Logistic and $\theta$-logistic models in population dynamics: General analysis and exact results
| Autor: | Petroni, Nicola Cufaro, De Martino, Salvatore, De Siena, Silvio |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8121/abb277 |
| Popis: | In the present paper we provide the closed form of the path-like solutions for the logistic and $\theta$-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 $\theta$-logistic equations in a unified context, within which also the Gompertz model emerges from an anomalous scaling. Comment: 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 |
| Databáze: | arXiv |
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