Emergence and evolution of hierarchical structures in complex systems

复杂系统的定义特征之一是我们可以称之为互动诱导的合作涌现：组件的定义及其相互作用由一个层次结构组成，在不同层次上具有不同的因果关系。多组分系统可以作为内部和外部动态相互作用的结果而进化和适应，例如进化生态系统。在这种情况下，系统的统计特性将随时间变化。该项目将强调间歇性，进化和时间依赖统计之间的关系，作为复杂系统的基本特征。在基于智能体的系统中，进化动力学导致了不同类型的智能体或有机体的不断变化的配置，即生态系统。这些结构可以根据在给定时间存在的不同生物体之间的相互作用网络来分析。这些网络的层次性质将通过使用基因型中的职业密度进行数学分析。生成的生态系统只是准稳定的，并将不断经历从一种配置到另一种配置的转变。该项目将详细分析出现的宏观结构和动力学与潜在的微观个体进化动力学之间的关系。特别关注将集中在：1)动态对称破缺的起源，2)观察到的宏观转变速率逐渐下降的性质，3)分析和描述动态和新兴网络的特性，4)分析新兴网络的网络层次结构，以及5)研究相互作用与物种多样性之间的联系。虽然该项目将以进化动力学为中心，但也将探索与其他表现出缓慢关系动力学的复杂系统的相似性，例如自旋玻璃和超导体中的涡旋系统。

One of the defining characteristics of complex systems is what one might call interaction-induced co-operative emergence: the definition of components and their interactions consists of a hierarchical structure with different causations at different levels. Multiple-component systems can evolve and adapt as a consequence of internal and external dynamical interaction, think e.g. of evolutionary ecosystems. When this is the case the statistical properties of the system will change with time. The project will emphasis the relation between intermittency, evolution and time dependent statistics as an essential characteristic of complex systems. In agent based systems evolutionary dynamics gives rise to ever-changing configurations of different types of agents, or organisms, i.e. ecosystems . These configurations can be analysed in terms of the network of interactions between the different organisms present at a given time. The hierarchical nature of these networks will be analysed mathematically by use of the occupation density in the genotype. The generated ecosystems are only quasi-stable and will continuously undergo transitions from one configuration to another. The project will carry out a detailed analysis of the relation between the emergent macroscopic structures and dynamics and the underlying microscopic individual based evolutionary dynamics. In particular attention will be focused on:1) the origin of the dynamical symmetry breaking, 2) the nature of the observed gradual decrease in the rate of macroscopic transitions, 3) analysis and characterisation of the dynamics and properties of emergent networks, 4) analysis of the emergent hierarchy of networks of networks, and 5) study of the link between interaction and species diversity.Although the project will be centred about evolutionary dynamics, similarities with other complex systems exhibiting slow relational dynamics, such as spin-glasses and the vortex system in superconductors, will also be explored.