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