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

Abstract

Characterization of strange attractors exhibiting chaotic dynamics may be carried out through computation of metric, dynamical and topological invariants. The last of these are robust even under control parameter variations and hence have certain distinct advantages. In the present work, we carry out the topological analysis of the observed dynamics from a model autocatalytic 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 and relative rotational rates, is possible. The analyses of these invariants yield the template and the Markov transition matrix that contain in them valuable topological information about the system dynamics. The results obtained show that the two systems possess similar topological characteristics and follow the horseshoe mechanism. This information should help in developing design and control algorithms for these systems.