Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China.
Texas A&M University at Qatar, Doha 23874, Qatar.
Neural Netw. 2017 Oct;94:24-33. doi: 10.1016/j.neunet.2017.06.006. Epub 2017 Jun 29.
The paper considers a general neural networks model with variable-time impulses. It is shown that each solution of the system intersects with every discontinuous surface exactly once via several new well-proposed assumptions. Moreover, based on the comparison principle, this paper shows that neural networks with variable-time impulse can be reduced to the corresponding neural network with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the variable-time impulsive neural networks. Furthermore, a series of sufficient criteria are derived to ensure the existence and global exponential stability of periodic solution of variable-time impulsive neural networks, and to illustrate the same stability properties between variable-time impulsive neural networks and the fixed-time ones. The new criteria are established by applying Schaefer's fixed point theorem combined with the use of inequality technique. Finally, a numerical example is presented to show the effectiveness of the proposed results.
本文考虑了具有时变脉冲的广义神经网络模型。通过几个新的合理假设，证明了系统的每个解都恰好通过几个不连续面与每一个不连续面相交一次。此外，基于比较原理，本文表明在适当选择条件下，具有时变脉冲的神经网络可以简化为相应的具有固定时变脉冲的神经网络。同时，固定时变脉冲系统可以看作是时变脉冲神经网络的比较系统。进一步，给出了一系列充分条件，以确保时变脉冲神经网络周期解的存在性和全局指数稳定性，并说明时变脉冲神经网络和固定时变神经网络之间具有相同的稳定性特性。新的准则是通过应用 Schaefer 不动点定理并结合不等式技术建立的。最后，通过数值实例验证了所提出的结果的有效性。
