On catastrophic sliding bifurcations, and hunting ducks in nonsmooth flows

On catastrophic sliding bifurcations, and hunting ducks in nonsmooth flows
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Abstract: The theory of nonsmooth dynamical systems is still young, but fruitful. We will present some recent theoretical advances, with application to experimental results from a superconducting sensor, and open problems of relevance to mechanical systems with friction or impact, such as the occurrence of nondeterministic chaos.

Abstract: The theory of nonsmooth dynamical systems is still young, but fruitful. We will present some recent theoretical advances, with application to experimental results from a superconducting sensor, and open problems of relevance to mechanical systems with friction or impact, such as the occurrence of nondeterministic chaos. We consider dynamical systems defined by differential equations that have discontinuities on certain switching surfaces in phase space (Filippov systems). Solution trajectories can cross a switching surface, or stick to and slide along it. Sliding describes stick-slip motion in dry-friction systems, switched feedback in control systems... in fact it can occur in any system whose differential equation jumps at some threshold. The consequences of discontinuity are revealed by `sliding bifurcations', a classification of which was completed only recently. The classification revealed catastrophic sliding bifurcations that can instantly destroy stable and periodic behaviour. We will discuss why these bifurcations are only revealed in nonsmooth systems, and show that they include, for instance, the "Canard" phenomenon.

Speaker
Dr Mike Jeffrey, Engineering Mathematics, University of Bristol
Venue
FN 110