右端不连续时滞神经网络的多稳定性与分岔控制

项目名称： 右端不连续时滞神经网络的多稳定性与分岔控制

项目编号： No.61203300

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 聂小兵

作者单位： 东南大学

项目金额： 25万元

中文摘要： 近年来，关于神经网络的多稳定性研究涌现出了许多有价值的成果，但这些成果基本上都是建立在网络右端的激活函数是连续的假设基础上。事实上，具有右端不连续激活函数的神经网络，称之为右端不连续神经网络，是非常重要的而且在实际中有着广泛的应用。本项目拟运用微分包含与集值映射理论研究右端不连续时滞神经网络的多稳定性和分岔控制问题。内容包括：基于不连续的动力学特征，建立更贴近实际的右端不连续时滞神经网络模型；确定新建模型微分包含平衡态的精确数目、正向不变集和吸引域；深入分析系统在饱和区域内的复杂动力学行为，建立可验证的局部稳定性准则，揭示有限时间收敛产生的机理，精确估计系统达到局部稳定的有限时间区间；探讨系统在不饱和区域内的分岔行为，并提出相应的控制策略。这些问题的解决不仅可以促进右端不连续微分方程和神经网络多稳定性理论的进一步发展与完善，而且为不连续系统在实际工程中的应用提供有力的理论保障。

中文关键词： 多稳定性；不连续激活函数；时滞；神经网络；不稳定性

英文摘要： In recent years, some valuable results have been obtained about multistability of neural networks. However, it should be noted that in most existing multistability results, there is a basic assumption: the neuron activation functions are continuous. In fact, neural networks with discontinuous activation functions are of importance and do frequently arise in practice. Based on the theory of differential inclusion and set-valued map, we study the issues of multistability analysis and bifurcation control for delayed neural networks with discontinuous activation functions. Firstly, a general class of delayed neural networks model is established, according to the peculiar features of discontinuous dynamical system. Secondly, the exact number of equilibrium points(periodic solutions) is given and the positively invariant sets and basins of attraction for these stationary equilibrium points(periodic solutions) are estimated. Thirdly, the dynamical behavior of equilibrium points(periodic solutions) in saturation regions is completely analyzed, some testable sufficient conditions are derived which ensure local convergence of equilibrium points(periodic solutions). Moreover, how the discontinuities and time delays lead to local convergence in finite time is revealed and the finite convergence time is accurately estimated.

英文关键词： multistability；discontinuous activation functions；time delays；neural networks；instability