An upper limit for slow-earthquake zones: self-oscillatory behavior through the Hopf bifurcation mechanism from a spring-block model under lubricated surfaces

Abstract

The complex oscillatory behavior of a spring-block model is analyzed via the Hopf bifurcation mechanism. The mathematical spring-block model includes Dieterich–Ruina's friction law and Stribeck's effect. The existence of self-sustained oscillations in the transition zone – where slow earthquakes are generated within the frictionally unstable region – is determined. An upper limit for this region is proposed as a function of seismic parameters and frictional coefficients which are concerned with presence of fluids in the system. The importance of the characteristic length scale L, the implications of fluids, and the effects of external perturbations in the complex dynamic oscillatory behavior, as well as in the stationary solution, are take into consideration.