Normal form analysis of Chua's circuit with applications for trajectory recognition

Abstract

Nonlinear analysis techniques are applied to Chua's circuit equations in which the piecewise-linear characteristic is replaced by a cubic nonlinearity. Center manifold theory is used to derive a reduced order expression for Chua's circuit near the equilibria. Normal form theory is applied to simplify the form of the dynamics on the center manifold. Closed-form expressions for the normal form coefficients are obtained in terms of the dynamics on the center manifold. A one parameter bifurcation function is derived from the normal form expression that describes the amplitude of stable limit cycles transverse to the Hopf bifurcation curve. The results of the analysis are illustrated by an array of Chua's circuits used for trajectory recognition.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>