A Gauss–Newton Method for the Synthesis of Periodic Outputs With Central Pattern Generators

It is assumed that a central pattern generator possesses an exponentially stable limit cycle, which originates a periodic output signal. We propose a method based on a Gauss-Newton iteration to determine the values of the neural coupling parameters that allows to approximate a given reference output signal. We present two applications. The first is a ring network of Morris-Lecar neurons, where the output of the system is the sum of the membrane potential of all neurons. The second is a network of six neural cells for the generation of the leg movements of a hexapod.