Exercises for Chaos Under Control

Chapter 4: Chaos

In this set of exercises "BANKING" and "TENT MAP" refer to Rules and "HISTOGRAM," "BIFURCATION," and "TIMESERIES" refer to Options in the IterateAgainSam Program.

In Noise, Noise, Noise we investigate some properties of the pendulum.

In Linear Dynamics we study the dynamics of linear processes, modeled on banking. We discover a graphical formulation of fixed points, and visual cues to their stability.

In Limits to Growth we study dynamics of very simple nonlinear systems.

In the Tent Map we introduce one of the simplest systems exhibiting chaos. We locate fixed points and 2-cycle points analytically, and determine the band-merging point.

In the Butterfly Effect we perform numerical experiments on sensitive dependence on initial conditions.

In Strange Attractors we study the variety of attractors for the tent map in the chaotic range of its behavior.

In the Family Portrait of Attractors we paste together the information of the previous section into a single, global picture.

In Some Dust in the Tent we see what happens to the tent dynamics when s > 2 and most points "end tragically at -infinity.".

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