Frequency Domain Method for the Dichotomy of Modified Chua's Equations

On condition of dichotomy, it is pointed out that in Lorenz and a kind of Rössler-like system chaotic attractors or limit cycles will disappear if nonlinearity of the product of two variables is replaced by some single variable nonlinearity, for example, nonlinearity of Chua’s circuit. Furthermore, an extended Chua’s circuit with two nonlinear functions is presented. By computer simulation it is shown that oscillating phenomena in the extended Chua’s circuit are richer than the single Chua’s circuit. The corresponding extension for smooth Chua’s equations is also considered. The effects of input and output coupling are analyzed for the extended Chua’s circuit.