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Chaos, Dynamics, and Fractals by Joseph L. McCauley

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2

Introduction to deterministic chaos

2.1   The Lorenz model, the Lorenz plot, and the binary tent map

We begin with the way that deterministic chaos was discovered numerically in a system of three coupled nonlinear differential equations by the meteorologist E. Lorenz, in an attempt to integrate the model on a computer. In addition, Lorenz showed analytically that orbits are attracted to enter a certain phase space volume from which escape is impossible, but which contains no stable classical attractors (equilibria, limit cycles, and tori). Consequently, he discovered numerically that nearby initial conditions yielded trajectories with entirely different spatial patterns.

The bifurcation sequence for the Lorenz model was discussed in the first ...

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