一维递归神经网络的定性分析

Qualitative Analysis for 1- D Recurrent Neural Networks

该文讨论一维递归神经网络模型的定性分析。利用一元三次方程的求根公式,获得了系统平衡点个数与系统参数之间的关系,进一步通过泰勒定理和函数的单调性得到了每个平衡点的稳定性和吸引域,完善了已有文献的结论。最后,通过两个数值模拟验证了所得结论。

This paper studies the qualitative characteristics of 1 - D recurrent neural networks. By employing the formula of cubic function root, the relationships between the coefficients of the system and the number of equilibria are revealed. Furthermore, the stability and attractive domains of all equilibria are derived by using the Taylor theorem and the monotonicity. This paper improves and completes the previous conclusions. Finally, two examples and simulations are illustrated to validate our theory.