Dynamic Hebbian learning in adaptive frequency oscillators
Dynamic Hebbian learning in adaptive frequency oscillators
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DOI：
10.1016/j.physd.2006.02.009
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发表时间：
2006-04-15
影响因子：
4
通讯作者：
Ijspeert, Auke Jan
中科院分区：
文献类型：
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作者：
Righetti, Ludovic;Buchli, Jonas;Ijspeert, Auke Jan
非线性振荡器广泛应用于生物学、物理学和工程领域的建模和控制。它们之所以有趣，是因为它们在与其他动力系统耦合时具有同步特性。在本文中，我们提出了一种振荡器的学习规则，使其频率适应任何周期性或伪周期性输入信号的频率。学习是以动态方式完成的：它是动态系统的一部分，而不是离线过程。我们模型的一个有趣的特性是，它可以很容易地推广到一大类振荡器，从相位振荡器到张弛振荡器以及具有通用学习规则的奇怪吸引子。我们的学习规则的一个主要特征是，所构建的振荡器可以调整其频率，而无需任何信号处理或需要指定时间窗口或类似的自由参数。所有处理都嵌入到自适应振荡器的动态中。证明了Hopf振子的学习收敛性，并通过数值实验探讨了系统的学习能力。最后。我们将学习规则推广到非谐波振荡器，例如张弛振荡器和奇异吸引子。 (c) 2006 Elsevier B.V. 保留所有权利。
Nonlinear oscillators are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for oscillators which adapts their frequency to the frequency of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of oscillators, from phase oscillators to relaxation oscillators and strange attractors with a generic learning rule. One major feature of our learning rule is that the oscillators constructed can adapt their frequency without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive oscillator. The convergence of the learning is proved for the Hopf oscillator, then numerical experiments are carried out to explore the learning capabilities of the system. Finally. we generalize the learning rule to non-harmonic oscillators like relaxation oscillators and strange attractors. (c) 2006 Elsevier B.V. All rights reserved.