Harris S
Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Sep;62(3 Pt B):4032-5. doi: 10.1103/physreve.62.4032.
We consider the Fisher equation and its generalization for an asocial population in a linear, hostile environment. The method of center manifold analysis is used to obtain the time-dependent solution of the former, nonlinear equation. The correct critical habitat size is obtained; in addition, the result for the steady state central density compares favorably with the exact result for relatively large population sizes (up to one half of the carrying capacity). For a model of asocial growth we obtain the expanded criteria for survival. This includes the habitat size, the population size at which positive growth begins, and also the minimum initial central density.
我们考虑在一个线性、恶劣环境中针对非群居种群的费希尔方程及其推广形式。运用中心流形分析方法来求解前者的非线性方程的时间相关解。得出了正确的临界栖息地大小；此外，对于稳态中心密度的结果与相对较大种群规模（高达承载能力的一半）的精确结果相比表现良好。对于一个非群居增长模型，我们得出了扩展的生存标准。这包括栖息地大小、开始正增长时的种群规模，以及最小初始中心密度。
