I have been reading James Gleick’s Chaos and I must confess that I am very impressed with the book so far. I am beginning to realize some of the practical applications of non-linear dynamics to analog circuit design, however, more on that later. What has been very interesting is the slow change in the mentality of the scientific world, from the notion that a small change in a systems initial conditions only warrants a small change in the output, to the reality that small changes in initial conditions can generate wildly different results. One of the pioneers in this field was the late Edward Lorenz. He discovered that a slight change (less than 1%) in the initial conditions of his deterministic weather model, which was numerically integrated, would cause the outcome to diverge from the unperturbed simulation to the point that the two weather systems were completely different after several days. The error in his integrator could not account for this disparity, therefore, he went through some analytic computations and found that simple differential equations can have very complex behaviors that were very dependent on initial conditions. He published his results in the Journal of Atmospheric Sciences, a paper that is well worth looking over. For those who are not mathematically inclined, looking over the introduction and conclusion should provide some insight into the paper. Additionally, this is the paper where the often duplicated Lorenz attractor, or butterfly attractor (figure 2) makes its first appearance.

( 1963lorenz-deterministic-nonperiodic-flow )

 
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