Yes, this is possible. This is also called "recurrence on a nominal scale" or "symbolic recurrences". There are several studies already using this approach. The difference to the standard recurrence approach is that instead of a neighbourhood of some size ε a recurrence can now be defined by the exact match of
x(
i) and
x(
j). Embedding of such binary or symbolic series mean that we consider words of length
m instead of reconstructing an
m-dimension phase space.
Here is some literature related to this variant of recurrence:
- C. Bandt, A. Groth, N. Marwan, M. C. Romano, M. Thiel, M. Rosenblum, J. Kurths: Analysis of Bivariate Coupling by Means of Recurrence, In: Mathematical Methods in Time Series Analysis and Digital Image Processing, Eds.: R. Dahlhaus and J. Kurths and P. Maas and J. Timmer, Springer, Berlin, Heidelberg, ISBN: 978-3-540-75631-6, 153–182 (2008). DOI:10.1007/978-3-540-75632-3_5
- R. V. Donner, U. Hinrichs, B. Scholz-Reiter: Symbolic recurrence plots: A new quantitative, European Physical Journal – Special Topics, 164(1), 85–104 (2008). DOI:10.1140/epjst/e2008-00836-2
- P. Faure, A. Lesne: Recurrence plots for symbolic sequences, International Journal of Bifurcation and Chaos, 20(6), 1731–1749 (2010). DOI:10.1142/S0218127410026794
- P. beim Graben, A. Hutt: Detecting Recurrence Domains of Dynamical Systems by Symbolic Dynamics, Physical Review Letters, 110(15), 154101 (2013). DOI:10.1103/PhysRevLett.110.154101