BioND — Dynamics of Biological Networks

Self-organization in continuous adaptive networks

Anne-Ly Do
PhD thesis in Natural Sciences, Carl-von-Ossietzky Universität Oldenburg, 2011.

Abstract

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Complex systems of coupled dynamical units can often be understood as adaptive networks. In such networks the dynamical exchange of information between the local and topological degrees of freedom gives rise to a plethora of self-organization phenomena. Analytical studies can elucidate the mechanisms behind these phenomena. The development of respective approaches, however, is impeded by the necessity to capture both, the dynamical as well as structural aspects of the network.

This work explores a new analytical approach, which combines tools from dynamical systems theory with tools from graph theory to account for the dual nature of adaptive networks. To our knowledge, it is the first approach that is applicable to continuous networks. We use it to study the mechanisms behind three emergent phenomena that are prominently discussed in the context of biological and social sciences: synchronization, spontaneous diversification, and self-organized criticality.

First, we analyze the relation between structure and dynamics in a network of coupled, synchronized phase oscillators. By constructing a topological interpretation of Jacobi’s signature criterion, we show that synchronization can only be achieved if the network obeys specific topological conditions. These conditions pertain to subgraphs on all scales, pinpointing the impact of mesoscale topological structures on the collective dynamical state.

Second, we study the emergence of social diversification and social coordination in a self-assembled collaboration network. Our model generalizes the continuous snowdrift game, a paradigmatic model from game theory, to a multi-agent setting. In this generalization, the agents can continuously, selectively, and independently adapt the amount of resources allocated to each of their collaborations in order to maximize the obtained payoff. We show that both, social coordination and diversification, are emergent features of the model, and that both phenomena can be traced back to symmetries of the local pairwise interactions.

Third, we examine the ability of adaptive networks to self-organize toward dynamically critical states. We derive a generic recipe for the construction of local rules that generate self-organized criticality. Our analysis allows on the one hand side to relate details of the setup of hitherto studied models to particular functions within the self-organization process. On the other hand, it can guide the construction of technical systems featuring the desired critical behavior.

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