On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density
| Autor: | Leyza Baldo Dorini, Fabio Antonio Dorini, Moiseis dos Santos Cecconello |
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| Rok vydání: | 2016 |
| Předmět: |
Numerical Analysis
Uniform distribution (continuous) Applied Mathematics Principle of maximum entropy Monte Carlo method Probability density function Density estimation 01 natural sciences 010305 fluids & plasmas 010101 applied mathematics Inflection point Modeling and Simulation 0103 physical sciences Statistics Applied mathematics 0101 mathematics Logistic function Random variable Mathematics |
| Zdroj: | Communications in Nonlinear Science and Numerical Simulation. 33:160-173 |
| ISSN: | 1007-5704 |
| Popis: | It is recognized that handling uncertainty is essential to obtain more reliable results in modeling and computer simulation. This paper aims to discuss the logistic equation subject to uncertainties in two parameters: the environmental carrying capacity, K , and the initial population density, N 0 . We first provide the closed-form results for the first probability density function of time-population density, N ( t ), and its inflection point, t * . We then use the Maximum Entropy Principle to determine both K and N 0 density functions, treating such parameters as independent random variables and considering fluctuations of their values for a situation that commonly occurs in practice. Finally, closed-form results for the density functions and statistical moments of N ( t ), for a fixed t > 0, and of t * are provided, considering the uniform distribution case. We carried out numerical experiments to validate the theoretical results and compared them against that obtained using Monte Carlo simulation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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