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 1/λ lncosh(λx) nonlinearity. In contrast to the other smooth approximation, the equation approximation has the property of yielding the absolute value nonlinearity |x| as the limit case when λ parameter goes to infinity. The bifurcation maps and attractors of introduced Chua's circuit obtained for different λ 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.