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Methods for constructing limit cycles in oscillatory neural networks

振荡神经网络中构造极限环的方法

基本信息

批准号：
15560387
负责人：
INABA Hiroshi
金额：
$ 2.43万
依托单位：
Tokyo Denki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

(1)Expressing a two-dimensional state by a complex variable z=x+iy and describing a dynamical system asdz(t)/dt=f(z(t))the problem of constructing a given set of limit cycles in the dynamical system was studied. However it turns out that this problem seems much more complicated than expected and satisfactory results have been obtained. However various difficulties and important observations on the problem have been clarified and they would be useful for future study on this problem.(2)Let us consider a neural network consisting of many oscillatory neurons with a single stable limit point. It has been pointed out that if all the frequencies of limit cycles are set to equal then an associative memory can be implemented by storing information in their phase differences. The present investigators studied various associative memories using discrete type neural networks in some detail, and analogous to these it is examined by various numerical experiments that most of associative memories using discrete type neural networks can be realized. However it was seen that since each phase can take continuous values a neural network consisting of oscillatory neurons could store much more information than discrete type neurons.(3)We also studied neural networks consisting of many oscillatory neurons with different frequencies of limit cycles. Although it has been also pointed out that the network is eventually decomposed into various groups according to their frequencies so that each group has the common frequency, its detailed behavior has not investigated but computer simulations show various interesting facts.

(1)用复变量z=x+iy表示二维状态，描述动力系统dz(T)/dt=f(z(T))，研究了动力系统中给定极限环集的构造问题。然而，事实证明，这个问题似乎比预期的要复杂得多，并取得了令人满意的结果。然而，关于这一问题的各种困难和重要的观察结果已经被澄清，它们将有助于未来对这一问题的研究。(2)让我们考虑一个由多个具有单个稳定极限点的振荡神经元组成的神经网络。已经指出，如果极限环的所有频率都被设置为相等，则可以通过存储它们的相位差中的信息来实现关联存储器。目前的研究人员比较详细地研究了使用离散型神经网络的各种联想记忆，并通过各种数值实验检验了大多数使用离散型神经网络的联想记忆都是可以实现的。然而，由于每个阶段都可以取连续的值，所以由振荡神经元组成的神经网络比离散型神经元可以存储更多的信息。(3)我们还研究了由多个具有不同极限环频率的振荡神经元组成的神经网络。虽然也有人指出，网络最终会根据它们的频率被分解成不同的组，使得每个组都有共同的频率，但它的详细行为还没有被研究，但计算机模拟显示了各种有趣的事实。