Department of Mathematics, Southeast University, Nanjing, China.
Neural Netw. 2010 Mar;23(2):201-9. doi: 10.1016/j.neunet.2009.10.004. Epub 2009 Oct 29.
In this article, we focus on the delay-dependent multistability in recurrent neural networks. By constructing Lyapunov functional and using matrix inequality techniques, a novel delay-dependent multistability criterion is derived. The obtained results are more flexible and less conservative than previously known criteria. Two examples are given to show the effectiveness of the obtained criteria. Furthermore, some interesting delay-dependent dynamic behaviors have been showed in a special case, for example, we find that there is the coexistence of stable equilibria and stable limit cycles in the single neuron. Also, when the neurons are coupled, then the stable patterns are more complex.
在本文中，我们关注的是递归神经网络中的时滞相关多稳定性。通过构造 Lyapunov 泛函并利用矩阵不等式技术，推导出了一个新的时滞相关多稳定性准则。与已知的准则相比，所得结果更加灵活，保守性更小。给出了两个例子来说明所得到的准则的有效性。此外，在一个特殊情况下还展示了一些有趣的时滞相关动态行为，例如，我们发现单个神经元中存在稳定平衡点和稳定极限环的共存现象。而且，当神经元耦合时，稳定模式会更加复杂。
