分数阶BAM神经网络的全局渐进稳定性

研究了分数阶BAM神经网络平衡点的唯一存在性和全局渐近稳定性,利用压缩映像原理得到了系统平衡点唯一存在的充分条件;通过构造Lyapunov函数,运用Lyapunov函数理论、矩阵不等式法和Laplace积分变换法,得到了所研究模型平衡点的全局渐进稳定的充分条件,以矩阵不等式的形式给出了更为严格和更易验证的条件,并通过数值仿真验证了结论的正确性。

Global Asymptotic Stability of Fractional order BAM Neural Networks

This paper studies the unique existence and global asymptotic stability of the equilibrium point of fractional order BAM neural networks, obtains the sufficient condition for the unique existence of the systematic equilibrium point by using contraction mapping principle, receives the sufficient condition of the global asymptotic stability of the equilibrium point of the studied model by constructing Lyapunov function and by using Lyapunov function theory, matrix inequality method and Laplace integral transform method, gives more strict and easier verification condition by the form of matrix inequalities and verifies the correctness of the conclusion by numerical simulation.