论文标题
人口动态中的逻辑和$θ$ - 逻辑模型：一般分析和精确结果
Logistic and $θ$-logistic models in population dynamics: General analysis and exact results
论文作者
论文摘要
在本文中，我们为逻辑和$θ$ logistic随机微分方程提供类似路径的解决方案的封闭形式，以及其概率密度函数及其矩的精确表达式。我们还模拟了一些典型的样本轨迹，并提供了一些在不同噪声强度下上述封闭公式的数值计算的示例：这特别表明，同时越来越多的随机性 - 使过程变得更加不可预测 - 渐近地倾向于平均抑制物流增长。在这些模型的无噪声，确定性版本的讨论之前，这些主要结果是：根据一些简化但功能性的假设，它具有工具性，以构建统一上下文中的逻辑和$θ$ logistic方程，在此中，gompertz模型也从异端范围中出现。
In the present paper we provide the closed form of the path-like solutions for the logistic and $θ$-logistic stochastic differential equations, along with the exact expressions of both their probability density functions and their moments. We simulate in addition a few typical sample trajectories, and we provide a few examples of numerical computation of the said closed formulas at different noise intensities: this shows in particular that an increasing randomness - while making the process more unpredictable - asymptotically tends to suppress in average the logistic growth. These main results are preceded by a discussion of the noiseless, deterministic versions of these models: a prologue which turns out to be instrumental - on the basis of a few simplified but functional hypotheses - to frame the logistic and $θ$-logistic equations in a unified context, within which also the Gompertz model emerges from an anomalous scaling.
