Unified Analysis on the Global Dissipativity and Stability of Fractional-Order Multidimension-Valued Memristive Neural Networks With Time Delay

The unified criteria are analyzed on the global dissipativity and stability for the delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) in this article. First, based on the comprehensive knowledge about multidimensional algebra, fractional derivatives, and nonsmooth analysis, we establish the unified model for the studied FSMVMNNs in order to propose a more uniform method to analyze the dynamic behaviors of multidimensional neural networks. Then, by mainly applying the Lyapunov method, employing several new lemmas, and solving some mathematical difficulties, without any separation, we acquire the unified and concise criteria. The derived criteria have many advantages in a smaller calculation, lower conservatism, more diversity, and higher flexibility. Finally, we provide two numerical examples to express the availability and improvements of the theoretical results.

Automated summary

In this article, unified criteria for the global dissipativity and stability of delayed fractional-order systems of multidimension-valued memristive neural networks (FSMVMNNs) are analyzed. By establishing a unified model, applying the Lyapunov method, and solving mathematical difficulties, the derived criteria are shown to have advantages in smaller calculation, lower conservatism, more diversity, and higher flexibility. Two numerical examples are provided to demonstrate the effectiveness and improvements of the theoretical results.