A frequency‐domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential‐algebraic equations

Abstract

Abstract A general numerical technique is proposed for the assessment of the stability of periodic solutions and the determination of bifurcations for limit cycles in autonomous nonlinear systems represented by ordinary differential equations in the differential‐algebraic form. The method is based on the harmonic balance (HB) technique, and exploits the same Jacobian matrix of the nonlinear system used in the Newton iterative numerical solution of the HB equations for the determination of the periodic steady state. To demonstrate the approach, it is applied to the determination of the bifurcation curves in the parameters' space of Chua's circuit with cubic nonlinearity, and to the study of the dynamics of the limit cycle of a Colpitts oscillator. Copyright © 2007 John Wiley & Sons, Ltd.