POL SCI 1 Lecture Notes - Lecture 7: Asteroid Family, Gw-Basic, Time Series
18 Sep 2017
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Document Summary
In this chapter we will teach the computer to search for chaotic solutions of simple equations with a single variable. The solutions are segments of lines, but the lines can wiggle in an incredibly complicated manner. The logistic equation (equation 1c) is an example of a dynamical system. Such systems are described by deterministic initial-value equations. This particular system has a single parameter r whose value determines the solution"s behavior for all initial values of x within the basin of attraction. This parameter is like a knob on a radio or on a stove that you can turn up or down to control the sound emitted by the radio or the convection in a pot of boiling soup. You can do a simple experiment to observe the period-doubling route to chaos. Go into your bathroom or kitchen and turn on the tap, only slightly, to produce a regular periodic pattern of drips.
