中文摘要：

探讨了一类二维神经网络可能存在的复杂动力学行为。首先利用反证法,获得了这类神经网络的一个不变集,以保证从这个集合出发的所有轨迹最终都在这个集合中。然后利用向量场的旋转数理论,通过构建一个封闭曲线证明了这类网络平衡点的存在性。此外,利用反证法证明了该网络的有界性。最后通过数值模拟,验证了分析结果。

英文摘要：

This paper investigated complex dynamical behaviors of a class of 2-D neural networks.Firstly,by the use of contradiction,obtained an invariant set so that the trajectories of neural networks originated from the set would enter it for ever.Proved the existence of the interior equilibrium point by constructing a closed curve and using the winding number of the vector field.Furthermore,proved the boundedness of the networks by using contradiction.Finally,carried digital simulations to validate the findings.