Application of symbolic recurrence to experimental data, from firearm prevalence to fish swimming

Recurrence plots and recurrence quantification analysis are powerful tools to study the behavior of dynamical systems. What we learn through these tools is typically determined by the choice of a distance threshold in the phase space, which introduces arbitrariness in the definition of recurrence. Not only does symbolic recurrence overcome this difficulty, but also it offers a richer representation that book-keeps the recurrent portions of the phase space. Using symbolic recurrences, we can construct recurrence plots, perform quantification analysis, and examine causal links between dynamical systems from their time-series. Although previous efforts have demonstrated the feasibility of such a symbolic framework on synthetic data, the study of real time-series remains elusive. Here, we seek to bridge this gap by systematically examining a wide range of experimental datasets, from firearm prevalence and media coverage in the United States to the effect of sex on the interaction of swimming fish. This work offers a compelling demonstration of the potential of symbolic recurrence in the study of real-world applications across different research fields while providing a computer code for researchers to perform their own time-series explorations.