中文摘要：

研究了分数阶复值神经网络的稳定性.针对一类基于忆阻的分数阶时滞复值神经网络,利用Caputo分数阶微分意义上Filippov解的概念,研究其平衡点的存在性和唯一性.采用了将复值神经网络分离成实部和虚部的研究方法,将实数域上的比较原理、不动点定理应用到稳定性分析中,得到了模型平衡点存在性、唯一性和全局渐近稳定性的充分判据.数值仿真实例验证了获得结果的有效性.

英文摘要：

The global stability of fractional-order complex-valued neural networks was investi- gated. For a class of memristor-based fractional-order complex-valued neural networks with time delays, under the concept of the Filippov solution in the sense of Caputo＇ s fractional deri- vation, the existence and uniqueness of the equilibrium point were discussed. The comparison principle and the fixed-point theorem were applied to the stability analysis through division of the complex values into the real part and the imaginary part. Some sufficient criteria for the global asymptotic stability of memristor-based fractional-order complex-valued neural networks were derived. Finally, a simulation example shows the effectiveness of the obtained results.