Computational Study of Complex Dynamics in Engineering Systems

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The study of the dynamic behavior of engineering systems (through experiments, modelling, and computation) is an integral part of the understanding, design, operation, and control of engineering processes, ranging from laboratory-scale experiments to operating chemical plants. Treating problems that range from periodic harvesting of a bioreactor to the response of large structures to oscillatory loads as time marching problems, initial value problems, has traditionally provided most of the information for systems dynamics. During the last ten years local bifurcation analysis have been developed as an alternative method to classify the behavior of nonlinear systems. In fact, algorithms are available for bifurcation analysis, e.g. AUTO, PITCON, DERPAR, PEFLOQ, etc. The algorithms are based on the numerical implementation of analytical procedures close to bifurcation points and iterative solution of nonlinear equations. However, most of these treat only periodic responses and local bifurcations. This research project will extend dynamic system studies to more general system response with special emphasis on interactive graphic data manipulation at the work station level.