HOPF BIFURCATIONS AND DEGENERACIES IN CHUA'S CIRCUIT — A PERSPECTIVE FROM A FREQUENCY DOMAIN APPROACH

DOI10.1142/S0218127499000171zbMath0937.37028WikidataQ129039273 ScholiaQ129039273MaRDI QIDQ4941645

Leon O. Chua, Jorge L. Moiola

Publication date: 8 June 2000

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

limit cyclesHopf bifurcationharmonic balanceLyapunov index

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Dynamical systems in control (37N35) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

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Control of Pyragas applied to a coupled system with unstable periodic orbits ⋮ Zero-Hopf bifurcation in a Chua system ⋮ A BIPARAMETRIC BIFURCATION IN 3D CONTINUOUS PIECEWISE LINEAR SYSTEMS WITH TWO ZONES: APPLICATION TO CHUA'S CIRCUIT ⋮ Bistable phase control via rocking in a nonlinear electronic oscillator ⋮ HOPF BIFURCATION FROM LINES OF EQUILIBRIA WITHOUT PARAMETERS IN MEMRISTOR OSCILLATORS ⋮ Control algorithm for creation of Hopf bifurcations in continuous-time systems of arbitrary dimension ⋮ IMPLICIT CRITERIA OF EIGENVALUE ASSIGNMENT AND TRANSVERSALITY FOR BIFURCATION CONTROL IN FOUR-DIMENSIONAL MAPS ⋮ DESIGNING HOPF BIFURCATIONS INTO NONLINEAR DISCRETE-TIME SYSTEMS VIA FEEDBACK CONTROL ⋮ Bifurcation analysis of a van der Pol-Duffing circuit with parallel resistor ⋮ DYNAMICS AT INFINITY OF A CUBIC CHUA'S SYSTEM ⋮ DEGENERATE HOPF BIFURCATIONS IN CHUA'S SYSTEM

Uses Software

• LOCBIF

Cites Work

• Classification and unfoldings of degenerate Hopf bifurcations
• A frequency method for predicting limit cycle bifurcations
• Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics
• Analytical approximation for period-doubling following a Hopf bifurcation
• Symmetry-breaking and first-period-doubling following a Hopf bifurcation in a three-dimensional system
• Some cubic systems with several limit cycles
• The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems
• CHUA’S CIRCUIT: RIGOROUS RESULTS AND FUTURE PROBLEMS
• ON PERIODIC ORBITS AND HOMOCLINIC BIFURCATIONS IN CHUA’S CIRCUIT WITH A SMOOTH NONLINEARITY
• Eleven small limit cycles in a cubic vector field
• Efficient determination of higher-order periodic solutions using n-mode harmonic balance