On the normalized spectral entropy of the chaotic states (Q1371306)

An extremely accurate method to characterize the chaotic states of a nonlinear system consists in the calculus of its frequency spectrum's entropy. This is the method used in his paper. The author presents several conclusions which allow to decide whether a nonlinear system is chaotic or not. One of them regards the high values of the normalized spectral entropy which reflect chaos; another one is that sharp variations in the normalized spectral entropy diagram result from the fact that the system becomes highly sensitive to the control parameters within the chaotic region. A clear correspondence is established between the bifurcation diagram and the normalized spectral entropy diagram for nonlinear dynamical systems. As an application, a numerical integration scheme is used to calculate the normalized spectral entropies for the Lorenz, Duffing and van der Pol equations.