On the generalized logistic random differential equation: Theoretical analysis and numerical simulations with real-world data
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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INVESTIGACIONMetadata
Title
On the generalized logistic random differential equation: Theoretical analysis and numerical simulations with real-world dataDate
2022-08-27Publisher
ElsevierBibliographic citation
BEVIA, V., et al. On the generalized logistic random differential equation: Theoretical analysis and numerical simulations with real-world data. Communications in Nonlinear Science and Numerical Simulation, 2023, vol. 116, p. 106832.Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
Based on the previous literature about the random logistic and Gompertz models, the aim of this paper is to extend the investigations to the generalized logistic differential equation in the random setting. First, ... [+]
Based on the previous literature about the random logistic and Gompertz models, the aim of this paper is to extend the investigations to the generalized logistic differential equation in the random setting. First, this is done by rigorously constructing its solution in two different ways, namely, the sample-path approach and the mean-square calculus. Secondly, the probability density function at each time instant is derived in two ways: by applying the random variable transformation technique and by solving the associated Liouville’s partial differential equation. It is also proved that both the stochastic solution and its density function converge, under specific conditions, to the corresponding solution and density function of the logistic and Gompertz models, respectively. The investigation finishes showing some examples, where a number of computational techniques are combined to construct reliable approximations of the probability density of the stochastic solution. In particular, we show, step-by-step, how our findings can be applied to a real-world problem. [-]
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Communications in Nonlinear Science and Numerical Simulation, 2023, vol. 116Funder Name
Agencia Estatal de Investigación (AEI), Spain | Universitat Politècnica de València
Project code
PID2020-115270GB-I00
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© 2022 The Author(s). Published by Elsevier B.V.
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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