A classification of nonlinear systems: an entropy based approach

This paper exploits concepts derived from the thermodynamics of curves for the analysis and classification of dynamic systems. In particular, a new indicator based on an entropy measure is used to retrieve some information about the degree of irregularity of a curve. Irregularity is meant as a distance from the ordered situation of a sequence of points on a straight line. The proposed indicator is used to compare the evolution of trajectories in the state space for any dynamic system, and some of its properties are very interesting for the study and classification of nonlinear systems. Nowadays classification of nonlinear systems is still a tough subject, and there are not yet systematic approaches to tackle it. It would be useful however, especially for industrial applications, to know how much a dynamic system behaves like a linear system. The proposed indicator has interesting properties, in particular it provides a finite value which does not depend on stability issues and it always provides a constant unitary outcome when applied to linear systems. Nonlinearity of a dynamic system can hence be evaluated as a distance from the ideal linear condition. The proposed indicator was then tested for several benchmark problems, also for chaotic systems to emphasize the theoretical expectations.