Control instabilities and incite slow-slip in generalized Burridge-Knopoff models

TL;DR

This paper introduces a control method for generalized Burridge-Knopoff models to prevent avalanches, stabilize dynamics, and promote slow-slip, with potential applications in earthquake mitigation and complex system management.

Contribution

It applies the Theory of Control to stabilize and steer GBK models, enabling control over chaos, dissipation, and equilibrium states without precise frictional knowledge.

Findings

Successfully stabilizes and restricts chaos in GBK models

Guarantees slow frictional dissipation

Tunes models toward lower energy equilibria

Abstract

Generalized Burridge-Knopoff (GBK) models display rich dynamics, characterized by instabilities and multiple bifurcations. GBK models consist of interconnected masses that can slide on a rough surface under friction. All masses are connected to a plate, which slowly provides energy to the system. The system displays long periods of quiescence, interrupted by fast, dynamic events (avalanches) of energy relaxation. During these events, clusters of blocks slide abruptly, simulating seismic slip and earthquake rupture. Here we propose a theory for preventing GBK avalanches, control its dynamics and incite slow-slip. We exploit the dependence of friction on pressure and use it as a backdoor for altering the dynamics of the system. We use the mathematical Theory of Control and, for the first time, we succeed in (a) stabilizing and restricting chaos in GBK models, (b) guaranteeing slow frictional dissipation and (c) tuning the GBK system toward desirable global asymptotic equilibria of lower energy. Our control approach is robust and does not require exact knowledge of the frictional behavior of the system. Finally, GBK models are known to present Self-Organized Critical (SOC) behavior. Therefore, the presented methodology shows an additional example of SOC Control (SOCC). Given that the dynamics of GBK models show many analogies with earthquakes, we expect to inspire earthquake mitigation strategies regarding anthropogenic and/or natural seismicity. In a wider perspective, our control approach could be used for improving understanding of cascade failures in complex systems in geophysics, access hidden characteristics and improve their predictability by controlling their spatio-temporal behavior in real-time.