On the generalized logistic random differential equation: Theoretical analysis and numerical simulations with real-world data
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Otros documentos de la autoría: Bevia, Vicente; Calatayud, Julia; Cortés, Juan Carlos; Jornet, Marc
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Mostrar el registro completo del ítemcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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On the generalized logistic random differential equation: Theoretical analysis and numerical simulations with real-world dataFecha de publicación
2022-08-27Editor
ElsevierCita bibliográfica
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.Tipo de documento
info:eu-repo/semantics/articleVersión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
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. [-]
Publicado en
Communications in Nonlinear Science and Numerical Simulation, 2023, vol. 116Entidad financiadora
Agencia Estatal de Investigación (AEI), Spain | Universitat Politècnica de València
Código del proyecto o subvención
PID2020-115270GB-I00
Derechos de acceso
© 2022 The Author(s). Published by Elsevier B.V.
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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