Andrzej Stefański

Chaos in coupled clocks

We consider the dynamics of two pendulum clocks (with pendulums of the same length but different masses) suspended on the same beam. We give evidence that besides the complete and phase synchronizations, the considered system can exhibit long period synchronization and chaotic behavior. We argue that the observed phenomena are robust.

Synchronization Properties in Coupled Dry Friction Oscillators

Self-excited vibrations in friction oscillators are known as stick-slip phenomenon. The non-linearity in the friction force characteristics introduces instability to the steady frictional sliding. The self-excited friction oscillator consists of the mass pushed horizontally on the surface, elastic element (spring) and a drive (convey or belt). Described system serves as a classic toy model for representation of stick-slip motion. Synchronization is an interdisciplinary phenomenon and can be defined as correlation in time of at least two different processes. This chapter focuses on synchronization thresholds in networks of oscillators with dry friction oscillators coupled by linear springs. Oscillators are connected in the nearest neighbour fashion into topologies of open and closed ring. In course of the numerical modelling we are interested in identification of complete and cluster synchronization regions. The thresholds for complete synchronization are determined numerically using brute force numerical integration and by means of the master stability function (MSF). Estimation of the MSF is conducted using approach called two-oscillator probe. Moreover, we perform a parameter study in two-dimensional space, where different cluster synchronization configurations are explored. The results indicate that the MSF can be applied to non-smooth system such as stick-slip oscillator. Synchronization thresholds determined using MSF occur to be in line with the one obtained numerically.