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Russell

AR01p95 Time Pioi

0    100    200    300    400    500

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FigurÄ™ 2. A time ordered plot of the observations of a synthetic AR(1) time senes. This is the same data as was displayed in the plot in FigurÄ™ 1.

Background from Chaos Theory

There are sonie properties of the iterates of dynamical systems that we will be interested in. These properties concem the convergence or apparent lack of convergence of the iterates in these systems. It tums out that there are several possibilities: the iterates may converge to a single point, the iterates may cycle among a set of points, and the iterates may fail to converge. If they fail to converge, then the iterates may either remain "close" to some set of points or fail to remain "close" to some set of points.

A good example of many of these conditions is provided by the Verhulst population growth model with the growth parameter set to different values. The Yerhulst population growth model is given by: