Revealing fractionality in the Rössler system by recurrence quantification analysis

Abstract

AbstractThis study discusses the results of a Recurrence quantification analysis (RQA) of the Rössler system with a fractional order ($$q_1$$ q 1 ) of the derivative in the first equation. The fractional order $$q_1$$ q 1 changes slightly in the range $$q_1 \in \langle 0.9,1.0\rangle$$ q 1 ∈ ⟨ 0.9 , 1.0 ⟩ . Even with such relatively small changes in the $$q_1$$ q 1 derivative, significant changes in the dynamics of the system are observed between the bifurcation diagrams determined for the bifurcation parameter a. Nevertheless, as $$q_1$$ q 1 decreases one can notice the preservation of some structures of the bifurcation diagram, in particular the main periodic windows of the integer-order Rössler 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.