Connectionists: New paper on adaptive frequency oscillators

[Ludovic Righetti]

Dear Connectionist,


Researchers in dynamical systems and especially in nonlinear oscillators 
might be interested in the following paper published in Physica D about 
adaptive frequency oscillators, i.e. nonlinear oscillators that can 
adapt to the frequency of any periodic signal.


L. Righetti, J. Buchli, and A.J. Ijspeert.
Dynamic Hebbian learning in adaptive frequency oscillators.
Physica D, 216(2):269-281, 2006.

http://birg2.epfl.ch/publications/fulltext/righetti06b.pdf

Abstract:

Nonlinear oscillators are widely used in biology, physics and 
engineering for modeling and control. They are interesting because of 
their synchronization properties when coupled to other dynamical 
systems. In this paper, we propose a learning rule for oscillators which 
adapts their frequency to the frequency of any periodic or 
pseudo-periodic input signal. Learning is done in a dynamic way: it is 
part of the dynamical system and not an offline process. An interesting 
property of our model is that it is easily generalizable to a large 
class of oscillators, from phase oscillators to relaxation oscillators 
and strange attractors with a generic learning rule. One major feature 
of our learning rule is that the oscillators constructed can adapt their 
frequency without any signal processing or the need to specify a time 
window or similar free parameters. All the processing is embedded in the 
dynamics of the adaptive oscillator. The convergence of the learning is 
proved for the Hopf oscillator, then numerical experiments are carried 
out to explore the learning capabilities of the system. Finally, we 
generalize the learning rule to non-harmonic oscillators like relaxation 
oscillators and strange attractors.


More papers can be found on http://birg.epfl.ch


Best regards,

Ludovic Righetti


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Ludovic Righetti
Research Assistant

Biologically Inspired Robotics Group (BIRG)
Ecole Polytechnique Fédérale de Lausanne
EPFL - Station 14 - CH1015 Lausanne

Tel: +41 21 693 6620   Fax: +41 21 693 3705
URL: http://birg.epfl.ch   Email: ludovic.righetti at a3.epfl.ch
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