MURPHYS-HSFS-2014 - 7th International Workshop on Multi-Rate Processes & Hysteresis, 2nd International Workshop on Hysteresis and Slow-Fast Systems, April 7-11, 2014 - Abstract
Gol'dshtein, Vladimir
The chemical kinetic model reduction is often based on the observation that the full chemical kinetics set accesses only a small portion of the state space during its evolution. This is mainly due to the fact that such system has several different time scales. Fast reactions dominate initially and equilibrate quickly. If a corresponding fast-slow division is explicit then the classical theory of Singularly Perturbed System (SPS) is applicable. It permits us to decompose any solution (trajectory) to fast and slow parts that belongs correspondingly to a fast and slow invariant manifolds. Most known and popular technics of the model reduction such as Intrinsic Low-Dimensional Manifolds and Computational Singular Perturbation methods realized importance of slow invariant manifolds. Both quoted methods based on local analysis in a vicinity of slow invariant manifolds. However, the importance of fast invariant manifolds is much less transparent, though without an accurate knowledge about fast manifolds (fast fibers in other terminology) slow manifolds cannot be appropriately identified. We shall discuss a concept of Singularly Perturbed Vector Fields (SPVF) that is a coordinate free theory of singularly perturbed systems with the main emphasis made on fast invariant manifolds. The method is based on a special algorithm (global quasi-linearization) that permits us to find a global fast-slow division. Motivation and application of the method will be demonstrated by a simple model example and practical models.