离散观测对Chua模式同步的影响及其在资料同化中的应用
Effect of discrete time observations on synchronization in Chua model and applications to data assimilation
摘要：
最近的研究表明，当频繁观测的变量数量较少时，同步作为小尺度或中尺度预报的数据同化工具是有效的。我们的主要目的是了解在低维混沌系统，即蔡氏电路模型中，观测频率和观测噪声的变化对同步和预测的影响。我们执行{ \it同卵双生实验}，以研究同步使用离散的时间观测产生的独立的模型运行和单向耦合到模型分别通过$x$，$y$和$z$。当耦合蔡氏模型的x和y变量时，我们在有限的耦合常数范围内观察到同步，但当耦合z变量时则没有。耦合常数的范围随着观测中噪声水平的增加而减小。当观测时间间隔大于李雅普诺夫时间的七分之一时，蔡氏系统不表现出同步性。最后，我们还注意到，当使用有噪声的观测值时，预测误差比使用无噪声的观测值时大得多。
英文摘要：
Recent studies show indication of the effectiveness of synchronization as a data assimilation tool for small or meso-scale forecast when less number of variables are observed frequently. Our main aim here is to understand the effects of changing observational frequency and observational noise on synchronization and prediction in a low dimensional chaotic system, namely the Chua circuit model. We perform {\it identical twin experiments} in order to study synchronization using discrete-in-time observations generated from independent model run and coupled unidirectionally to the model through $x$, $y$ and $z$ separately. We observe synchrony in a finite range of coupling constant when coupling the x and y variables of the Chua model but not when coupling the z variable. This range of coupling constant decreases with increasing levels of noise in the observations. The Chua system does not show synchrony when the time gap between observations is greater than about one-seventh of the Lyapunov time. Finally, we also note that prediction errors are much larger when noisy observations are used than when using observations without noise.
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