Abstract
Percolation is a process that impairs network connectedness by deactivating links or nodes. This process features a phase transition that resembles paradigmatic critical transitions in epidemic spreading, biological networks, traffic and transportation systems. Some biological systems, such as networks of neural cells, actively respond to percolation-like damage, which enables these structures to maintain their function after degradation and aging. Here we study percolation in networks that actively respond to link damage by adopting a mechanism resembling synaptic scaling in neurons. We explain critical transitions in such active networks and show that these structures are more resilient to damage as they are able to maintain a stronger connectedness and ability to spread information. Moreover, we uncover the role of local rescaling strategies in biological networks and indicate a possibility of designing smart infrastructures with improved robustness to perturbations.
Highlights
Percolation is a process that impairs network connectedness by deactivating links or nodes
Percolation-like processes that conceptualize random damage in networks have been since long viewed as prototypical models for complex systems resilience
We have presented a theory that naturally extends the classical percolation framework to a more complex one that incorporates the principle of homeostatic plasticity
Summary
Percolation is a process that impairs network connectedness by deactivating links or nodes. When links feature different strengths ( called weights or capacities), both the structure and link weights contribute to network resilience, for example, as it happens with road and airline networks, the Internet, electricity grid, and financial networks The role of such weights in network resilience can be mathematically studied with filtration[13,14], a process that removes all edges with a weight less than a given threshold. Apart from wide use in the top-down design, several biological complex systems were observed to employ local self-regulation of link strengths with a positive effect on the global functioning of the whole network[16,17] Both brain networks and food webs are believed to perform link strengths optimization by virtue of a selfregulatory mechanism that is triggered in response to damage. Self-regulation-inspired principles were proposed to be used in top-down intervention scenarios for preventing species extinction in ecosystems[27]
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