On the normalized spectral entropy of the chaotic states

The chaotic states of a nonlinear system can be characterized by calculating the entropy of its frequency spectrum. Three examples of nonlinear differential equations, the Lorenz, Duffing and van der Pol equations, are included as illustrations. High values of the normalized spectral entropy are found to reflect chaos. 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. Thus, the above characteristics are considered to be useful to decide whether a nonlinear system is chaotic or not.