Filippov solutions in the analysis of piecewise linear models describing gene regulatory networks

DOI10.1016/j.na.2010.09.039zbMath1213.34022OpenAlexW1964901569MaRDI QIDQ611195

Arcady Ponosov, Anna Machina

Publication date: 14 December 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.09.039

zbMATH Keywords

differential inclusionFilippov solutiongene regulatory networksingular stationary pointsigmoid-type function

Mathematics Subject Classification ID

Ordinary differential inclusions (34A60) Protein sequences, DNA sequences (92D20)

Related Items (16)

Convergence properties of posttranslationally modified protein-protein switching networks with fast decay rates ⋮ Classification of Hidden Dynamics in Discontinuous Dynamical Systems ⋮ Solutions leaving a codimension-\(2\) sliding ⋮ A modelling framework for gene regulatory networks including transcription and translation ⋮ Hybrid models of genetic networks: mathematical challenges and biological relevance ⋮ 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 ⋮ Stability of stationary solutions of piecewise affine differential equations describing gene regulatory networks ⋮ Sensitive dependence on initial conditions in gene networks ⋮ Zeno breaking, the Contact effect and sensitive behaviour in piecewise-linear systems ⋮ The infinitesimal phase response curves of oscillators in piecewise smooth dynamical systems ⋮ 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 ⋮ Ramp approximations of sigmoid control functions in gene networks ⋮ An efficient algorithm for solving piecewise-smooth dynamical systems

Cites Work

• Unnamed Item
• Qualitative simulation of genetic regulatory networks using piecewise-linear models
• Logical identification of all steady states: The concept of feedback loop characteristic states
• Sliding modes in control and optimization. Transl. from the Russian
• Stable oscillations in mathematical models of biological control systems
• 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-smooth dynamical systems. Theory and applications
• A class of piecewise linear differential equations arising in biological models
• Global analysis of steady points for systems of differential equations with sigmoid interactions
• Analysis of continuous-time switching networks

This page was built for publication: Filippov solutions in the analysis of piecewise linear models describing gene regulatory networks