Logistic and $θ$-logistic models in population dynamics: General analysis and exact results
Nicola Cufaro Petroni, Salvatore De Martino, Silvio De Siena
备注：
25 pages, 8 figures. The second part of the paper (from p. 10, Section 3.1 on) is substantially improved w.r.t. the old version. As a consequence Title, Abstract, Introduction, Conclusions and References have been accordingly updated
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.
Estimation of population infected by Covid-19 using regression Generalized logistics and optimization heuristics
在这项工作中，提出了一个建议，估计的人口使用逻辑曲线拟合。这种类型的曲线用于研究人口增长，在这种情况下，感染Covid-19病毒的人口;它也可以用于近似精算和西班牙语类似研究中使用的生存曲线：En este trabajos se presenta una propuesta para la estimación de la poblaciones usando ajuste de curvas del tipo logística. Este tipo de curvas se utilizan para el estudio de crecimiento de poblaciones，en este casos población de personas infectadas por el virus Covid-19; y también se puede utilizar para aproximar la curva de supervencia que se utiliza en estudios actuariales y otras similares
Logistic dynamics of small populations with demographic stochasticity
Consejo Nacional de Investigaciones Científicas y Técnicas（国家科学研究委员会）；Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica and Universidad Nacional de Cuyo（巴里洛切原子中心与巴尔塞罗研究所，国家原子能委员会与门多萨国立大学）
Predator Extinction arose from Chaos of the Prey: the Chaotic Behavior of a Homomorphic Two-Dimensional Logistic Map in the Form of Lotka-Volterra Equations
Flow-Based Modelling of Population Dynamics with Consecutive Continuous Mutations
Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences（俄罗斯科学院马丘克数值数学研究所）；Moscow Center for Fundamental and Applied Mathematics at INM RAS（俄罗斯科学院数值数学研究所莫斯科基础与应用数学中心）；Institute of Management and Digital Technologies, Russian University of Transport（俄罗斯交通大学管理与数字技术研究所）；A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation（阿·伊·阿里汉尼扬国家科学实验室（叶里温物理研究所）基金会）
Population Growth and Competition Models with Decay and Competition Consistent Delay
我们推导出一个延迟的Logistic方程的另一种表达，其中人口的变化率涉及的增长率，取决于人口密度在较早的时间段。在我们的公式中，增长项的延迟与模型给出的人口瞬时下降率一致。我们的公式是[Arino et al.，J.~理论~生物学~ 241（1）：109--119，2006]，并考虑了成虫和幼虫之间的种内竞争。我们提供了一个完整的全球分析表明，没有持续的振荡是可能的。给出灭绝和生存之间的接口的阈值确定在模型中的参数。利用链传递集理论和合作时滞微分方程的比较定理确定了模型的全局动力学性质。我们扩展我们的延迟逻辑方程的两个物种的竞争建模系统。对于竞争模型，我们提供了局部稳定性，分岔图和自适应动力学的结果。假设具有较短延迟的物种比具有较长延迟的物种一次产生较少的后代，我们证明了存在一个临界值$τ^*$，使得延迟的进化趋势是接近$τ^*$。
