Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process

Saúl Díaz Infante Velasco, Silvia Jerez, Benito Chen-Charpentier

Resultado de la investigación: Contribución a una revistaArtículoInvestigaciónrevisión exhaustiva

3 Citas (Scopus)

Resumen

In this work, we model osteoclast-osteoblast population dynamics with random environmental fluctuations in order to understand the random variations of the bone remodeling process in real life. For this purpose, we construct a stochastic differential model for the interactions between the osteoclast and osteoblast cell populations using the parameter perturbation technique. We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p ≥ 1. Finally, we show that the introduction of noise in the deterministic model provides a fluctuating periodic solution. Numerical evidence supports our theoretical results and a discussion of the results is carried out.
Idioma originalEspañol (México)
Páginas (desde-hasta)153
Número de páginas164
PublicaciónMathematical Biosciences
Volumen299
DOI
EstadoPublicada - 8 mar 2018

Palabras clave

  • Bone remodeling Stochastic differential equations Brownian motion Moment boundedness Fluctuating periodic solution Osteoclasts Osteoblasts

Citar esto

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abstract = "In this work, we model osteoclast-osteoblast population dynamics with random environmental fluctuations in order to understand the random variations of the bone remodeling process in real life. For this purpose, we construct a stochastic differential model for the interactions between the osteoclast and osteoblast cell populations using the parameter perturbation technique. We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p ≥ 1. Finally, we show that the introduction of noise in the deterministic model provides a fluctuating periodic solution. Numerical evidence supports our theoretical results and a discussion of the results is carried out.",
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Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process. / Díaz Infante Velasco, Saúl; Jerez, Silvia; Chen-Charpentier, Benito.

En: Mathematical Biosciences, Vol. 299, 08.03.2018, p. 153.

Resultado de la investigación: Contribución a una revistaArtículoInvestigaciónrevisión exhaustiva

TY - JOUR

T1 - Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process

AU - Díaz Infante Velasco, Saúl

AU - Jerez, Silvia

AU - Chen-Charpentier, Benito

PY - 2018/3/8

Y1 - 2018/3/8

N2 - In this work, we model osteoclast-osteoblast population dynamics with random environmental fluctuations in order to understand the random variations of the bone remodeling process in real life. For this purpose, we construct a stochastic differential model for the interactions between the osteoclast and osteoblast cell populations using the parameter perturbation technique. We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p ≥ 1. Finally, we show that the introduction of noise in the deterministic model provides a fluctuating periodic solution. Numerical evidence supports our theoretical results and a discussion of the results is carried out.

AB - In this work, we model osteoclast-osteoblast population dynamics with random environmental fluctuations in order to understand the random variations of the bone remodeling process in real life. For this purpose, we construct a stochastic differential model for the interactions between the osteoclast and osteoblast cell populations using the parameter perturbation technique. We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p ≥ 1. Finally, we show that the introduction of noise in the deterministic model provides a fluctuating periodic solution. Numerical evidence supports our theoretical results and a discussion of the results is carried out.

KW - Bone remodeling Stochastic differential equations Brownian motion Moment boundedness Fluctuating periodic solution Osteoclasts Osteoblasts

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