Life and death near a windy oasis

Journal of Mathematical Biology

Volumn 41, Issue 1, 2000, Pages 1-23

  Dahmen, Karin A ^a,c   Nelson, David R ^a   Shnerb, Nadav M ^b  

^a HARVARD UNIVERSITY   (United States)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^c University of Illinois at Urbana Champaign   (United States)

Author keywords

Delocalization; Disorder; Extinction; Fisher equation

Indexed keywords

ARTICLE; BACTERIUM; BIOLOGICAL MODEL; GROWTH, DEVELOPMENT AND AGING; MATHEMATICAL COMPUTING; STATISTICAL MODEL;

BACTERIA; LINEAR MODELS; MODELS, BIOLOGICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED;

EID: 0034218896     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850000025     Document Type: Article

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18. Here we present results for the dynamics of continuous populations, while the process is actually discrete, with events such as reproduction A → 2A, death A → 0, and competition A + A → 0, where A denotes an individual bacterium. Throughout this paper, we neglect this effect and study a continuum ("mean field") approximation to this process. Discreteness, which will only be important very close to the extinction transition, can be modeled by inclusion of a multiplicative Langevin noise term, see, e.g. Privman, V.: Trends in Stat. Phys. 1 (1994);
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31. n(x) of (10) must decay sufficiently fast far away from the oasis. We check this condition at the end of the calculation; when it is violated, the eigenvalues become complex
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