(CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications. (21st January 2019)

• Record Type: Journal Article
• Authors: Cortés, Juan Carlos; Navarro‐Quiles, Ana; Romero, José‐Vicente; Roselló, María‐Dolores
• Other Names: Vigo-Aguiar Jesus guestEditor.; Kumam Poom guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 17(2019)
• Page Start: 5708
• Page End: 5717
• Publication Date: 2019-01-21
• Subjects: first probability density function -- modelling real data -- Pielou logistic equation -- population dynamics -- random difference stochastic equations -- random variable transformation technique; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5440
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However, discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state, and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples: The first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.