School of Mathematics Science, Tianjin Normal University, Tianjin, 300387, China.
ISA Trans. 2022 Mar;122:205-217. doi: 10.1016/j.isatra.2021.04.041. Epub 2021 May 6.
This paper tackles the global polynomial periodicity (GPP) and global polynomial stability (GPS) for proportional delay Cohen-Grossberg neural networks (PDCGNNs). By adopting two transformations, designing opportune Lyapunov functionals (LFs) with tunable parameters and taking inequality skills, several delay-dependent criteria of GPP and GPS are acquired for the PDCGNNs. Here the GPP is also a kind of global asymptotic periodicity (GAP), but it has obvious convergence rate and convergence order, and its convergence rate is slower than that of global exponential periodicity (GEP). This is of great significance to the detailed division of periodicity in theory. These acquired criteria are confirmed by a numerical example with four cases. Simultaneously, through the numerical example, the acquired criteria also fully demonstrate their superiority in comparison with existing results. And, in another example, a GPS criterion is used to solve a quadratic programming problem (QPP) to reflect one of the practical applications of the PDCGNNs.
本文研究了比例时滞 Cohen-Grossberg 神经网络（PDCGNN）的全局多项式周期性（GPP）和全局多项式稳定性（GPS）。通过采用两个变换，设计了具有可调参数的合适的李雅普诺夫泛函（LF）并运用不等式技巧，得到了 PDCGNN 的 GPP 和 GPS 的几个时滞相关判据。这里的 GPP 也是一种全局渐近周期性（GAP），但它具有明显的收敛速度和收敛阶，其收敛速度比全局指数周期性（GEP）慢。这对于理论上的周期性详细划分具有重要意义。通过四个案例的数值例子验证了所获得的判据。同时，通过数值例子也充分证明了与现有结果相比，所获得的判据具有优越性。此外，在另一个例子中，利用 GPS 判据来解决二次规划问题（QPP），以反映 PDCGNN 的实际应用之一。
