非光滑动力学系统描述长期累积渐变后的突变行为，广泛应用于神经系统、电路系统、机械系统、生态、甚至社会经济系统的动力学行为研究。相关研究具有重要的学术意义和实际价值。本项目旨在研究分段光滑映象及其耦合系统中具有新特征的分岔和时空动力学新现象，发展同步、控制及预测的新方法。以神经元和开关电路两类实际系统为基础，建立相应的分段光滑模型，确定不连续性和不可逆性发生的条件，发现新的分岔机制，揭示分段光滑不连续映象系统特征动力学的新例证。据此构建具有规则网络和复杂网络拓扑结构的不光滑映象耦合系统，进而研究系统同步、斑图及其演化等集体动力学行为。结合传统方法和机器学习算法，发展实现同步、控制和预测的新方法。本研究将加深非光滑映象及其耦合系统中特征动力学的认识，拓展机器学习的应用领域，使之可用于非光滑系统的研究，最终为理解神经系统的活动规律及其它实际系统的动力学机制提供借鉴。

Nonsmooth dynamical systems are often employed to describe the abrupt change of the dynamical state of a system after a long time accumulation of gradual change which have been broadly applied in studying the dynamics of many practical systems, such as nervous, circuit, ecological, mechanical, even economic and social systems. The related research has significant academic and practical values. The principal goals of this project are to investigate the bifurcations and spatiotemporal dynamical phenomena with new characteristics in the piece-wise smooth maps and the coupled systems consist of them, and to develop the new methods to deal with synchronization, control and prediction. Based upon the practical systems such as neurons and switch circuit, piece-wise smooth maps will be built, and the conditions for the discontinuity and non- invertibility will be derived to uncover new kind of bifurcations and new examples for the characteristic dynamics of the systems of this kind. The coupled systems of those maps via regular and complex network topologies will be set up, and then their collective dynamical behaviors, such as synchronization, spatiotemporal patterns and their evolution will be studied. Combined with the conventional methods and the machine learning algorithms, new strategies to realize synchronization, control and prediction will be proposed, trying to synchronize systems, make a system tend to a desired state or forecast future state of a system. The result of this proposal will enhance our understanding on the characteristics of the nonsmooth maps and their coupled counterparts, extend the application of machine learning to the nonsmooth systems. It will finally provide reference and guidance for revealing the law of neuron activity and dynamical mechanism of some practical systems.