Synchronization conditions for stochastic landslide chain model with delayed coupling

Abstract

We examine the conditions for synchronization of landslide stochastic chain model with delayed coupling. Firstly, a new chain model for landslide dynamics is proposed, with the included effect of delayed coupling and background noise. The model is of the microscopic type, where the state of each block in the chain is influenced by the previous state of the same block and its neighbors as well as by noise. Secondly, we examine the stochastic synchronization of such a system of stochastic delay-differential equations. A sufficient condition for the exponential mean square stability of the synchronization is obtained. The sufficient condition indicates that the uni-directional asymmetric coupling induces the synchronization much more efficiently than the bi-directionally symmetric one. From the practical viewpoint, the results obtained confirm that different parts of the large unstable slope could exhibit synchronized activity under certain conditions, which indicates their possible larger influence on the structures (and generation of corresponding deformation) compared to the individual effect of unsynchronized activities.