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

机译：两个摆锤的多个同步状态悬挂在摆动支架上

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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.
机译：我们研究了悬挂在摆动支撑的两个摆锤的动态，研究了振荡器悬架的对称和不对称几何学的场景。确定可能的动态图案的区域，并描述了系统的典型行为。我们显示，根据参数和初始条件，可以出现多用途同步状态，包括同相，抗阶段和锁相同步，以及QuaSiodic，不规则运动。共同的吸引力盆地通过分叉分析向呈现现有的解决方案，并且通过分叉分析研究了一种类型的图案的转变。后者由能量平衡方法支持，这允许了解系统中发生定性变化的机制。我们的结果由盆地稳定性工具确认，并在经典分岔方法和现代概率方法之间表明良好的一致性。本文进行的研究可以广泛地推广和开发其他类型的系统，以及研究模型参数对可能动态的影响。

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