Title of the talk: "Flow curvature method applied to dynamical systems analysis"
The Flow Curvature Method is based on the idea that the trajectory curve, integral of any n-dimensional dynamical system may be considered as curve in Euclidean n-space having local metrics properties of curvatures. Thus, the location of the points where the curvature of the trajectory curve, integral of any ndimensional dynamical system, vanishes defines a manifold called: flow curvature manifold. This manifold (a curve in dimension, a surface in dimension 3, a hypersurface in higher dimension) enables to find again the main features of such n-dimensional dynamical system (fixed points and their stability, center manifolds, local bifurcation of codimension 1,…). More particularly, it has been established that the flow curvature manifold directly provides an approximation (up to a suitable order) of the slow invariant manifold of n-dimensional slow fast autonomous dynamical systems. Then the Flow Curvature Method (FCM) will be applied for determining an approximation of the slow invariant manifold of the Van der Pol system in dimension 2, of the Chua’s models in dimension 3, 4 and 5. Then, in order to compare the FCM with the so-called Computational Singular Perturbation Method (CSPM), the slow invariant manifold of the “Davis–Skodje problem” in dimension 2, of “a 3-species kinetics problem” in dimension 3, of the Lorenz-Krishnamurthy model in dimension 5 and of a model of a network of coupled enzymatic reactions in dimension 6 will be also analytically computed.
Jean-Marc Ginoux is a senior lecturer at the université de Toulon. He has a phd in applied mathematicis as well as history of sciences.
In his talk he wants to show us his differential geometric view on slow invariant manifolds. All those interested are very welcome to listen to his talk.