Network Dynamics Group, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37073 Göttingen, Germany.
Phys Rev Lett. 2011 Dec 9;107(24):244101. doi: 10.1103/PhysRevLett.107.244101.
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization so far has been found to be chaotic only in systems with inhomogeneities. Here we show that even symmetric systems of identical oscillators may not only exhibit chaotic dynamics, but also chaotically fluctuating order parameters. Our findings imply that neither inhomogeneities nor amplitude variations are necessary to obtain chaos; i.e., nonlinear interactions of phases give rise to the necessary instabilities.
相位耦合振荡器是物理学和生物学中弱相互作用振荡单元网络的典型模型。迄今为止，用于量化同步的序参量仅在具有非均匀性的系统中被发现是混沌的。在这里，我们表明，即使是相同振荡器的对称系统，也不仅可能表现出混沌动力学，而且可能表现出混沌波动的序参量。我们的发现意味着，获得混沌既不需要非均匀性，也不需要幅度变化；也就是说，相位的非线性相互作用产生了必要的不稳定性。
