On friction effects as a mechanism to induce complex dynamical behavior in earthquakes

"In this paper we analyze a nonlinear dynamical system that describes the kinetic mechanism between tectonic plates on the crust´s earth undergoing stick slip movement. The analysis includes friction effects and an empirical friction law of granite rocks. The phenomena involved in the analyzed model are Stribeck´s effect; Dieterich- Ruina´s law; and properties of media as a presence of fluids and deformation. Outcomes arise from analysis of the system, which is conceived by a single slider block of one degree of freedom over a roughness and lubricated surface and formulated by space-state model through a differential equation system. We describe the oscillatory behavior for both continuous and switched conditions in terms of the mathematical solutions. Periodic and aperiodic orbits exist under a driven force and even more complex behavior. A relationship is given between the stability of the switched system and the parameter related with the oscillation frequency associated to characteristic longitude of displacement of slider. A necessary condition for stability in an unstable regime is deduced, under certain conditions in terms of frictional and seismic parameters of the analyzed model. Thus, we show the stationary and aperiodic solutions that describe the friction mechanism inducing earthquakes with a complex and nonlinear behavior.