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CLUSTER SYNCHRONIZATION OF DRY FRICTION OSCILLATORS
Last modified: 2017-12-19
Abstract
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 (MSF) 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
We have performed a parameter study of complete and cluster synchronization properties in two-parameter space (coupling coefficient vs. angular frequency of excitation) of arrays of dry friction stick-slip oscillator. Two different network topologies have been applied, namely, open ring and closed ring. Analyzing synchronous regions we can conclude that the complete synchronization tends to occur for low coupling coefficients in both of these ring configurations. Such a situation results from configuration of eigenvalues of connectivity matrix. Increasing coupling causes that all eigenvalues can be found in synchronous interval of the MSF only for smaller values of coupling coefficient. Moreover, for lower values of excitation frequency friction oscillators synchronize even without spring coupling because we observe periodic behavior of network oscillators. In such a periodic case only the common drive is a sufficient factor for stabilizing the synchronous motion. For larger values of drive frequency, non-periodic dynamics of network nodes (chaotic or quasi-periodic) begins to dominate and then lower limit of synchronous interval of the MSF becomes nonzero.
We have performed a parameter study of complete and cluster synchronization properties in two-parameter space (coupling coefficient vs. angular frequency of excitation) of arrays of dry friction stick-slip oscillator. Two different network topologies have been applied, namely, open ring and closed ring. Analyzing synchronous regions we can conclude that the complete synchronization tends to occur for low coupling coefficients in both of these ring configurations. Such a situation results from configuration of eigenvalues of connectivity matrix. Increasing coupling causes that all eigenvalues can be found in synchronous interval of the MSF only for smaller values of coupling coefficient. Moreover, for lower values of excitation frequency friction oscillators synchronize even without spring coupling because we observe periodic behavior of network oscillators. In such a periodic case only the common drive is a sufficient factor for stabilizing the synchronous motion. For larger values of drive frequency, non-periodic dynamics of network nodes (chaotic or quasi-periodic) begins to dominate and then lower limit of synchronous interval of the MSF becomes nonzero.