FREQUENCY DOMAIN APPROACH TO COMPUTATION AND ANALYSIS OF BIFURCATIONS AND LIMIT CYCLES: A TUTORIAL

Abstract

This paper introduces a frequency domain approach together with some techniques and methodologies for the computation and analysis of bifurcations and limit cycles arising in nonlinear dynamical systems. The frequency domain approach discussed in this paper originates from the classical feedback control systems theory, which has been proven to be successful and efficient for the computation and analysis of regular as well as singular bifurcations and stable as well as unstable limit cycles. While describing these techniques and methods, two representative yet distinct applications of the approach are studied in detail: The graphical analysis of multiple parametric bifurcation curves and the numerical computation of multiple limit cycles. Compared to the classical time domain methods, both the advantages and the limitations of the frequency domain approach are analyzed and discussed. It is believed that this frequency domain approach to the study of nonlinear dynamics has great potential and promising future in both theory and applications.