Abstract
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply. Theoretical and experimental studies have found that real-world transport networks exhibit both tree-like motifs and cycles. When the network is subject to load fluctuations, the presence of cyclic motifs may help to reduce flow fluctuations and, thus, render supply in the network more robust. While previous studies considered network topology via optimization principles, here, we take a dynamical systems approach and study a simple model of a flow network with dynamically adapting weights (conductances). We assume a spatially non-uniform distribution of rapidly fluctuating loads in the sinks and investigate what network configurations are dynamically stable. The network converges to a spatially non-uniform stable configuration composed of both cyclic and tree-like structures. Cyclic structures emerge locally in a transcritical bifurcation as the amplitude of the load fluctuations is increased. The resulting adaptive dynamics thus partitions the network into two distinct regions with cyclic and tree-like structures. The location of the boundary between these two regions is determined by the amplitude of the fluctuations. These findings may explain why natural transport networks display cyclic structures in the micro-vascular regions near terminal nodes, but tree-like features in the regions with larger veins.
Highlights
Network structures are found in all of our everyday life, ranging from social interactions over technological infrastructure to natural systems
-called stoma evaporate the sap, and their periodic opening and closing correspond to fluctuating sinks [28, 33]. Inspired by these natural networks, we wish to address two questions: How strong do load fluctuations need to be so that cyclic shunts1 emerge in the network that break the topology of a spanning tree? How far do these cyclic shunts reach into the tree toward the feeding vessel, so that a nonuniform network structure emerges, divided into two subgraphs, one tree-like and the other with cycles?
We have studied how fluctuating loads affect the re-configuration of vessels in an adaptive flow network
Summary
Network structures are found in all of our everyday life, ranging from social interactions over technological infrastructure to natural systems. In the language of vascular physiology, we model a bifurcating arterial network where the only inlet is a feeding artery, bifurcating in a tree-structure to the terminal nodes interfacing via capillaries to the venous network At this interface, changing supply demands constitute load fluctuations which are rapid compared to the adaptive network dynamics. -called stoma evaporate the sap, and their periodic opening and closing correspond to fluctuating sinks [28, 33] Inspired by these natural networks, we wish to address two questions: How strong do load fluctuations need to be so that cyclic shunts (loops) emerge in the network that break the topology of a spanning tree?
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