Articles | Volume 15, issue 1
Nonlin. Processes Geophys., 15, 1–12, 2008
https://doi.org/10.5194/npg-15-1-2008
Nonlin. Processes Geophys., 15, 1–12, 2008
https://doi.org/10.5194/npg-15-1-2008

  07 Jan 2008

07 Jan 2008

A model for aperiodicity in earthquakes

B. Erickson1, B. Birnir1, and D. Lavallée2 B. Erickson et al.
  • 1Department of Mathematics, University of California, Santa Barbara, USA
  • 2Institute of Crustal Studies, University of California, Santa Barbara, USA

Abstract. Conditions under which a single oscillator model coupled with Dieterich-Ruina's rate and state dependent friction exhibits chaotic dynamics is studied. Properties of spring-block models are discussed. The parameter values of the system are explored and the corresponding numerical solutions presented. Bifurcation analysis is performed to determine the bifurcations and stability of stationary solutions and we find that the system undergoes a Hopf bifurcation to a periodic orbit. This periodic orbit then undergoes a period doubling cascade into a strange attractor, recognized as broadband noise in the power spectrum. The implications for earthquakes are discussed.