Introduction to Nonlinear Models
Gerard V. Middleton, David M. Rubin, 1995. "Introduction to Nonlinear Models", Nonlinear Dynamics and Fractals: New Numerical Techniques for Sedimentary Data, Gerard V. Middleton, Roy E. Plotnick, David M. Rubin
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In the following discussion we will use the term “model” as a short form of “mathematical model”, that is, a set of equations that are designed to represent some aspect of the real world. We recognize that other types of models are possible, e.g., conceptual models that cannot be exactly quantified, or physical models, that are generally models built of real materials, but at a smaller scale than the real phenomenon. We can recognize two different extreme types of mathematical models.
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The intention of these notes is to provide sedimentary geologists with an introduction to the new techniques for analyzing experimental and observational data provided by the rapid development of those disciplines generally known as Fractals and Nonlinear Dynamics (chaos theory). A general introduction to a minimum of theory is given, but most of the space is devoted to show how these ideas are useful for interpreting sedimentary data. The main applications are likely to be time series or spatial profiles or two-dimensional maps or images. Sedimentary geologists deal every day with actual time series, such as measurements of current velocity or suspended concentration at a station, or with virtual time series, such as stratigraphic sections, well logs, or topographic profiles yet few geologists know much about the new numerical techniques available to analyze such data.