Stability of stationary solutions of piecewise affine differential equations describing gene regulatory networks

DOI10.1016/j.jmaa.2011.02.034zbMath1225.34056OpenAlexW2022604204MaRDI QIDQ536277

Arcady Ponosov, Anna Machina

Publication date: 16 May 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.02.034

zbMATH Keywords

stability analysisdifferential inclusionFilippov solutiongene regulatory networksingular stationary point

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Ordinary differential inclusions (34A60) Stability of solutions to ordinary differential equations (34D20) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (7)

State transition graph and stability of singular equilibria for piecewise linear biological models ⋮ Numerical simulation of piecewise-linear models of gene regulatory networks using complementarity systems ⋮ Coarse-grained optimization-driven design and piecewise linear modeling of synthetic genetic circuits ⋮ Sensitive dependence on initial conditions in gene networks ⋮ Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability ⋮ Periodic solutions of gene networks with steep sigmoidal regulatory functions ⋮ On inclusions arising in neural field modeling

Cites Work

• Filippov solutions in the analysis of piecewise linear models describing gene regulatory networks
• Logical identification of all steady states: The concept of feedback loop characteristic states
• Chaos, fractals, and noise: Stochastic aspects of dynamics.
• A methodological basis for description and analysis of systems with complex switch-like interactions
• Analysis and generic properties of gene regulatory networks with graded response functions
• Piecewise-linear models of genetic regulatory networks: equilibria and their stability
• A class of piecewise linear differential equations arising in biological models
• Global analysis of steady points for systems of differential equations with sigmoid interactions
• Unnamed Item

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