Anne-Ly Do

Adaptive-network models of swarm dynamics

We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model using a low-dimensional system of equations permitting analytical investigation. We find that the model reproduces several characteristic features of swarms, including spontaneous symmetry breaking, noise- and density-driven order-disorder transitions that can be of first or second order, and intermittency. Reproducing these experimental observations using a non-spatial model suggests that spatial geometry may have less of an impact on collective motion than previously thought.

Patterns of cooperation: fairness and coordination in networks of interacting agents

We study the self-assembly of a complex network of collaborations among self-interested agents. The agents can maintain different levels of cooperation with different partners. Further, they continuously, selectively and independently adapt the amount of resources allocated to each of their collaborations in order to maximize the obtained payoff. We show analytically that the system approaches a state in which the agents make identical investments, and links produce identical benefits. Despite this high degree of social coordination, some agents manage to secure privileged topological positions in the network, enabling them to extract high payoffs. Our analytical investigations provide a rationale for the emergence of unidirectional non-reciprocal collaborations and different responses to the withdrawal of a partner from an interaction that have been reported in the psychological literature.

Analytical investigation of self-organized criticality in neural networks.

Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity-dependent synaptic plasticity. Here, we model neurons as discrete-state nodes on an adaptive network following stochastic dynamics. At a threshold connectivity, this system undergoes a dynamical phase transition at which persistent activity sets in. In a low-dimensional representation of the macroscopic dynamics, this corresponds to a transcritical bifurcation. We show analytically that adding activity-dependent rewiring rules, inspired by homeostatic plasticity, leads to the emergence of an attractive steady state at criticality and present numerical evidence for the systems evolution to such a state.

Engineering mesoscale structures with distinct dynamical implications

The dynamics of networks of interacting systems depends intricately on the interaction topology. When the dynamics is explored, generally the whole topology has to be considered. However, here we show that there are certain mesoscale subgraphs that have precise and distinct consequences for the system-level dynamics. In particular, if mesoscale symmetries are present then eigenvectors of the Jacobian localize on the symmetric subgraph and the corresponding eigenvalues become insensitive to the topology outside the subgraph. Hence, dynamical instabilities associated with these eigenvalues can be analysed without considering the topology of the embedding network. While such instabilities are thus generated entirely in small subgraphs, they generally do not remain confined to the subgraph once the instability sets in and thus have system-level consequences. Here we illustrate the analytical investigation of such instabilities in an ecological metapopulation model consisting of a network of delay-coupled delay oscillators.

Contact processes and moment closure on adaptive networks

Contact processes describe the transmission of distinct properties of nodes via the links of a network. They provide a simple framework for many phenomena, such as epidemic spreading and opinion formation. Combining contact processes with rules for topological evolution yields an adaptive network in which the states of the nodes can interact dynamically with the topological degrees of freedom. By moment-closure approximation it is possible to derive low-dimensional systems of ordinary differential equations that describe the dynamics of the adaptive network on a coarse-grained level. In this chapter we discuss the approximation technique itself as well as its applications to adaptive networks. Thus, it can serve both as a tutorial as well as a review of recent results.

Coordination, Differentiation and Fairness in a Population of Cooperating Agents

In a recent paper, we analyzed the self-assembly of a complex cooperation network. The network was shown to approach a state where every agent invests the same amount of resources. Nevertheless, highly-connected agents arise that extract extraordinarily high payoffs while contributing comparably little to any of their cooperations. Here, we investigate a variant of the model, in which highly-connected agents have access to additional resources. We study analytically and numerically whether these resources are invested in existing collaborations, leading to a fairer load distribution, or in establishing new collaborations, leading to an even less fair distribution of loads and payoffs.

Topological stability criteria for networking dynamical systems with Hermitian Jacobian

The central theme of complex systems research is to understand the emergent macroscopic properties of a system from the interplay of its microscopic constituents. The emergence of macroscopic properties is often intimately related to the structure of the microscopic interactions. Here, we present an analytical approach for deriving necessary conditions that an interaction network has to obey in order to support a given type of macroscopic behaviour. The approach is based on a graphical notation, which allows rewriting Jacobis signature criterion in an interpretable form and which can be applied to many systems of symmetrically coupled units. The derived conditions pertain to structures on all scales, ranging from individual nodes to the interaction network as a whole. For the purpose of illustration, we consider the example of synchronization, specifically the (heterogeneous) Kuramoto model and an adaptive variant. The results complete and extend the previous analysis of Do et al. ( 2012 Phys. Rev. Lett. 108 , 194102).