A statistical tool for analysing nonlinear properties of dynamical systems

A novel statistical indicator is introduced to evaluate the nonlinear behaviour of dynamical systems, as a support to other classic methods (e.g., Lyapunov exponents, entropy of curve methods). According to the theoretical properties of the proposed method, it is possible to infer the actual dimension of the phase space where the system dynamics evolve; it is possible to differentiate linear from nonlinear systems also in the presence of measurement noise; different dynamical systems that appear similar according to other indicators are further correctly distinguished. Theoretical expectations are confirmed by several examples of classic benchmark dynamical systems.