Delay-dependent and delay-independent passivity of a class of recurrent neural networks with impulse and multi-proportional delays

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.

Global Exponential Stability and Synchronization for Novel Complex-Valued Neural Networks With Proportional Delays and Inhibitory Factors

In this article, complex-valued neural networks (CVNNs) with proportional delays and inhibitory factors are proposed. First, the global exponential stability of the model addressed is investigated by employing the Halanay inequality technique and the matrix measure method. Some criteria are derived to guarantee the global exponential stability of CVNNs with proportional delays and inhibitory factors. The obtained criteria are applicable not only to systems with proportional delays but also to systems with arbitrary delays. Here, the Lyapunov functions are not constructed. Compared with the Lyapunov method, the matrix measure method makes the obtained criteria more concise, and the Halanay inequality makes the analytical procedure more compact. Furthermore, the global exponential synchronization of two neural-network models with proportional delays and inhibitory factors is also studied. By designing a feedback controller and giving some limitation conditions, the drive system and the response system realize global exponential synchronization. Finally, numerical simulation examples are provided to validate the effectiveness of the theoretical results obtained.

Polynomial dissipativity of proportional delayed BAM neural networks

This paper pays close attention to the global polynomial dissipativity (GPD) for proportional delayed BAM neural networks (PDBAMNNs). The global exponential dissipativity (GED) and the global dissipativity (GD) are also talked about. Under the help of novel Lyapunov functionals and a generalized Halanay inequality, a set of dissipative criteria for such systems are led out, together with the global polynomial attracting set (GPAS) and the global attracting set (GAS). Further, the relationship among GPD, GED and GD is unveiled. Finally, a proposed theoretical condition is validated through a simulation experiment.