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

nonlinear processes in geophysics

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