Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach

This paper presents a spectral approach, based on the harmonic-balance technique, for detecting limit-cycle bifurcations in complex nonlinear circuits. The key step of the proposed approach is a method for a simple and effective computation of the Floquet multipliers (FMs) that yield stability and bifurcation conditions. As a case-study, a quite complex system, Chua's circuit, is considered. It is shown that the spectral approach is able to accurately evaluate the most significant bifurcation curves.

[1]  Alberto L. Sangiovanni-Vincentelli,et al.  Simulation of Nonlinear Circuits in the Frequency Domain , 1986, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[2]  Carlo Piccardi,et al.  Bifurcations of limit cycles in periodically forced nonlinear systems: the harmonic balance approach , 1994 .

[3]  Alberto L. Sangiovanni-Vincentelli,et al.  Steady-state methods for simulating analog and microwave circuits , 1990, The Kluwer international series in engineering and computer science.

[4]  A. Michel Dynamics of feedback systems , 1984, Proceedings of the IEEE.

[5]  Alberto Tesi,et al.  A Frequency Method for Predicting Limit Cycle Bifurcations , 1997 .

[6]  Guanrong Chen,et al.  Predicting period-doubling bifurcations and multiple oscillations in nonlinear time-delayed feedback systems , 1998 .

[7]  Rabinder N Madan,et al.  Chua's Circuit: A Paradigm for Chaos , 1993, Chua's Circuit.

[8]  Alberto Tesi,et al.  A HARMONIC BALANCE APPROACH FOR CHAOS PREDICTION: CHUA’S CIRCUIT , 1992 .

[9]  C. Piccardi Harmonic balance analysis of codimension-2 bifurcations in periodic systems , 1996 .

[10]  Leon O. Chua,et al.  ON PERIODIC ORBITS AND HOMOCLINIC BIFURCATIONS IN CHUA’S CIRCUIT WITH A SMOOTH NONLINEARITY , 1993 .

[11]  Y. Kuznetsov Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[12]  A. Neri,et al.  State of the art and present trends in nonlinear microwave CAD techniques , 1988 .

[13]  Raymond Qu,et al.  Synchronization Analysis of Autonomous Microwave Circuits Using New Global-Stability Analysis Tools , 1998 .

[14]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis , 2021 .

[15]  Leon O. Chua,et al.  Steady-state analysis of nonlinear circuits based on hybrid methods , 1992 .

[16]  J. A. Kuznecov Elements of applied bifurcation theory , 1998 .

[17]  C. Piccardi Bifurcation analysis via harmonic balance in periodic systems with feedback structure , 1995 .

[18]  V. Rizzoli,et al.  Local stability analysis of microwave oscillators based on Nyquist's theorem , 1997 .