Limit cycle perturbations for parametric modulation of central pattern generators

We study the modulation of the output signal of a Central Pattern Generator (CPG) through variations of the coupling parameters between the neurons. It is assumed that a given CPG possesses an exponentially stable limit cycle which originates a periodic output signal. We propose a method that allows to find the variations of the coupling parameters that change the network output in order to approximate a given reference signal. This problem is relevant in many applications. For instance, in robotics locomotion is desirable to change the output of a network in order to change the frequency or the amplitude of the legs movements. We present applications to ring networks and to the quadruped model developed by Golubitsky and coworkers.