新一代人工智能的发展规划为神经网络的研究及应用提出了挑战，发挥高维度、长时记忆与非定域性的优势、提升系统的模拟功能是神经网络应用研究的核心及热点问题。项目聚焦多维神经网络应用的基础理论，以微分方程稳定性和控制理论为指导，以神经网络动力学行为特性研究为主线，建立并转化分数阶多维忆阻神经网络模型，厘清系统中状态变量、连接权重和激活函数与分数阶导数、多维代数、切换忆阻之间的耦合关系；探索新型不等式，拓展能量函数结构，开展相应模型的无源性、耗散性、广义耗散性和同步意义下的耗散性分析；探讨控制器的有效设计，提出复杂多维神经网络系统协调切换的控制方法，实现相应系统的全局、有限时间、固定时间和耗散性意义下的Mittag-Leffler同步，获得其动力学行为的灵活判据，丰富多维神经网络系统动力学研究的理论体系，为分数阶多维忆阻神经网络系统在人工智能、信号处理等实际应用中奠定理论基础。

The development plan for the new generation of artificial intelligence poses a challenge to the research and application of neural networks. It is the core and hot issue that exploiting the advantages such as higher dimension, long-term memory, non-locality of neural networks and improving the system simulation function in the application of neural networks. Guided by the differential equation stability and control theory, this project which focuses on the basic research for the application of multidimension-valued neural networks builds and transforms different models of multidimension-valued neural networks with the main line of dynamic behaviors characteristic research, and clarifies the coupling relationships among multiple factors such as state variables, connection weights, activation functions, fractional-order derivatives, multidimensional algebras, and switching memristors. Meanwhile, this project also carries out the analysis on the passivity, dissipativity, extended dissipativity and synchronization-based dissipativity for the corresponding models by exploring the novel inequalities and expanding the structure of the energy functions. Moreover, this project discusses the effective design of the controllers and proposes the coordinated and switched control methods for the complex systems of multidimension-valued neural networks. Furthermore, this project realizes the different Mittag-Leffler synchronization such as global, finite-time, fixed-time and dissipativity-based synchronization of the corresponding systems, and obtains the relevant flexible criteria of dynamic behaviors. The research can enrich theoretical system for dynamics study of multidimension-valued neural networks and provide the theoretical basis for their practical applications such as artificial intelligence and signal control and so on.