Harmonic Balance Analysis of Lur’e Oscillator Network With Non-Diffusive Weak Coupling

The central pattern generator (CPG) is a group of interconnected neurons, existing in biological systems as a control center for oscillatory behaviors. We propose a new approach based on the multivariable harmonic balance to characterize the relationship between the oscillation profile (frequency, amplitude, phase) and interconnections within the CPG, modeled as weakly coupled oscillators. In particular, taking advantage of the weak coupling, we formulate a low-dimensional matrix whose eigenvalue/eigenvector capture the perturbation in the oscillation profile due to the coupling. Then we develop an algorithm to estimate the perturbed oscillation profile of a given CPG, and suggest an optimization to synthesize the interconnections to produce a given oscillation profile.