The synchronization of coupled stochastic systems driven by symmetric α-stable process and Brownian motion

The synchronization of stochastic differential equations (SDEs) driven by symmetric ?-stable process and Brownian Motion is investigated in pathwise sense. This coupled dynamical system is a new mathematical model, where one of the systems is driven by Gaussian noise, another one is driven by non- Gaussian noise. In this paper, we prove that the synchronization still persists for this coupled dynamical system. Examples and simulations are given.

Predictability of a low-order interactive ensemble

In this paper, numerical and analytical studies were performed to uncover the mechanisms controlling the changes in ensemble spread of a low-order coupled model with multiple atmospheric realizations. An interactive ensemble approach was applied to a coupled dynamical system based on two versions of the Lorenz 63 model designed in order to imitate the behavior of a coupled system with different time scales. In the dynamic system used in this work the spread of ensemble members is highly dependent on the mean state corresponding to asymmetries in predictability. The slowness of the slow model and the intensity of the boundary forcing anomalies both contribute to the asymmetry and phase locking of both subsystems. The mechanisms controlling the fast model spread were uncovered revealing uncertainty dynamics depending on the location of ensemble members in the fast model phase space and implicitly on the slowness and magnitude of the slow model anomalies.