Stability Analysis of Genetic Regulatory Networks
Summary
The stability analysis of genetic regulatory networks explores how interconnected genes and their regulatory molecules maintain stable expression patterns in the face of intrinsic delays, stochastic fluctuations and spatial heterogeneity. Such networks are modelled by systems of differential or fractional-order equations, often with time-varying lags to represent transcriptional and translational processes, reaction–diffusion terms to capture spatial transport and probabilistic elements for molecular noise. Stability criteria assess whether network equilibria or periodic orbits persist under perturbations, distinguishing between global asymptotic, finite-time and robust stability. Methods typically employ Lyapunov–Krasovskii and Razumikhin functionals to manage delays, linear matrix inequalities for computational efficiency, and switching or dwell-time schemes for networks undergoing topological changes. Insights from stability analysis inform the design of synthetic circuits, disease modelling and targeted therapies by revealing parameter regimes that ensure reliable gene expression despite environmental or genetic disturbances.
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Stability Analysis of Genetic Regulatory Networks publication trend
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Technical terms
Lyapunov–Krasovskii functional: A generalisation of Lyapunov functions that incorporates integrals over past states to handle time-delay effects in dynamical systems.
Linear matrix inequality (LMI): A convex constraint on matrix variables used to formulate stability and control conditions that can be efficiently solved by numerical software.
Fractional-order system: A dynamical model incorporating derivatives of non-integer order to capture memory and hereditary properties of biological processes.
Razumikhin theorem: A criterion for stability of delay systems based on pointwise comparison of a Lyapunov function at current and past states without integral terms.
References
- State estimation for delayed genetic regulatory networks with reaction diffusion terms and Markovian jump. Complex & Intelligent Systems (2023).
- A Razumikhin approach to stability and synchronization criteria for fractional order time delayed gene regulatory networks. AIMS Mathematics (2021).
- Stability analysis of genetic regulatory networks via a linear parameterization approach. Complex & Intelligent Systems (2021).
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