复杂网络的多吸引性与多协同性及在基因调控网络中的应用

According to the ubiquitous complexity,such as emergence,attraction and coordination phenomena in nature, and combining with biological networks especially with gene regulatory networks, two kinds of multi-attraction and multi-coordination concepts and problems are proposed, one relating to the initial state of network and another concerning with the grouping evolution of node states. The evolution laws and regulation mechanisms of multi-attraction and multi-coordination in complex networks will be investigated in this project. Considering characteristics of natural networks and artificial networks, a class of complex dynamical networks will be established. These models will incorporate the dynamic switching, random disturbance and environmental constraint of networks. Then the intrinsic relations between the network structure parameters, initial regions, grouping evolution and the dynamics of multi-attraction will be revealed and the control algorithms of network multi-attraction will be given. Moreover, the complex multi-agent network models, based on the nonlinear dynamic characteristics, structural dynamic switching and communication constraints of the multi-agent, will be proposed. Also the multi-coordination in multi-agent networks and its control strategies will be considered in this project.Finally, the dynamics analysis as well as the control and computing theories and methods of gene regulatory networks will be established, which are based on the multiple attraction and multiple coordination of complex networks. In a word, this project will provide new perspectives, theories and methods for exploring the diverse complexity in actual networks and present the theoretical guidance for the regulation of biological networks and the design of large storage, fast calculation and multi-purpose computing systems.

本项目针对实际中广泛存在的涌现、吸引、协同等复杂性现象，结合生物网络特别是基因调控网络，提出网络的两类多吸引性和多协同性问题（即一类与网络初始状态有关，另一类与网络节点状态演化分组有关），研究复杂动态网络的多吸引性和多协同性的演化规律和调控机制。结合自然网络和人工网络特点，建立有动态切换、随机扰动、环境约束的复杂动态网络模型，揭示网络的结构参数、初始区域、演化分组与网络最终多吸引性的内在联系，给出网络多吸引性的控制算法。基于多智能体的非线性动力学特性、结构动态切换和通信受限等特点，建立复杂多智能体网络模型，研究多智能体网络的多协同性和控制策略。在复杂网络的多吸引性与多协同性研究基础上，建立基因调控网络的动力学分析、控制与计算的相关理论和方法。本项目将为探索实际网络的多种复杂性提供新思路、理论和方法，并为调控生物网络和设计大存储、快计算、多功能的计算系统和多自主体网络提供理论上的指导

四年来，该项目组成员按计划开展了该项目的研究，完成了计划预期的研究任务，取得了预期的研究成果。该项目针对实际中广泛存在的涌现、吸引、协同等复杂性，结合生物网路和人工网络，提出和建立了复杂网络与多智能体网络的典型模型，揭示了复杂动态网络的多吸引特性，建立了复杂多智能体网络的多协同控制机制。具体包括结合基因调控网络，研究了复杂动态网络的建模问题，分析了网络的多吸引性，探讨了网络的结构参数、初始区域、演化分组与网络最终吸引性的内在联系；根据网络的动态切换、随机扰动、环境约束等特点，研究了复杂动态网络的多吸引性的控制问题；结合生物网络和人工网络，研究了复杂多智能体网络的建模问题，提出和建立了一些典型的具有非线性、动态切换、通信约束等特点的复杂多智能体网络的模型与协议算法；研究了复杂多智能体网络的多协同性，分析了网络的非线性、动态切换、通信约束对网络多协同性的影响；提出了复杂多智能体网络的多协同性控制策略，建立了相关理论和方法。项目的研究成果对于认识复杂生物网络的演化规律，控制设计复杂智能人工网络具有重要的理论和实际意义。在国内外刊物和会议上发表论文共30篇，其中在Automatica、SIAM Journal on Applied Dynamical Systems、IEEE Transactions on Neural Networks and Learning Systems、Systems & Control Letters等SCI源刊上发表23篇。