变时滞非自治神经网络的有界性和全局指数稳定性

Boundedness and Global Exponential Stability for Non-autonomous Neural Networks with Time-varying Delays

主要研究了一类变时滞的非自治神经网络的一致有界性、最终一致有界性和全局指数稳定性.通过构造恰当的Lyapunov泛函并应用广义泛函微分方程的有界性原理和Young不等式给出了多变时滞非自治神经网络解的有界性和稳定性的新的充分条件.文中无需考查模型平衡点的数目,同时也不要求激活函数可导、单调或是有界,所得结果更具有一般特性和新颖性,改善了相关文献的理论结果.通过举例进一步验证了所得结果的有效性.

The uniform boundedness, uniformly ultimate boundedness and global exponential stability for non-autonomous neural networks with time-varying delays are investigated. By constructing a suitable Lyapunov functional and applying the boundedness principle for general functional-differential equations, new sufficient conditions on the boundedness and global exponential stability of the solution for the non-autonomous neural networks with time-varying delays are obtained. Meanwhile, the considered model has not been assumed any equilibrium and the activation functions are not supposed to be differentiable, nondecreasing or bounded. So, the results obtained are more general, new and improving the previous works. An illustrative example is also given to demonstrate the effectiveness of the results.