噪声激励下时滞网络系统的随机动力学研究

项目名称： 噪声激励下时滞网络系统的随机动力学研究

项目编号： No.11272258

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 孙中奎

作者单位： 西北工业大学

项目金额： 82万元

中文摘要： 网络系统以其理论的深刻性和应用的普适性成为解释、描述和研究自然界真实系统最合适的模型。由于噪声和时滞的普遍存在，使得对噪声激励下时滞网络系统随机动力学的研究正在成为新的学科前沿和研究热点。有鉴于此，本项目将针对网络系统的两个主要类别- - 规则网络系统和复杂网络系统，应用随机动力学理论方法，系统开展对噪声激励下时滞网络系统随机动力学的研究：讨论mean-field方法在噪声激励下时滞网络系统中的应用条件，开展对噪声激励下时滞规则网络（全局耦合网络、最近邻耦合网络）系统和时滞复杂网络系统随机共振、随机分岔、时空混沌及相关随机动力学的研究。通过研究，提出适用于时滞网络系统的新分析方法、阐明时滞网络系统随机动力学的演化规律和行为特征、构建时空混沌控制方案，最终揭示时滞网络系统动力学时空复杂性。本项目的研究成果将加深对真实系统复杂性的认识、促进对高维动力学系统的了解，并将进一步完善随机动力学理论体系。

中文关键词： 随机动力学；网络系统；时滞；噪声；

英文摘要： Networks are all around us, which describe a wide range of systems in nature and society, and have gotten their potential applications in real-world complex systems. As is now well-known, time delay(s) and noise are unavoidable in nature. Hence, it is becoming a fresh frontier of nonlinear science and attracting increasing attention to study the stochastic dynamics of networks contained time delay(s) under noise. Motivated by this, we will devote ourselves to investigating the stochastic dynamics of networks contained time delay under noise in the current project, based on the theory and tools of stochastic dynamical systems accompanied by the topology of networks and efficient numerical simulations. The mean-field theory will be studied at first for its potential usage in networks with time delay. Then an investigation on the stochastic resonance and its relatives will be carried out in a network with global coupling, a network with nearest neighbor coupling and/or a complex network. Finally, stochastic bifurcation and spatiotemporal chaos will be well studied in networks with time delay under noise, and some strategies will be designed to control spatiotemporal chaos. The results of the current project may demonstrate the laws of dynamics and evolution of networks, and the important roles played by the time de

英文关键词： stochastic dynamics；networks；time delay；noise；