Frictional auto oscillations in the simple models of the earthquake

Annotation In the present work for modeling of seismic processes the dynamics of tectonic plate motion with Stribeck –effect of friction force is considered. In Khaickin problem of simple single block system for low velocities Van der Pol equation of friction auto-oscillations is obtained. Existence of „stick-slip“ dynamics investigation of which is important for relevance of possible mechanisms of the earthquake processes, is shown. Dynamics of two connected Van der Pol oscillator is considered, in which at presence of external periodic force on the background of low frequency periodic “tectonic” signal the high “seismic” oscillations are obtained. Such signals are obtained due to real seismic signal treatment, which reveals good agreement of our model with actual seismic observations. In the work also the nonlinear dynamics of one and two-block systems due to different analytical models of dry frictions without velocity restrictions is studied using numerical methods and possibility of „stick-slip“ motion as well as determined chaos taking into account the Stribeck – effect is shown. In the model regular and chaotic motions are studied by virtue of spectral analysis of obtained signals, bifurcation diagrams and Puancare section of phase trajectories. Existence of determined chaos in such simple models complicate Earthquake forecasting by seismic signal analyzing, but gives physical scenario of the process.