Multiplicity of positive periodic solutions for a discrete impulsive blood cell production model

Yan Yan; Yan Yan

doi:10.3934/math.20231354

AIMS Mathematics

2023, Volume 8, Issue 11: 26515-26531. doi: 10.3934/math.20231354

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Research article

Multiplicity of positive periodic solutions for a discrete impulsive blood cell production model

Yan Yan ^,

Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Received: 15 May 2023 Revised: 12 August 2023 Accepted: 28 August 2023 Published: 18 September 2023
MSC : 39A23, 39A60, 47H10, 92C37

In this paper, we investigate the multiplicity of positive periodic solutions of a discrete blood cell production model with impulse effects. This model is described by periodic coefficients and time delays, as well as nonlinear feedback with exponential terms. By employing the Krasnosel'skii fixed point theorem, we establish a sufficient condition for the existence of at least two positive periodic solutions. To this end, we construct solution transformation between an impulsive delay difference equation and the corresponding nonimpulsive delay difference equation. Aditionally, a solution representation of the positive periodic solution of the blood cell production model is presented. Moreover, a numerical example and its simulations are given to illustrate the main result.
- discrete blood cell production,
- positive periodic solutions,
- impulse effects,
- nonlinear feedback,
- Krasnosel'skii fixed point theorem
Citation: Yan Yan. Multiplicity of positive periodic solutions for a discrete impulsive blood cell production model[J]. AIMS Mathematics, 2023, 8(11): 26515-26531. doi: 10.3934/math.20231354

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Abstract

In this paper, we investigate the multiplicity of positive periodic solutions of a discrete blood cell production model with impulse effects. This model is described by periodic coefficients and time delays, as well as nonlinear feedback with exponential terms. By employing the Krasnosel'skii fixed point theorem, we establish a sufficient condition for the existence of at least two positive periodic solutions. To this end, we construct solution transformation between an impulsive delay difference equation and the corresponding nonimpulsive delay difference equation. Aditionally, a solution representation of the positive periodic solution of the blood cell production model is presented. Moreover, a numerical example and its simulations are given to illustrate the main result.

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