非自治离散时间单种群模型的持久性

PERSISTENCE OF A NONAUTONOMOUS MODEL ABOUT DISCRETE-TIME SINGER POPULATION

本文考虑非自治离散时间单种群模型x(τ+1=一x(τ)expf(τ,x(τ)),其中x(τ)表示种群数量。这里影响种群生长速度的各种因素可以因时间而改变,如果存在某个长度固定的时间阶段,在任何这样长的时间阶段上,种群所经历的环境变化可以代表在所有时间出现的环境变化,那么我们可以得到种群生长的最终行为,即在什么条件下种群将持续不断的生存下去,又在什么条件下,种群灭绝。最后,对于自治系统x(τ+1)=x(τ)expf(x(τ))也相应地给出了种群持续生存及灭绝的条件。

With x(r)=population size, the nonautonomous equation x(r+1)=x(r)expf(r, x(r)) provides a very general description of population growth in which any of the many factors that influence the growth rate may vary through time. If there is some fixed length of time such that during any interval of this length the population experiences environmental variability representative of the variation that occurs in all time, then definite conclusions about the population's long term behavior apply. Specifically, conditions that produce population presistence can be distinguished from conditions that cause extinction. These attributes resemble corresponding features of the related autonomous population growth model x(τ+1)=x(r)expf(x(τ)).