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Dynamical behaviors of fuzzy reaction-diffusion periodic cellular neural networks with variable coefficients and delays

机译：变系数和时滞的模糊反应扩散周期细胞神经网络的动力学行为

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摘要

When modeling neural networks in a real world, not only diffusion effect and fuzziness cannot be avoided, but also self-inhibitions, interconnection weights, and inputs should vary as time varies. In this paper, we discuss the dynamical behaviors of delayed reaction-diffusion fuzzy cellular neural networks with varying periodic self-inhibitions, interconnection weights as well as inputs. By using Halanay's delay differential inequality, M-matrix theory and analytic methods, some new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential stability of the periodic solution, and the exponentially convergent rate index is also estimated. In particular, the traditional assumption on the differentiability of the time-varying delays is no longer needed. The methodology developed in this paper is shown to be simple and effective for the exponential periodicity and stability analysis of neural networks with time-varying delays. Two examples are given to show the usefulness of the obtained results that are less restrictive than recently known criteria.
机译：在现实世界中对神经网络进行建模时，不仅无法避免扩散效果和模糊性，而且随着时间的变化，自我约束，互连权重和输入也应发生变化。在本文中，我们讨论了具有变化的周期性自约束，互连权重和输入的时滞反应扩散模糊细胞神经网络的动力学行为。通过使用Halanay的时滞微分不等式，M-矩阵理论和解析方法，获得了一些新的充分条件来确保周期解的存在性，唯一性和全局指数稳定性，并估计了指数收敛速率指数。特别地，不再需要关于时变延迟的可微性的传统假设。结果表明，本文开发的方法对于时变时延神经网络的指数周期性和稳定性分析非常简单有效。给出了两个例子，以显示所获得结果的实用性，其限制性不如最近已知的标准。

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