Institute of Molecular Biology and Genetics, Seoul National University, Seoul, South Korea.
Bull Math Biol. 2013 May;75(5):845-70. doi: 10.1007/s11538-013-9838-1. Epub 2013 Apr 12.
The purpose of this article is to introduce a diffusion model for biological organisms that increase their motility when food or other resource is insufficient. It is shown in this paper that Fick's diffusion law does not explain such a starvation driven diffusion correctly. The diffusion model for nonuniform Brownian motion in Kim (Einstein's random walk and thermal diffusion, preprint http://amath.kaist.ac.kr/papers/Kim/31.pdf , 2013) is employed in this paper and a Fokker-Planck type diffusion law is obtained. Lotka-Volterra type competition systems with spatial heterogeneity are tested, where one species follows the starvation driven diffusion and the other follows the linear diffusion. In heterogeneous environments, the starvation driven diffusion turns out to be a better survival strategy than the linear one. Various issues such as the global asymptotic stability, convergence to an ideal free distribution, the extinction and coexistence of competing species are discussed.
本文的目的是介绍一种扩散模型，用于描述当食物或其他资源不足时生物体会增加其运动性。本文表明，菲克扩散定律不能正确解释这种饥饿驱动的扩散。本文采用 Kim（Einstein 的随机游走和热扩散，预印本 http://amath.kaist.ac.kr/papers/Kim/31.pdf，2013）中的非均匀布朗运动扩散模型，并得到了福克-普朗克型扩散定律。本文测试了具有空间异质性的 Lotka-Volterra 竞争系统，其中一种物种遵循饥饿驱动的扩散，另一种遵循线性扩散。在异质环境中，饥饿驱动的扩散比线性扩散更有利于物种的生存。讨论了各种问题，如全局渐近稳定性、收敛到理想自由分布、竞争物种的灭绝和共存。
