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Transients in the Synchronization of Asymmetrically Coupled Oscillator Arrays
The European Physical Journal Special Topics
  • Carlos E. Cantos, Portland State University
  • David K. Hammond, Oregon Institute of Technology
  • J.J.P. Veerman, Portland State University
Document Type
Publication Date
  • Boundary value problems,
  • Autonomous vehicles -- Mathematical models,
  • Transients (Dynamics) -- Mathematical models,
  • Linear oscillators

We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.


This is the authors' version of a manuscript which was published online September 30, 2016 in The European Physical Journal Special Topics. The final publication is available at Springer via

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Citation Information
Cantos, C. E., Hammond, D. K., & Veerman, J. J. P. (2016). Transients in the synchronization of asymmetrically coupled oscillator arrays. The European Physical Journal Special Topics, 225(6-7), 1199-1209.