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Snaking bifurcations in a self-excited oscillator chain with cyclic symmetry

机译:具有循环对称性的自激振荡器链中的蛇形分叉

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摘要

Snaking bifurcations in a chain of mechanical oscillators are studied. The individual oscillators are weakly nonlinear and subject to self-excitation and subcritical Hopf-bifurcations with some parameter ranges yielding bistability. When the oscillators are coupled to their neighbours, snaking bifurcations result, corresponding to localised vibration states. The snaking patterns do seem to be more complex than in previously studied continuous systems, comprising a plethora of isolated branches and also a large number of similar but not identical states, originating from the weak coupling of the phases of the individual oscillators.
机译:研究了机械振荡器链中的蛇形分支。单个振荡器是弱非线性的,会受到自激和亚临界霍普夫分支的影响,其中某些参数范围会产生双稳态。当振荡器耦合到其邻居时,会产生与局部振动状态相对应的蛇形分叉。蛇行模式的确比以前研究的连续系统更为复杂,后者包括大量孤立的分支以及大量相似但不相同的状态,这是由于各个振荡器相位的弱耦合引起的。

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