GROWTH WITH REGULATION IN RANDOM ENVIRONMENT
GROWTH WITH REGULATION IN RANDOM ENVIRONMENT
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DOI：
10.1007/bf00274586
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发表时间：
1974-01-01
期刊：
影响因子：
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通讯作者：
RICCIARDI, LM
中科院分区：
文献类型：
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作者：
CAPOCELLI, RM;RICCIARDI, LM
将马尔萨斯增长的种群扩散模型推广到包含调控效应的情形。这是通过在调节函数中加入对数项来实现的，在没有噪声的情况下，获得保留逻辑增长曲线定性特征的S形增长律。生长现象被建模为扩散过程，其过渡p.d.f.是以封闭的形式获得的。其稳态行为被证明是由对数正态分布描述。给出了过渡过程的期望值和模式。的时间过程，并证明了它们的时间过程也表示为单调递增的函数渐近接近饱和值。然后考虑第一通过时间问题。首次通过时间p.d.f.的拉普拉斯变换。对于任意阈值获得，并用于计算第一通过时间的期望值。然后，针对等于在不存在随机分量的情况下由群体大小获得的饱和值的阈值来确定逆拉普拉斯变换。最后计算了任意势垒的吸收概率，作为双势垒问题中吸收概率的极限。
The diffusion model for a population subject to Malthusian growth is generalized to include regulation effects. This is done by incorporating a logarithmic term in the regulation function in a way to obtain, in the absence of noise, anS-shaped growth law retaining the qualitative features of the logistic growth curve. The growth phenomenon is modeled as a diffusion process whose transition p.d.f. is obtained in closed form. Its steady state behavior turns out to be described by the lognormal distribution. The expected values and the mode of the transition p.d.f. are calculated, and it is proved that their time course is also represented by monotonically increasing functions asymptotically approaching saturation values. The first passage time problem is then considered. The Laplace transform of the first passage time p.d.f. is obtained for arbitrary thresholds and is used to calculate the expected value of the first passage time. The inverse Laplace transform is then determined for a threshold equal to the saturation value attained by the population size in the absence of random components. The probability of absorption for an arbitrary barrier is finally calculated as the limit of the absorption probability in a two-barrier problem.