Passivity analysis of discrete-time genetic regulatory networks with reaction-diffusion coupling and delay-dependent stability criteria

Yongwei Yang; Yang Yu; Chunyun Xu; Chengye Zou; Yongwei Yang; Yang Yu; Chunyun Xu; Chengye Zou

doi:10.3934/era.2025136

Electronic Research Archive

2025, Volume 33, Issue 5: 3111-3134. doi: 10.3934/era.2025136

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Research article

Passivity analysis of discrete-time genetic regulatory networks with reaction-diffusion coupling and delay-dependent stability criteria

1.
School of Mathematics and Computer Science, Tongling University, Tongling 244061, China
2.
School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
3.
Department of Dermatology, Maternity and Child Health Hospital of Qinhuangdao, Qinhuangdao 066000, China

Received: 22 January 2025 Revised: 03 April 2025 Accepted: 27 April 2025 Published: 21 May 2025

Gene regulatory networks (GRNs) play a crucial role in biological processes, with their dynamic behaviors heavily influenced by the spatial organization of genes. In particular, reaction-diffusion mechanisms govern the coupling between adjacent spatial locations in continuous time GRNs. However, traditional models often ignore the spatial coupling and reaction-diffusion properties of these networks, especially in discrete-time settings. In order to solve this problem, a new discrete-time gene regulatory network model is proposed in this paper, which explicitly considers the mutual coupling between adjacent spatial positions. To ensure the passivity of the proposed model, delay-dependent stability criteria are established by constructing appropriate Lyapunov-Krasovskii functions formulated in terms of linear matrix inequalities. To showcase the effectiveness and validity of this approach, a numerical example is presented in this paper. The results reveal that the model accurately captures the spatial coupling and reaction-diffusion nature of gene regulatory networks in discrete time settings.
- discrete-time genetic regulatory networks,
- dirichlet boundary,
- reaction-diffusion,
- linear matrix inequalities
Citation: Yongwei Yang, Yang Yu, Chunyun Xu, Chengye Zou. Passivity analysis of discrete-time genetic regulatory networks with reaction-diffusion coupling and delay-dependent stability criteria[J]. Electronic Research Archive, 2025, 33(5): 3111-3134. doi: 10.3934/era.2025136

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Abstract

Gene regulatory networks (GRNs) play a crucial role in biological processes, with their dynamic behaviors heavily influenced by the spatial organization of genes. In particular, reaction-diffusion mechanisms govern the coupling between adjacent spatial locations in continuous time GRNs. However, traditional models often ignore the spatial coupling and reaction-diffusion properties of these networks, especially in discrete-time settings. In order to solve this problem, a new discrete-time gene regulatory network model is proposed in this paper, which explicitly considers the mutual coupling between adjacent spatial positions. To ensure the passivity of the proposed model, delay-dependent stability criteria are established by constructing appropriate Lyapunov-Krasovskii functions formulated in terms of linear matrix inequalities. To showcase the effectiveness and validity of this approach, a numerical example is presented in this paper. The results reveal that the model accurately captures the spatial coupling and reaction-diffusion nature of gene regulatory networks in discrete time settings.

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