arXiv 1406.65392014-06nlin.CD

快慢耦合动力系统的动力学抑制和频率同步

Suppression of dynamics and frequency synchronization in coupled slow and fast dynamical systems

Kajari Gupta, G. Ambika

备注：: 9 pages, 20 figures, submitted to European Physical Journal B

摘要：

本文研究了两个具有不同动力学时间尺度的相互作用非线性系统的涌现态。我们发现，相互作用系统的无法下降的步骤导致的相位差以及振幅的变化。如果失配很小，则系统稳定到具有恒定相位差的频率同步状态。但随着时间尺度失配的增加，系统不得不妥协到无振荡的状态。我们说明了这一点标准的非线性系统，并确定淬火动力学的参数平面中的区域。这种状态的过渡曲线进行了分析研究，并通过直接数值模拟确认。作为一个重要的特例，我们重新审视了气候研究中使用的著名的海气耦合系统模型，用于快速振荡的大气和缓慢变化的海洋的相互作用动力学。我们的研究表明，在这种情况下，多稳定的周期状态和对流的稳定状态共存的系统中，具有复杂的盆地结构的发生。

英文摘要：

We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in amplitude. If the mismatch is small, the systems settle to a frequency synchronized state with constant phase difference. But as mismatch in time scale increases, the systems have to compromise to a state of no oscillations. We illustrate this for standard nonlinear systems and identify the regions of quenched dynamics in the parameter plane. The transition curves to this state are studied analytically and confirmed by direct numerical simulations. As an important special case, we revisit the well-known model of coupled ocean atmosphere system used in climate studies for the interactive dynamics of a fast oscillating atmosphere and slowly changing ocean. Our study in this context indicates occurrence of multi stable periodic states and steady states of convection coexisting in the system, with a complex basin structure.

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