Efficient spectral domain technique for the frequency locking analysis of nonlinear oscillators

After discussing an implementation of the harmonic balance technique that enables the efficient determination of the limit cycles for a nonlinear autonomous dynamical system, we consider the frequency locking of a set of oscillators that is studied by means of a proper extension of the aforementioned approach. Harmonic balance is also used for the numerical computation of the Floquet exponents and eigenvectors of the frequency locked limit cycle, thus enabling the assessment of its stability properties. The proposed technique is applied to the study of the frequency locking properties of a set of coupled Chua’s oscillators as a function of several parameters.