Parameter study of global and cluster synchronization in arrays of dry friction oscillators

We investigate synchronization thresholds in arrays of identical classic stick-slip dry friction oscillators connected in a nearest neighbor fashion in closed and open ring network. Friction force is modeled by smoothened Stribeck model. Arrays of different length are checked in two parameter space (i.e., coupling coefficient vs. excitation frequency) for complete synchronization as well as cluster synchronization. Synchronization thresholds obtained by brute force numerical integration are compared with possible synchronization regions using the concept called master stability function in the form of two-oscillator reference probe. The results show existence of both complete synchronization and cluster synchronization regions in the investigated systems and confirm that two-oscillator probe can be applied for prediction of synchronization thresholds in systems with stick-slip phenomenon.