Generating series for drawing output of dynamical systems

摘要

We provide the drawing of the output of dynamical system ( ), particularly when the output is rough or near instability points. ( ) being analytical in a neighborhood of the initial state q(0) and de- scribed by its state equations, its output y(t) in a neighborhood of t = 0 is obtained by \evaluating" its generating series. Our algorithm consists in juxtaposing local approximating outputs on successive time intervals [ti; ti+1]0 i n1, to draw y(t) everywhere as far as possible. At every point ti+1 we calculate at order k an approximated value of each component qr of the state; on every interval [ti; ti+1]0 i n1 we calculate an approximated output. These computings are obtained from the symbolic expressions of the generating series of qr and y, truncated at order k, speci ed for t = ti and \evaluated". A Maple package is built, providing a suitable result for oscillating out- puts or near instability points when a Runge-Kutta method is wrong.