Using information-theory metrics to detect regime changes in dynamical systems

Dynamical systems can display a range of dynamical regimes (e.g. attraction to, fixed points, limit cycles, intermittency, chaotic behaviour) depending on the values of parameters in the system. In this work we demonstrate how non-parametric entropy estimation codes (in particular NPEET) based on the Kraskov method can be applied to find regime transitions in a 3D chaotic model (the Lorenz 1963 system) when varying the values of the parameters. These infromation-theory-based methods are simpler and cheaper to apply than more traditional metrics from dynamical systems (e.g. computation of Lyapunov exponents). The non-parametric nature of the method allows for handling long time series without a prohibitive computational burden.