Time-Series Analysis

Abstract

Up until now we have examined mathematical descriptions of dynamical systems and seen how different types of behavior can be generated, such as fixed points, limit cycles, and chaos. The goal of applied dynamics is to relate these mathematical systems to physical or biological systems of interest. The approach we have taken so far is model building—we use our understanding of the physical system to write dynamical equations. For example, we used our understanding of the interaction of predators and prey to motivate the Lotka-Volterra equations. These equations then suggested the types of dynamics we were likely to observe in the field, such as population oscillations around a fixed point, or extinction.