Analysis of Chaotic Dynamics of Chua's Circuit with lncosh Nonlinearity

Abstract

Chua's circuit, which demonstrates one of the most complicated nonlinear dynamical behaviors, i.e. chaos, contains a three-segment Piecewise Affine (PWA) resistor as the unique nonlinear element. In this study, the non-smooth nonlinearity of Chua's circuit represented by absolute value is approximated with employing the (smooth) lncosh nonlinearity. In contrast to the other smooth approximation, the 1/lambda lncosh (lambda x) approximation has the property of yielding the absolute value nonlinearity |x| as the limit case when lambda parameter goes to infinity. The bifurcation maps and attractors of introduced Chua's circuit obtained for different lambda parameters are presented in the paper in a comparative way. Computer simulations show that lncosh approximation preserves the chaotic behavior and hence provides the possibility of analyzing the behavior of the Chua's circuit by the methods requiring smoothness.