一类高阶Cohen-Grossberg神经网络的多周期性分析

Multiperiodicity analysis of a class of high-order Cohen-Grossberg neural networks

利用状态空间分解方法,探讨一类具有特殊激励函数的高阶Cohen-Grossberg神经网络的多周期性问题.该类神经网络的激励函数包括带有饱和区的非递减函数以及一般的细胞神经网络激励函数等.给出了保证此类网络的周期环在饱和区内局部指数收敛的充分条件.所得结果表明,一个n维网络可以有2n个局部指数收敛的周期环存在于饱和区.最后以一个数值例子说明了所得结果的有效性.

The multiperiodicity of a class of high-order Cohen Grossberg neural networks with special activation functions is discussed by using decomposition of the state space. The activation functions of this class of neural networks indude nondecreasing functions with saturation, standard activation functions of cellular neural networks, etc. A sufficient condition for guaranteeing periodic orbits of this kind of networks to be locally exponentially convergent in saturation regions is obtained. The results show that an n dimension neural network can have 2＂ periodic orbits located in saturation regions and these periodic orbits are locally exponentially convergent. Finally, a numerical example shows the effectiveness of the results.