Exploring the Lorenz Equations through a Chaotic Waterwheel

نویسنده

  • Stephanie Moyerman
چکیده

were derived by Edward Lorenz in 1963 as an over-simplified model of convection rolls within the atmosphere [1]. These coupled differential equations appear quite harmless; only two terms appear that cause non-linearity. Lorenz found, however, that the behavior of the system changed drastically over a wide range of parameters. For certain parameter values, Lorenz discovered that the system exhibited unpredictable and even chaotic behavior! Our goal in this paper is to directly explore the properties of the Lorenz equations and their exact mechanical analog, a chaotic waterwheel. In subsequent sections, the reader will encounter the derivation of these amazing equations, an exploration of parameter space, computational results and trajectories, and an in-depth look at chaos.

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تاریخ انتشار 2006