Finite-time stability analysis of interacting genetic regulatory networks with spatial diffusion term.
Qi Liu1, Zhiqiang Lv2, Chengye Zou3
1School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, China.
Computers in Biology and Medicine
|June 25, 2025
Summary
This study analyzes stability in interacting genetic regulatory networks (GRNs) with diffusion. Novel methods ensure finite-time stability for these complex biological systems, validated by simulations.
Area of Science:
- Systems Biology
- Computational Biology
- Biophysics
Background:
- Genetic regulatory networks (GRNs) govern gene expression.
- Understanding the stability of interacting GRNs is crucial for cellular processes.
- Spatial diffusion and time delays introduce complexity in GRN dynamics.
Purpose of the Study:
- To investigate the finite-time stability of coupled genetic regulatory networks with spatial diffusion.
- To develop a robust analytical framework for analyzing the dynamic interactions within these systems.
- To establish less conservative stability criteria for GRNs under time-delayed and spatially influenced conditions.
Main Methods:
- Development of a coupled model for interacting GRNs.
- Utilizing a novel Lyapunov-Krasovskii functional for stability analysis.
- Application of a delay partitioning approach to handle time delays (zero or non-zero).
- Incorporation of Dirichlet boundary conditions to model spatial diffusion.
Main Results:
- Derivation of novel, less conservative stability criteria for the interacting GRNs.
- Demonstration of finite-time stable behavior under specified conditions.
- Validation of the theoretical criteria through numerical simulations.
Conclusions:
- The proposed methods effectively ensure finite-time stability for interacting GRNs with spatial diffusion and time delays.
- The derived stability criteria offer improved accuracy and reduced conservatism compared to existing methods.
- Numerical simulations confirm the efficacy of the analytical approach in predicting system behavior.
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