Articles | Volume 24, issue 3
Nonlin. Processes Geophys., 24, 419–433, 2017
Nonlin. Processes Geophys., 24, 419–433, 2017

Research article 04 Aug 2017

Research article | 04 Aug 2017

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

Valentina Castellanos-Rodríguez1,2, Eric Campos-Cantón2,3, Rafael Barboza-Gudiño1, and Ricardo Femat2 Valentina Castellanos-Rodríguez et al.
  • 1Instituto de Geología, Universidad Autónoma de San Luis Potosí, San Luis Potosí, México
  • 2Instituto Potosino de Investigación Científica y Tecnológica A.C., San Luis Potosí, México
  • 3Mathematics Department, University of Houston, Houston, Texas 77204-3008, USA

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.

Short summary
A spring-block model is used to determine an upper limit of slow-earthquake zones through study of self-oscillatory behavior with the Hopf bifurcation mechanism. What is the role of fluids in the mechanism of energy dissipation? Are the variations in oscillatory behavior (in the transition zone) due to external forces? What are the limits of parameters for this to occur? The proposed limit makes a difference to oscillatory behavior. Oscillation frequency, L, and fluids are related to results.