A note on the logistic equation subject to uncertainties in parameters

• Published in: Computational & applied mathematics Vol. 37; no. 2; pp. 1496 - 1506
• Main Authors: Dorini, Fabio A., Bobko, Nara, Dorini, Leyza B.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.05.2018; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Carrying capacity; Computational mathematics; Computational Mathematics and Numerical Analysis; Independent variables; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Parameter uncertainty; Population density; Probability density functions; Random variables; Logistic equation; Random variable transformation technique; First probability density function; Primary 34F05; Uncertainties; Secondary 60H10
• ISSN: 0101-8205; 2238-3603; 1807-0302
• DOI: 10.1007/s40314-016-0409-6

This paper discusses the logistic equation subject to uncertainties in the intrinsic growth rate, α , in the initial population density, N 0 , and in the environmental carrying capacity, K . These parameters are treated as independent random variables. The random variable transformation method is applied to compute the first probability density function of the time–population density, N ( t ), and of its inflection point, t ∗ . Results for the density functions of N ( t ), for a fixed t > 0 , and t ∗ are also provided for α , N 0 and K uniformly distributed. Finally, numerical experiments illustrate the proposed theoretical results.