Emergence and evolution of hierarchical structures in complex systems

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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.