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Abstract
A twofold is a singular point on the discontinuity surface of a piecewisesmooth vector field, at which the vector field is tangent to the discontinuity surface on both sides. If an orbit passes through an invisible twofold (also known as a Teixeira singularity) before settling to regular periodic motion, then the phase of that motion cannot be determined from initial conditions, and in the presence of small noise the asymptotic phase of a large number of sample solutions is highly random. In this paper we show how the probability distribution of the asymptotic phase depends on the global nonlinear dynamics. We also show how the phase of a smooth oscillator can be randomised by applying a simple discontinuous control law that generates an invisible twofold. We propose that such a control law can be used to desynchronise a collection of oscillators, and that this manner of phase randomisation is fast compared to existing methods (which use fixed points as phase singularities) because there is no slowing of the dynamics near a twofold.
Original language  English 

Article number  20150782 
Number of pages  19 
Journal  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 
Volume  472 
DOIs  
Publication status  Published  17 Feb 2016 
Research Groups and Themes
 Engineering Mathematics Research Group
Keywords
 piecewisesmooth
 desynchronization
 Filippov system
 sliding motion
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Dive into the research topics of 'Fast phase randomisation via twofolds'. Together they form a unique fingerprint.Projects
 2 Finished

Resolving discontinuities in the behaviour of dynamical systems
Jeffrey, M. R. (Principal Investigator)
1/03/16 → 30/06/18
Project: Research

When Worlds Collide: the asymptotics of interacting systems (Career Acceleration Fellowship)
Jeffrey, M. R. (Principal Investigator)
1/08/12 → 1/08/16
Project: Research