具变系数和无穷时滞的双向联想记忆神经网络的动力学行为

摘要

In this paper, the bidirectional associative memory neural networks with variable coefficients and. infinite distributed delay is studied. By introducing the phase space Cg(R_) x Cg(R_) and applying Lyapunov functional method, we establish a series of criteria on the boundedness, global asymptotic stability.As applications of these results and combining the existence theorems of periodic solutions for general functional differential equations with infinite delay, we obtain the existence of periodic solutions and its global asymptotic stability for the periodic bidirectional associative memory neural networks with infinite distributed delay. As a special case, we apply these results to the autonomous bidirectional associative memory neural networks with infinite distributed delay, and obtain the existence, uniqueness and global stability of equilibrium point.%研究了具有变系数和无穷时滞的双向联想记忆神经网络,通过引入相空间Cg(R_)×Cg(R_)和Lyapunov泛函方法,建立了一系列关于解的有界性和全局渐近稳定性的判别准则.对于具有变系数和无穷时滞周期的双向联想记忆神经网络,通过应用周期解存在定理,建立了该系统周期解存在和全局稳定的充分条件.将上述结果应用于自治双向联想记忆神经网络,得到了平衡点的存在性、唯一性和全局渐近稳定性.