Poincaré Map

 A continuous flow can generate a discrete map in at least two ways: by a time-T map and by a Poincaré map. A time-T map results when a flow is sampled at a fixed time interval T. That is, the flow is sampled whenever t = nT for n = 0, 1, 2, 3, and so on. The more important way (as described, for instance, […]

Linearization

   To calculate the stability of a fixed point consider a small perturbation,  The Taylor expansion (substituting eq. (4.16) into eq. (4.2)) about  gives It seems reasonable that the motion near the fixed point should be governed by the linear system since  . If  is an equilibrium point, then  is a matrix with constant entries. We can immediately write down the […]

Magnetic Deflection of Electrons

If you have not already done so please read the General Introduction to Experiments EF-1 and EF-2. In this experiment we consider the effect of a magnetic field on the motion of electrons. Just as the electric field represents the interaction of two charged particles at rest, the magnetic field represents the interaction of charged […]

Experimental Approach to Nonlinear Dynamics and Chaos

An Experimental Approach to Nonlinear Dynamics and Chaos is a textbook and areference work designed for advanced undergraduate and beginning graduate students. This book provides an elementary introduction to the basic theoretical andexperimental tools necessary to begin research into the nonlinear behavior of mechanical, electrical, optical, and other systems. A focus of the text is […]

Quadratic Map Program

The Quadratic Map Program for the Apple Macintosh computer allows the user to easily run, analyze, see, and hear data from the quadratic map (aka, the logistic map): which is the simplest example of a nonlinear system exhibiting chaotic and complex behavior. Like it’s cousin, the bouncing ball program, the quadratic map program strictly follows the Macintosh interface guidelines. Several windows […]