外部输入与两单元CNN的完全稳定性

Complete Stability of Two-cell Cellular Neural Networks with External Inputs

细胞神经网络(CNN)在图像处理、模式识别等领域有非常广泛的应用,应用的基础取决于对网络动力学特性的认识,尤其是网络在什么条件下有极限环,什么条件下是稳定的。研究了一类在没有外部输入条件下已经被证明是不稳定的两单元细胞神经网络(CNN)在加上外部输入后的特性。该网络在不加外部输入时的特点是:全局只在0区存在唯一齐点,并且存在一个围绕0区的极限环。证明:加上外部输入后,外部输入在一定的区域取值,网络仍保持这样的特点,即网络仍不是完全稳定的,存在一个围绕0区的极限环。这表明,不加外部输入时的情况只是加外部输入的一种特例。此外,还给出了这个外部输入值的取值区域。这个两单元细胞神经网络的结果有助于进一步研究较大规模细胞神经网络的非线性动力学特性,也有助于进一步拓展其在函数逼近、模式识别及图像处理等方面的应用。

Cellular neural networks have been widely used in image processing, pattern recognition and other fields. The base of the appli- cations is the realization of the dynamics, especially when there will be a limit cycle and how the network is stable. In this paper, a case of two-cell cellular neural networks with external inputs is studied which has been proved it is not completely stable without external inputs. The feature of the network without external inputs is that there is only one fixed point in region 0 and there is a limit cycle around region 0. It will prove that with external inputs and their values in given domain, the network still has the feature that it is not completely stable and there is a limit cycle around region 0. This indicates the CNN（2） without external inputs is only a special sub-case of that with exter- nal inputs. The domain of the external inputs values is also given. The result has expanded the understandings about the dynamics of the CNN（2）. He results on two-cell cellular neural networks will help to further study the nonlinear dynamics of large-scale cellular neural networks, and Will also help to further expand its applications in function approximation,pattern recognition,image processing,and others.