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首页> 外文期刊>Mathematical Problems in Engineering: Theory, Methods and Applications >Noise-Induced Transitions in a Population Growth Model Based on Size-Dependent Carrying Capacity
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Noise-Induced Transitions in a Population Growth Model Based on Size-Dependent Carrying Capacity

机译：基于人口承载力的人口增长模型中的噪声诱导转变

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摘要

The stochastic dynamics of a population growth model with size-dependent carrying capacity is considered. The effect of a fluctuating environment on population growth is modeled as a multiplicative dichotomous noise. At intermediate values of population size the deterministic counterpart of the model behaves similarly to the Von Foerster model for human population, but at small and very large values of population size substantial differences occur. In the stochastic case, an exact analytical solution for the stationary probability distribution is found. It is established that variation of noise correlation time can cause noise-induced transitions between three different states of the system characterized by qualitatively different behaviors of the probability distributions of the population size. Also, it is shown that, in some regions of the system parameters, variation of the amplitude of environmental fluctuations can induce single unidirectional abrupt transitions of the mean population size.
机译：考虑具有规模依赖的承载能力的人口增长模型的随机动力学。波动的环境对人口增长的影响被建模为乘性二分法噪声。在人口规模的中间值时，该模型的确定性对应物的行为与人类人口的Von Foerster模型相似，但是在人口规模小的和非常大的值时，会发生很大的差异。在随机情况下，找到了固定概率分布的精确解析解。可以确定的是，噪声相关时间的变化会导致系统三个不同状态之间的噪声诱发的跃迁，这些跃迁的特征在于总体大小的概率分布的质的不同行为。此外，还表明，在系统参数的某些区域中，环境波动幅度的变化会引起平均人口规模的单个单向突变。

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