Analog realization of arbitrary one-dimensional maps
Analog realization of arbitrary one-dimensional maps
复制标题
任意一维图的模拟实现
DOI：
10.1109/tcsi.2003.819805
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发表时间：
2003
影响因子：
5.1
通讯作者：
N. Farhat
中科院分区：
文献类型：
--
作者：
E. Hernandez;Geehyuk Lee;N. Farhat
在人工神经网络、图像处理系统和安全通信系统的文献中，一维（1-D）地图作为信息处理元素的应用越来越多。在寻找1-D地图的有效硬件实现时，我们发现分叉神经元（BN）可以提供一个紧凑的解决方案，该方法在其他地方被引入作为受外部正弦信号影响的生物神经元的数学模型。对BN的原始研究表明，当BN受到正弦驱动信号时，其发射时间序列与正弦圆映射有关，表明BN可以计算正弦圆映射。尽管其丰富的动态特性阵列，BN的数学描述是足够简单的，以使其成为一个紧凑的电路实现。在本文中，我们推广了原来的工作，并证明了BN的计算能力可以扩展到计算任意1-D映射。此外，我们还描述了BN的两种可能的电路模型：可编程单结晶体管振荡器神经元，这是在原始工作中作为BN的电路模型引入的，以及集成电路松弛振荡器神经元（IRON），这是为了更精确地建模BN而开发的。为了证明BN的计算能力，我们使用IRON来生成正弦圆图、逻辑图以及帐篷图的分岔图，然后将它们与精确的数值版本进行比较。BN的编程计算任意映射可以简单地通过改变驱动信号的波形来完成，这是给BN的外部；这一特点使得BN的电路模型在1-D地图网络的电路实现中特别有用。
An increasing number of applications of a one-dimensional (1-D) map as an information processing element are found in the literature on artificial neural networks, image processing systems, and secure communication systems. In search of an efficient hardware implementation of a 1-D map, we discovered that the bifurcating neuron (BN), which was introduced elsewhere as a mathematical model of a biological neuron under the influence of an external sinusoidal signal, could provide a compact solution. The original work on the BN indicated that its firing time sequence, when it was subject to a sinusoidal driving signal, was related to the sine-circle map, suggesting that the BN can compute the sine-circle map. Despite its rich array of dynamical properties, the mathematical description of the BN is simple enough to lend itself to a compact circuit implementation. In this paper, we generalize the original work and show that the computational power of the BN can be extended to compute an arbitrary 1-D map. Also, we describe two possible circuit models of the BN: the programmable unijunction transistor oscillator neuron, which was introduced in the original work as a circuit model of the BN, and the integrated-circuit relaxation oscillator neuron (IRON), which was developed for more precise modeling of the BN. To demonstrate the computational power of the BN, we use the IRON to generate the bifurcation diagrams of the sine-circle map, the logistic map, as well as the tent map, and then compare them with exact numerical versions. The programming of the BN to compute an arbitrary map can be done simply by changing the waveform of the driving signal, which is given to the BN externally; this feature makes the circuit models of the BN especially useful in the circuit implementation of a network of 1-D maps.