# David Barton : Numerical continuation for investigating nonlinear systems: from model to experiment

Numerical continuation is a tool for investigating the bifurcation structure of a nonlinear dynamical system with respect to the system parameters. It is most often used to "carve up" parameter space into regions of qualitatively different behaviour by finding and tracking bifurcations (e.g., Hopf bifurcations) as the system parameters change. This talk will give an introduction to the theory behind numerical continuation and go on to discuss recent developments in the field.

Particular attention will be paid to numerical continuation of systems with non-smoothness, motivated by the example of intermittent contacts in a model of orthogonal cutting (turning). Rich dynamical behaviour is present in this model due to the presence of a grazing bifurcation which denotes the transition point from constant contact of the cutting tool with the workpiece to intermittent contact. Using numerical continuation it is possible to elucidate the full bifurcation structure of the system, something that would be extremely difficult with other methods.

Finally, numerical continuation will be demonstrated as applied to a physical experiment (so-called control-based continuation): a nonlinear energy harvesting device. Numerical continuation in this context allows the investigation of a physical device without prior knowledge of a model. Both stable and unstable motions can be investigated and bifurcations found directly. As such these investigations may aid in establishing what an appropriate mathematical model could be.

**Category**: Nonlinear and Complex Systems**Duration**: 01:39:53**Date**: December 1, 2009 at 2:45 PM-
**Tags:**seminar, CNCS Seminar

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