Measuring the direction and the strength of coupling in nonlinear Systems-a modeling approach in the State space

We present a novel signal processing methodology to determine the direction and the strength of coupling between coupled nonlinear systems. The methodology is based on multivariate local linear prediction in the reconstructed state spaces of the observed variables from each multivariable nonlinear system. Application of the method is illustrated with systems of coupled Rossler and Lorenz oscillators in various coupling configurations. The obtained results are compared with ones produced by the use of the directed transfer function, a model-based method in the time domain. Through a surrogate analysis, it is shown that the proposed method is more reliable than the directed transfer function in identifying the direction and strength of the involved interactions.