Multistable synchronous states of two pendulum clocks suspended on a swinging support

摘要

We study the dynamics of two pendulum clocks suspended on a swinging support, investigating the scenarios of symmetrical and asymmetrical geometry of the oscillators' suspension. The regions of possible dynamical patterns are determined and typical behaviours of the system are described. We show, that depending on the parameters and the initial conditions, multistable synchronous states can arise, including in-phase, anti-phase and phase-locked synchronization, as well as the quasiperiodic, irregular motion.The basins of attraction of the co-existing solutions are presented and the transitions from one type of pattern into another are investigated through bifurcation analysis. The latter is supported by the energy balance method, which allows to understand the mechanisms responsible for qualitative changes occurring in the system. Our results are confirmed by the basin stability tool and indicate a good agreement between the classical bifurcation approach and modern probabilistic methods. The studies performed in this paper can be generalized and developed further for other types of systems, as well as to study the influence of the model's parameters on possible dynamics.