Applications of the multi-sigmoidal deterministic and stochastic logistic models for plant dynamics
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916109928628224 |
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| author | Di Crescenzo, Antonio Paraggio, Paola Román-Román, Patricia Torres-Ruiz, Francisco |
| author_facet | Di Crescenzo, Antonio Paraggio, Paola Román-Román, Patricia Torres-Ruiz, Francisco |
| contents | We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main properties of the curve, such as the limit behavior, the inflection points and the threshold-crossing-time through a fixed boundary. We also present an application in population dynamics of plants based on real data. Then, we define two different birth-death processes, one with linear birth and death rates and the other with quadratic rates, and we analyze their main features. The conditions under which the processes have a mean of multi-sigmoidal logistic type and the first-passage-time problem are also discussed. Finally, with the aim of obtaining a more manageable stochastic description of the growth, we perform a scaling procedure leading to a lognormal diffusion process with mean of multi-sigmoidal logistic type. We finally conduct a detailed probabilistic analysis of this process |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Applications of the multi-sigmoidal deterministic and stochastic logistic models for plant dynamics Di Crescenzo, Antonio Paraggio, Paola Román-Román, Patricia Torres-Ruiz, Francisco Populations and Evolution Probability 92D25, 60J85, 60J70 We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main properties of the curve, such as the limit behavior, the inflection points and the threshold-crossing-time through a fixed boundary. We also present an application in population dynamics of plants based on real data. Then, we define two different birth-death processes, one with linear birth and death rates and the other with quadratic rates, and we analyze their main features. The conditions under which the processes have a mean of multi-sigmoidal logistic type and the first-passage-time problem are also discussed. Finally, with the aim of obtaining a more manageable stochastic description of the growth, we perform a scaling procedure leading to a lognormal diffusion process with mean of multi-sigmoidal logistic type. We finally conduct a detailed probabilistic analysis of this process |
| title | Applications of the multi-sigmoidal deterministic and stochastic logistic models for plant dynamics |
| topic | Populations and Evolution Probability 92D25, 60J85, 60J70 |
| url | https://arxiv.org/abs/2401.15727 |