Robust Emergent Activity in Dynamical Networks

Abstract

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we develop a macroscopic description of the system in terms of the statistical features of the subnetwork of active nodes. We find the asymptotic characteristics of this subnetwork to be remarkably robust: the size of the active set is independent of the total number of nodes in the network, and the average degree of the active nodes is independent of both the network size and its connectivity. These results suggest that very different networks evolve to active subnetworks with the same characteristic features. This has strong implications for dynamical networks observed in the natural world, notably the existence of a characteristic range of links per species across ecological systems.

4 pages, 5 figures

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Cited by in corpus (7)

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• Network connectivity during mergers and growth: optimizing the addition of a module
• Noise Enhanced Activity in a Complex Network
• From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems
• Optimal interdependence enhances robustness of complex systems
• Enhancement of Extreme Events through the Allee effect and its Mitigation through Noise in a Three Species System
• Stability as a natural selection mechanism on interacting networks