ON THE STABILITY OF A POPULATION-GROWTH MODEL WITH SEXUAL REPRODUCTION ON Z(D), D-GREATER-THAN-OR-EQUAL-TO-2
成果类型：
Article
署名作者：
CHEN, HN
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176988600
发表日期：
1994
页码：
1195-1226
关键词：
摘要：
We continue our study on the stability properties of a population growth model with sexual reproduction on Z(d), d greater than or equal to 2. In the author's previous work, it was proved that in the type IV process (the two-dimensional symmetric model on Z(2)), the vacant state empty set is stable under perturbation of the initial state (the first kind of perturbation), and it is unstable under perturbation of the birth rate (the second kind of perturbation). In this paper we prove that in the type III process on Z(2), the vacant state empty set is stable under the second kind of perturbation, and in three or higher-dimensional symmetric models, the vacant state empty set is unstable under the first kind of perturbation. These results, combined with the results obtained earlier, provide a fairly complete picture concerning the stability properties of these models.
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