Inferring reaction systems from ordinary differential equations

Inferring reaction systems from ordinary differential equations

In Mathematical Biology, many dynamical models of biochemical reaction systems are presented with Ordinary Differential Equations (ODE). Once kinetic parameter values are fixed, this simple mathematical formalism completely defines the dynamical behavior of a system of biochemical reactions and provides powerful tools for deterministic simulations, parameter sensitivity analysis, bifurcation an...

A Unique Transformation from Ordinary Differential Equations to Reaction Networks

Many models in Systems Biology are described as a system of Ordinary Differential Equations, which allows for transient, steady-state or bifurcation analysis when kinetic information is available. Complementary structure-related qualitative analysis techniques have become increasingly popular in recent years, like qualitative model checking or pathway analysis (elementary modes, invariants, flu...

Ordinary Differential Equations and Dynamical Systems

Ordinary Differential Equations and Dynamical Systems

This manuscript provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore we consider linear equations, the Floquet theorem, and the autonomous...

From MIN model to ordinary differential equations

Biological interaction networks can be modeled using the Modular Interaction Network (MIN) formalism, which provides an intermediary modeling level between the biological and mathematical ones. MIN focuses on a simple but structured and versatile representation of biological knowledge, without targeting a particular analysis or simulation technique. In this paper, we propose a translation proce...