Multi-flag systems and ordinary differential equations

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...

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...

Summary: Ordinary Differential Equations

1 Initial Value Problem We are given a right hand side function f(t, y) with f : [t0, T ]×Rn → Rn and an initial value y0 ∈ Rn. We want to find a function y(t) with y : [t0, T ] → Rn such that y′(t) exists, is continuous and satisfies the initial value problem y′(t) = f (t, y(t)) , y(t0) = y0. (1) We assume that f(t, y) satisfies a Lipschitz condition with respect to y (at least for y with |y −...

Linearizable ordinary differential equations . ∗

Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential equations. We give several families of differential systems which illustrate how the integrability of the system passes through the solutions of a linear diff...