Issues in Quantifying Variability from a Dynamical Systems Perspective

Variability is a critical aspect of a dynamical systems analysis. Because there are a number of numerical techniques that can be used in such an analysis, the calculation of variability has several issues that must be addressed. The purpose of this paper is to present a variety of quantitative methods for investigating variability from a dynamical systems perspective. The paper is divided into two major sections covering discrete and continuous methods. Each of these sections is subdivided into two sections. Within discrete methods, we discuss, first, the calculation of the discrete relative phase from a time-series history of two parameters and, second, the use of return maps. Using continuous methods, we present procedures for using angle-angle plots in the evaluation of relative phase. We then discuss the use of phase plots in the calculation of the continuous relative phase. Each of these methods presents unique problems for the researcher and the method to be used is determined by the nature of the question asked.