Assessing Deterministic Structures in Physiological Systems Using Recurrence Plot Strategies

The purpose of this paper is to review the basic principles of recurrence plot analysis (RPA) as applied to complex systems. Recurrence plots were first introduced in the physics literature by Eckmann et al.[1] in 1987. Seven years later, Webber and Zbilut[2] enhanced the technique by defining five nonlinear variables that were found to be diagnostically useful in the quantitative assessment of physiological systems and states. Starting with the working assumption that breathing patterns are inherently complex, we carefully define what is meant by the presence of determinism (constraining rules) in physiological systems. Then, as an instructive example, we illustrate how RPA can reveal deterministic structuring at the orthographic level of a well-known children’s poem. Next, we show how the multidimen- sional, nonlinear perspective of RPA can localize otherwise hidden rhythms in physiological systems and disambiguate between time series that are deceptively similar. Finally, we conclude with a discussion on new applications of RPA to nondeterministic systems and DNA orthography.