Dynamics of oscillators coupled by a medium with adaptive impact
Article first published online: 8 FEB 2013
Copyright © 2013 Wiley Periodicals, Inc.
Volume 18, Issue 4, pages 41–54, March/April 2013
How to Cite
Daneshvar, R. (2013), Dynamics of oscillators coupled by a medium with adaptive impact. Complexity, 18: 41–54. doi: 10.1002/cplx.21439
- Issue published online: 13 MAR 2013
- Article first published online: 8 FEB 2013
- Manuscript Accepted: 28 DEC 2012
- Manuscript Received: 3 OCT 2012
In this article, we study the dynamics of coupled oscillators. We use mechanical metronomes that are placed over a rigid base. The base moves by a motor in a one-dimensional direction and the movements of the base follow some functions of the phases of the metronomes (in other words, it is controlled to move according to a provided function). Because of the motor and the feedback, the phases of the metronomes affect the movements of the base, whereas on the other hand, when the base moves, it affects the phases of the metronomes in return. For a simple function for the base movement (such as y = γx[rθ1 + (1 − r)θ2] in which y is the velocity of the base, γx is a multiplier, r is a proportion, and θ1 and θ2 are phases of the metronomes), we show the effects on the dynamics of the oscillators. Then, we study how this function changes in time when its parameters adapt by a feedback. By numerical simulations and experimental tests, we show that the dynamic of the set of oscillators and the base tends to evolve towards a certain region. This region is close to a transition in dynamics of the oscillators, where more frequencies start to appear in the frequency spectra of the phases of the metronomes. We interpret this as an adaptation towards the edge of chaos.