Modified Burridge–Knopoff model with state dependent friction

A modified version of the Burridge–Knopoff model including a simple model for state dependent friction force was derived. The friction model describes a velocity weakening of friction between moving blocks and an increase of static friction during stick periods. It provides a simplified but qualitatively correct stability diagram for the transition from smooth sliding to stick-slip behavior as observed in various tribological systems. Attractor properties of the model dynamic equations were studied under a broad range of parameters for 1- and 2-dimensional systems.