A harmonic balance approach to bifurcation analysis of limit cycles

Abstract

This work provides an application of the harmonic balance (HE) technique to the stability and bifurcation analysis of limit cycles of dynamical systems amenable to be expressed in Lur'e system form. A numerically efficient spectral approach is exploited to evaluate the system limit cycle with an arbitrary number of harmonic components, which are then explouted to perform a linearized, small-change stability analysis of the limit cycle itself. On the basis of a Mittag-Leffer expansion of the determinant of the infinite matrix representing the linearized system, the limit cycle Floquet multipliers (FM) are evaluated and exploited to perform the bifurcation analysis. As an example of application, parameter space bifurcation conditions for classical Chua's circuit are thoroughly examined.