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Nonlinear Analysis

Bradford D. Allen, James Carifio

Abstract

Numerous nonlinear phenomena that exhibit discontinuous jumps in behavior have been modeled with catastrophe theory. Cobb's Cusp Surface Analysis Program (CUSP) provides a way to empirically estimate and test a nonlinear cusp catastrophe model. A model of emotion during problem solving is used to introduce catastrophe theory modeling and is discussed in conjunction with how to run CUSP, how to interpret the output, and how to improve CUSP's performance. Comparisons are made between linear regression and catastrophe theory models and between catastrophe theory gradient dynamics and Cobb's static statistical cusp model.

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Key concepts: Catastrophe theory, Cusp (singularity), Nonlinear system, Statistical theory, Statistical physics, Mathematics, Applied mathematics, Physics