生存。结果得到了使用平均场的框架，并通过计算机模拟证实。
英文摘要：
We study a simple reaction-diffusion population model [proposed by A. Windus and H. J. Jensen, J. Phys. A: Math. Theor. 40, 2287 (2007)] on scale-free networks. In the case of fully random diffusion, the network topology cannot affect the critical death rate, whereas the heterogeneous connectivity can cause smaller steady population density and critical population density. In the case of modified diffusion, we obtain a larger critical death rate and steady population density, at the meanwhile, lower critical population density, which is good for the survival of species. The results were obtained using a mean-field-like framework and were confirmed by computer simulations.
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