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Synchronization of a Network With Piecewise-Linear Dynamics

[+] Author Affiliations
Walter Gall, Ying Zhou

Rhode Island College, Providence, RI

Joseph Salisbury

Brandeis University, Waltham, MA

Paper No. DSCC2010-4230, pp. 297-303; 7 pages
doi:10.1115/DSCC2010-4230
From:
  • ASME 2010 Dynamic Systems and Control Conference
  • ASME 2010 Dynamic Systems and Control Conference, Volume 1
  • Cambridge, Massachusetts, USA, September 12–15, 2010
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-4417-5 | eISBN: 978-0-7918-3884-6
  • Copyright © 2010 by ASME

abstract

We consider two and three phase-oscillators as in the Kuramoto model of coupled oscillators, replacing the sine wave interaction with a sawtooth wave. We show that for the case of non-uniform input-symmetric coupling strengths, the non-smooth, piecewise-linear dynamics synchronizes when the coupling strengths are large enough to overcome the differences in the natural frequencies of the oscillators. Stability is analyzed separately in the regions where the dynamics is linearized. These regions are separated by the switching boundaries where the vector field is discontinuous.

Copyright © 2010 by ASME

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