@article{Yang2025, 
author = {Yongwei Yang and Yang Yu and Chunyun Xu and Chengye Zou},
title = {Passivity analysis of discrete-time genetic regulatory networks with reaction-diffusion coupling and delay-dependent stability criteria},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {5},
pages = {3111-3134},
keywords = {discrete-time genetic regulatory networks, dirichlet boundary, reaction-diffusion, linear matrix inequalities},
url = {https://www.sciopen.com/article/10.3934/era.2025136},
doi = {10.3934/era.2025136},
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.}
}