Stochastic Delay Modeling of Landslide Dynamics

In this chapter, we provide results on the qualitative modeling of landslide dynamics under the assumption of delayed failure and the effect of background noise. Results obtained indicate that the examined time series, which represent the actual recordings of background noise, belong to a group of stationary linear stochastic processes with Gaussian inputs. Such noise is introduced as the additive term in the system of delay differential equations governing the dynamics of a spring-block model composed of n units with delayed failure. The friction law assumed in the model represents the cubic friction force. Results of the performed research, using mean-field approximation and numerical computation, indicate the conditions for the occurrence of Andronov-Hopf direct supercritical bifurcation. In particular, it is shown that small-amplitude background noise could contribute to the onset of instability if the system under study is on the verge of stability.