Detecting Causality in complex systems

In this work, recent and classical results on causality detection and predicability of a complex system have been reviewed critically. In the first part, I have extensively studied the Convergent Cross Mapping method [1] and I testedin cases of particular interest. I have also confronted this approach with the classical Granger framework for causality [2]. A study with a simulated Lotka-Volterra model has shown certain limits of this method, and I have obtained counterintuitive results. In the second part of the work, I have made a description of the Analog method [3] to perform prediction on complex systems. I have also studied the theorem on which this approach is rooted, the Takens’ theorem. Moreover, we have investigated the main limitation of this approach, known as the curse of dimensionality: when the system increases in dimensionality the number of data needed to obtain sufficiently accurate predictions scales exponentially with dimension. Additionally, finding the effective dimension of a complex systemstill an open problem. I have presented methods to estimate the effective dimension of the attractor of dynamical systems known as Grassberger-Procaccia algorithm and his extensions [4]. Finally, I have tested all these data driven machineries to a well-studied dynamical system, i.e. the Lorenz system, finding that the theoretical results are confirmed and the data needed scales as an exponential law N~Єd.