Interaction Detection via Probabilistic Fuzzy Logic for Coupled Dynamical Systems

Interaction detection for coupled dynamical systems plays a key role in understanding natural complex systems, and it is a difficult problem to establish the presence of coupling and interaction in the case of nonlinearity and noise. In this paper, a novel interaction detection algorithm has been proposed based on the probabilistic fuzzy logic by testing the degree of changes of one dynamical system caused by the other dynamical system with the observation time series of these two systems. The simulation results on the weekly coupled Henon maps show that the proposed algorithm with higher order of Markov property becomes more robust as noise increase in the observation data.