期刊
BULLETIN OF MATHEMATICAL BIOLOGY
卷 75, 期 5, 页码 845-870出版社
SPRINGER
DOI: 10.1007/s11538-013-9838-1
关键词
Cross-diffusion; Fitness; Lotka-Volterra competition systems; Nonuniform random walk; Random dispersal; Spatial heterogeneity; Thermal diffusion
资金
- National Research Foundation of Korea [013-2011-1-C00002]
- National Research Foundation of Korea [013-2011-1-C00002] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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.
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