分数阶BAM神经网络的鲁棒稳定性  

The robust stability of fractional order BAM neural networks

作　　者：刘孝磊[1] 周刚[1] 赵文飞[1] 

机构地区：[1]海军航空工程学院系统科学与数学研究所,烟台264001

出　　处：《黑龙江大学自然科学学报》2015年第6期728-734,共7页Journal of Natural Science of Heilongjiang University

基　　金：山东省自然科学基金资助项目(ZR2014AM006)

摘　　要：分数阶BAM神经网络模型是整数阶BAM神经网络模型的一种推广。对分数阶BAM神经网络的鲁棒稳定性进行研究,通过构造分数阶辅助系统,利用积分变换的方法,将辅助系统变为积分方程。结合Mittag-Leffler函数的相关性质,利用广义Gronwall不等式,对积分方程进行处理,通过分数阶比较定理,得到分数阶BAM神经网络鲁棒稳定性的充分性条件。实例仿真验证了结论的正确性。The fractional order BAM neural networks are the general forms compared to the integer order ones. The robust stability of fractional order BAM neural networks is studied. A fractional order auxiliary systems is constructed, and by the method of the integral transform, translated it into a integral equation. And then making use of the property of Mittag-Leffler function and generalized Gronwall inequality, the integral equation is investigated. The sufficient conditions of robust stability for the fractional order BAM neural networks are gotten by the comparison theorem of fractional order systems. At last, the correctness of the conclusion is verified by emulating example.

关 键 词：分数阶 神经网络 Mittag-Leffler函数 鲁棒稳定性 

分 类 号：O175[理学—数学]