整体耦合Duffing振子的多稳定性
Multistability of globally coupled Duffing oscillators
摘要：
我们分析了集体动力学的整体耦合，外部强迫，相同的机械振子与立方非线性。重点放在解决方案中的合奏分裂成两个内部同步集群，作为一个后果的双稳态的个别振荡器。这些解决方案的多样性，诱导的许多可能的方式分配的振子之间的两个集群，意味着合奏可以表现出多稳定性。然而，随着耦合强度的增加，两个集群的解决方案被完全同步的状态所取代。通过分析和数值计算相结合的方法，我们研究了两群解的存在性和稳定性。的集群和两个稳定的解决方案的相对流行的振荡器之间的分布的作用被公开。
英文摘要：
We analyze the collective dynamics of an ensemble of globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where the ensemble splits into two internally synchronized clusters, as a consequence of the bistability of individual oscillators. The multiplicity of these solutions, induced by the many possible ways of distributing the oscillators between the two clusters, implies that the ensemble can exhibit multistability. As the strength of coupling grows, however, the two-cluster solutions are replaced by a state of full synchronization. By a combination of analytical and numerical techniques, we study the existence and stability of two-cluster solutions. The role of the distribution of oscillators between the clusters and the relative prevalence of the two stable solutions are disclosed.
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