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This study discusses the results of a Recurrence quantification analysis (RQA) of the R ̈ossler
system with a fractional order (q1) of the derivative in the first equation. The fractional order q1 changes
slightly in the range q1 ∈ 〈0.9, 1.0〉. Even with such relatively small changes in the q1 derivative, significant
changes in the dynamics of the system are observed between the bifurcation diagrams determined for the
bifurcation parameter a. Nevertheless, as q1 decreases one can notice the preservation of some structures
of the bifurcation diagram, in particular the main periodic windows of the integer-order R ̈ossler system.
The RQA shows clear differences between various regular windows of the integer system and only slight
changes in these windows are caused by an increase in the system’s fractionality. Nonetheless, by selecting
appropriate recurrence variables it is possible to expose the changes occurring in the regular windows under
the influence of the fractionality of the system. This approach allows for the detection of the fractional
character of the system through a recurrence analysis of the time series taken from periodic regions.
