Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities

In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for the considered drive-response systems. The inequalities in our paper, applied to obtaining the maximum-valued and designing the novel controllers, are different from those in existing papers.

Global polynomial periodicity and polynomial stability of proportional delay Cohen-Grossberg neural networks

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.