Fig. 1. Post-transient phase plane plot of autocatalytic reacting system dynamics.

Fig. 2. Composite recurrence plot for variables (x,y,z) for period-1 orbit for the autocatalytic reacting system.

Fig. 3. Typical orbits for the autocatalytic reacting system dynamics: (a) period-2 orbit encoded ‘10’; (b) period-4 orbit with the symbol sequence ‘1110’.

Fig. 4. Linking number calculation for period-2 and period-4 orbits ‘10’, ‘1110’ for the autocatalytic reacting system.

Fig. 5. Relative rotation rate calculations using initial conditions from a Poincare section for the ‘10’ and ‘1110’ orbits for the autocatalytic reacting system.

Fig. 6. The identified template for the autocatalaytic reacting system and the sheared polymer solution system.

Fig. 7. Post-transient phase plane plot for measurements from the sheared polymer solution. The data was denoised and standardized before carrying out integral–differential embedding.

Fig. 8. Periodic orbit visualizations for the sheared polymer solution: (a) period-2 orbit encoded by the symbol sequence ‘01’; (b) period-3 orbit encoded by the symbol sequence ‘011’.

Fig. 9. Sheared polymer solution linking number calculations for the period-2 orbit ‘01’ and period-3 orbit ‘011’.

Table 1. Intertwining matrix for the autocatalytic reacting system from all the extracted orbits. An identical matrix representation was obtained from the sheared polymer solution

Table 2. Linking matrix for the autocatalytic reacting system for extracted orbits. All topological indices are negative. An identical matrix was obtained from the sheared polymer solution data