Local minimum redundancy representation of a system for estimating the number of its degrees of freedom

Fractional dimension estimation is an important tool for characterizing chaotic systems. However it has been shown that a fractional dimension estimate may lead to a misinterpretation of the nature of a system. The authors present some new results on the local intrinsic dimension (LID) approach, based on a local linear minimum redundancy representation of the system, and using higher order statistics (HOS). They recall the formulation of the LID approach, and put forward a new justification of the method for autonomous by ordinary differential equations (ODE) driven systems. They present some qualitative analysis of the LID method, and justify the need of introducing HOS for discriminating stochastic from deterministic processes, via the definition of the number of degrees of freedom (DOF) involved in the system. These ideas are illustrated and discussed through examples.