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Synchronization of coupled mechanical oscillators

100%

Perlikowski P. , Stefański A.

tom Vol. 10, nr 1

110-116

Complete synchronization of coupled chaotic systems is usually a primary and crucial issue. Coupling in mechanical systems introduces mutual perturbation of their dynamics. In case of identical systems such perturbation can lead to the synchronization. We can predict the synchronization threshold of such systems using a concept called Master Stability Function (MSF). As a tool of MSF we use transverse Lyapunov exponents, which characterize the stability of synchronization state. We show areas of synchronization in coupling parameters space in typical nonlinear systems: Duffing and Duffing - Van der Pol oscillators.

Prediction of solutions of the Duffing system with tuned mass damper

67%

Mnich K.

2018

tom Vol. 22, nr 4

983--989

In this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffng oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.