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

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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.

Keywords

discrete-time genetic regulatory networks / dirichlet boundary / reaction-diffusion / linear matrix inequalities

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