Causal Stability and Synchronization

Synchronization of chaos arises between coupled dynamical systems and is very well understood as a temporal phenomena which leads the coupled systems to converge or develop a dependence with time. In this work, we provide a complementary spatial perspective to this phenomenon by introducing the novel idea of causal stability. We then propose and prove a causal stability synchronization theorem as a necessary and sufficient condition for synchronization. We also provide an empirical criteria to identify synchronizing variables in coupled identical chaotic dynamical systems based on causality analysis on time series data of the driving system alone.