移动脉冲耦合网络建模、动力学分析及应用

In the past few years, the analysis and control of complex dynamical networks has become a hot issue in the interdisciplinary field, is also one of the important research fields of network science and engineering. This project will focus on modeling, dynamic analysis and applications of one classic complex dynamical network - moving pulse-coupled oscillator networks. Firstly, combining the mathematical explanation of synchronous rhythmic flashing of fireflies with the advantages of the oscillators' mobility, the dynamical model of (non)identical moving pulse-coupled oscillator networks will be established. Secondly, by analyzing the dynamics of the model, the synchronization-achieving conditions and synchronization-maintaining conditions of the model will be derived, and the relationship among the oscillators' mobility, the proprieties of the pulse coupling and synchronization will be revealed. Thirdly, based on the concept of pinning control, the control strategy will be given to synchronize the networks to the object state. Next, the robustness and fragility of synchronization of the model with respect to random or intentional failures or attacks will be explored. Moreover, the optimal synchronization of the model will be investigated from setting system parameters, designing refractory periods and phase response curves. Furthermore, the above theory will be extended to the important cases of oscillators' moving on a sphere and random walks on complex networks. Finally, the theoretical results and schemes will be applied to synchronize clock in mobile wireless sensor networks. The project investigation will inject new life into the research of complex networks, is the in-depth extension and development of the present research on complex dynamical networks, and its feature, that is the combination of the basic theoretical and the applied research, is the trend of network science and engineering.

复杂动态网络的分析与控制，已成为交叉学科领域的一个研究热点问题，是网络科学与工程重要的研究领域之一。本项目研究一类典型的复杂动态网络——移动脉冲耦合网络——建模、动力学分析及应用。具体来说，结合萤火虫同步闪光的数学解释和振子移动性的优点，建立（非）恒同移动脉冲耦合网络模型，分析其动力学性质，研究该网络实现与保持同步的条件，揭示振子移动性和脉冲耦合属性对网络同步的影响规律，基于牵制控制思想设计控制策略使网络同步到目标状态，探讨网络对随机、故意的“故障”、“攻击”的同步鲁棒性和脆弱性，从配置系统参数、设计脉冲不应区间和相位响应曲线三个方面优化网络同步过程，并将相应结果推广到振子在球面上移动、网络上随机游走情形，最后将理论成果应用到移动无线传感器网络时钟同步中。本项目的研究将为复杂网络研究注入新的活力，是复杂动态网络研究的深入和发展，其基础理论研究和应用相结合的特点是网络科学与工程的发展趋势。

复杂动态网络的建模与动力学分析是网络科学与工程的重要研究领域之一。本项目利用非线性动力学理论、复杂网络理论、随机微分方程理论、现代控制理论和数值仿真的手段，建立移动脉冲耦合网络模型并分析其动力学行为与同步条件，并将脉冲作用应用到在一般复杂动态网络的脉冲耦合、脉冲控制中，取得重要的创新性成果。另外，在随机反馈控制、随机耦合、Markov交换拓扑等方面取得一系列重要的创新性成果。在 Automatica,Nonlinear Dynamic,Journal of the Franklin Institute,Applied Mathematics and Computation,等国际知名期刊上发表SCI期刊论文12篇，EI检索的会议论文4篇，协助培养硕士研究生3名。