Characterization of chaotic dynamics - II: topological invariants and their equivalence for an autocatalytic model system and an experimental shearedpolymer solution

Characterization of strange attractors exhibiting chaotic dynamics may be c arried out through computation of metric, dynamical and topological invaria nts. The last of these are robust even under control parameter variations a nd hence have certain distinct advantages. In the present work. we carry ou t the topological analysis of the observed dynamics from a model autocataly tic reacting system and an experimental polymer solution subjected to shear . Low dimensional chaotic dynamics are observed in both these systems. The results show the global characterization and classification of the dynamics for both systems based on topological invariants. viz., linking numbers an d relative rotational rates, is possible. The analyses of these invariants yield the template and the Markov transition matrix that contain in them va luable topological information about the system dynamics. The results obtai ned show that the two systems possess similar topological characteristics a nd follow the horseshoe mechanism. This information should help in developi ng design and control algorithms for these systems. (C) 2001 Elsevier Scien ce Ltd. All rights reserved.