Besicovitch almost periodic solutions for a stochastic generalized Mackey-Glass hematopoietic model

Xianying Huang; Yongkun Li; Xianying Huang; Yongkun Li

doi:10.3934/math.20241294

AIMS Mathematics

2024, Volume 9, Issue 10: 26602-26630. doi: 10.3934/math.20241294

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Research article

Besicovitch almost periodic solutions for a stochastic generalized Mackey-Glass hematopoietic model

Xianying Huang ,
Yongkun Li ^,

Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China

Received: 05 July 2024 Revised: 29 August 2024 Accepted: 10 September 2024 Published: 13 September 2024
MSC : 34K14, 34K50, 92D25

This article aimed to investigate the existence and stability of Besicovitch almost periodic ($ B_{ap} $) positive solutions for a stochastic generalized Mackey-Glass hematopoietic model. To begin with, we used stochastic analysis theory, inequality techniques, and fixed point theorems to prove the existence and uniqueness of $ \mathcal{L}^p $-bounded and $ \mathcal{L}^p $-uniformly continuous positive solutions for the model under consideration. Then, we used definitions to prove that this unique positive solution is also a $ B_{ap} $ solution in finite-dimensional distributions. In addition, we established the global exponential stability of the $ B_{ap} $ positive solution using reduction to absurdity. Finally, we provided a numerical example to verify the effectiveness of our conclusions.
- stochastic Mackey-Glass hematopoietic model,
- Besicovitch almost periodic solutions,
- finite-dimensional distributions,
- stability
Citation: Xianying Huang, Yongkun Li. Besicovitch almost periodic solutions for a stochastic generalized Mackey-Glass hematopoietic model[J]. AIMS Mathematics, 2024, 9(10): 26602-26630. doi: 10.3934/math.20241294

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Abstract

This article aimed to investigate the existence and stability of Besicovitch almost periodic ($ B_{ap} $) positive solutions for a stochastic generalized Mackey-Glass hematopoietic model. To begin with, we used stochastic analysis theory, inequality techniques, and fixed point theorems to prove the existence and uniqueness of $ \mathcal{L}^p $-bounded and $ \mathcal{L}^p $-uniformly continuous positive solutions for the model under consideration. Then, we used definitions to prove that this unique positive solution is also a $ B_{ap} $ solution in finite-dimensional distributions. In addition, we established the global exponential stability of the $ B_{ap} $ positive solution using reduction to absurdity. Finally, we provided a numerical example to verify the effectiveness of our conclusions.

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