Numerical simulation of piecewise-linear models of gene regulatory networks using complementarity systems
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Publication:2448782
DOI10.1016/j.physd.2013.11.013zbMath1402.92194OpenAlexW2995133334MaRDI QIDQ2448782
Hidde de Jong, Bernard Brogliato, Vincent Acary
Publication date: 5 May 2014
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://hal.inria.fr/hal-00924044/file/VAHJBB.pdf
differential inclusionspiecewise-linear modelscomplementarity systemsnonsmooth dynamical systemsFilippov solutions
Biochemistry, molecular biology (92C40) Cell biology (92C37) Computational methods for problems pertaining to biology (92-08) Systems biology, networks (92C42)
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Uses Software
Cites Work
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- Qualitative simulation of genetic regulatory networks using piecewise-linear models
- Stability of stationary solutions of piecewise affine differential equations describing gene regulatory networks
- Filippov solutions in the analysis of piecewise linear models describing gene regulatory networks
- Dynamics of actively regulated gene networks
- Control design for sustained oscillation in a two-gene regulatory network
- On the solution of NP-hard linear complementarity problems
- A high accuracy method for solving ODEs with discontinuous right-hand side
- Discontinuous systems. Lyapunov analysis and robust synthesis under uncertainty conditions
- Implicit Euler numerical scheme and chattering-free implementation of sliding mode systems
- Nonsmooth modeling and simulation for switched circuits.
- Sliding modes in control and optimization. Transl. from the Russian
- Foundations of a theory of discontinuous systems. I
- Stable oscillations in mathematical models of biological control systems
- Enumeration approach for linear complementarity problems based on a reformulation-linearization technique
- Interfaces to PATH 3.0: Design, implementation and usage
- A comparison of large scale mixed complementarity problem solvers
- A methodological basis for description and analysis of systems with complex switch-like interactions
- Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics
- Comparing different ODE modelling approaches for gene regulatory networks
- Analysis and generic properties of gene regulatory networks with graded response functions
- Piecewise-linear models of genetic regulatory networks: equilibria and their stability
- Symbolic reachability analysis of genetic regulatory networks using discrete abstractions
- Numerical methods for nonsmooth dynamical systems. Applications in mechanics and electronics
- Higher order Moreau's sweeping process: mathematical formulation and numerical simulation
- Differential variational inequalities
- Absolute stability and the Lagrange--Dirichlet theorem with monotone multivalued mappings
- On the equivalence between complementarity systems, projected systems and differential inclusions
- Singular Dynamics in Gene Network Models
- Convergence of Time-Stepping Schemes for Passive and Extended Linear Complementarity Systems
- An implicit enumeration procedure for the general linear complementarity problem
- Difference Methods for Differential Inclusions: A Survey
- Variable structure systems with sliding modes
- Variational Analysis
- A class of piecewise linear differential equations arising in biological models
- Linear Complementarity Systems
- Finite-Dimensional Variational Inequalities and Complementarity Problems
- Switching and Finite Automata Theory
- Consistency of a time-stepping method for a class of piecewise-linear networks
- Chattering-Free Digital Sliding-Mode Control With State Observer and Disturbance Rejection
- Analysis of continuous-time switching networks
