具反映扩散无穷连续分布时滞神经网络的全局渐近稳定性

Global Asymptotic Stability of Reaction-Diffusion Neural Networks with Distributed Delays

利用同伦不变性原理、Dini导数、格林公式 ,研究了一类具反应扩散的无穷时滞神经网络系统的平衡点的存在唯一性和全局渐近稳定性 .在去掉对神经元的激励函数有界性、可微性、去掉对平均时滞∫∞0 sk(s)ds有界性的要求 ,仅要求激励函数满足Lipchitz条件等较宽松的条件下 ,获得了该类系统的全局渐近稳定性的充分条件 .改进和推广了已有文献的最新结果 .并用实例说明了这些获得的结果的有效性 .

By employing homotopy invariability, Dini's derivative, Green formulation, the existence and uniqueness of the equilibrium point and global asymptotic stability of reaction-diffusion neural networks with distributed delays are investigated. Some new criteria for these types of asymptotic stability are derived without assuming the boundedness, monotonicity and differentiability of the activation functions and the boundedness of average time-delay ∫08 sk(s)ds. Earlier results are extended and improved. An example is also worked out to demonstrate the advantages of these results.