基于忆阻随机时滞神经网络的稳定性与同步研究

As a memory nonlinear resistor, the features of memristor most closely resemble cerebral synapses. The memristor-based neural network deeply depicts the mechanism of brain. Stability and synchronization of the neural network are the most important properties of dynamics. Memristor-based neural network is a nonlinear discontinuous system. We cannot use the continuous system theory to discuss its stability and synchronization. The main strategies we adopt are the theory of discontinuous dynamical systems, the stability theory, stochastic analysis theory, some inequalities techniques. In this project, we shall mainly study the stability of stochastic memristor-based recurrent neural networks with time-varying delays and the stability of stochastic memristor-based Cohen-Grossberg neural networks with time-varying elays. At the same time, we will study the finite-time synchronization of stochastic memristor-based recurrent neural networks with time-varying delays. The above researches on the dynamics theory of memristor-based neural networks systems lay the theoretical foundations for the establishment of nonlinear discontinuous system dynamics and it applied to various fields.

忆阻是一种具有记忆功能的非线性电阻，其记忆特性与生物神经元突触的学习功能极为相似，因此，基于忆阻神经网络深刻地揭示了大脑的工作机制。稳定性和同步性是神经网络最重要的动力学性质，而基于忆阻神经网络是非线性不连续网络系统，不能用连续系统相关理论来讨论其稳定性及同步性。本项目拟采用不连续动力系统理论、稳定性理论、随机分析理论和一些不等式技巧相结合的方法，研究基于忆阻随机时滞递归神经网络模型的稳定性、基于忆阻随机时滞Cohen-Grossberg神经网络模型的稳定性和基于忆阻随机时滞递归神经网络模型的有限时间同步问题。上述基于忆阻随机时滞神经网络模型动力学理论的研究为非线性不连续系统动力学的建立及其应用到各个领域奠定了理论基础。

忆阻是一种具有记忆功能的非线性电阻，其记忆特性与生物神经元突触的学习功能极为相似，因此，基于忆阻神经网络深刻地揭示了大脑的工作机制。稳定性和同步性是神经网络最重要的动力学性质，而基于忆阻神经网络是非线性不连续网络系统，不能用连续系统相关理论来讨论其稳定性及同步性。通过利用不连续动力系统理论、稳定性理论和一些不等式技巧相结合的方法，研究忆阻神经网络模型的稳定性及同步问题。完成情况如下：（1）讨论了具有两个交换子网络的连接循环网络系统的平衡点的个数和其动力学性质；得到忆阻时变时滞随机递归神经网络渐近稳定和指数稳定性的若干充分条件；（2）给出了忆阻时滞Cohen-Grossberg神经网络稳定性的充分条件，及其有限时间同步的时间上限；（3）得到了非耗散耦合复杂网络的函数矩阵投影同步的判据；研究了基于事件触发的不确定领导者异构多智能体协同输出调节问题。