Evolution of spatially embedded branching trees with interacting nodes
F. L. Forgerini, N. Crokidakis, S. N. Dorogovtsev, J. F. F. Mendes

TL;DR
This paper models the evolution of spatially embedded branching trees with suppressed close-node branching, revealing a transition from exponential to power-law growth and potential extinction in restricted spaces.
Contribution
It introduces a new model of cooperative branching with spatial suppression, capturing complex growth dynamics and phase transitions in embedded networks.
Findings
Initial exponential growth transitions to power-law growth after a crossover time
Spatial restrictions can lead to extinction of the branching process
Identifies a transition point analogous to a phase change in network size
Abstract
We study the evolution of branching trees embedded in Euclidean spaces with suppressed branching of spatially close nodes. This cooperative branching process accounts for the effect of overcrowding of nodes in the embedding space and mimics the evolution of life processes (the so-called "tree of life") in which a new level of complexity emerges as a short transition followed by a long period of gradual evolution or even complete extinction. We consider the models of branching trees in which each new node can produce up to two twigs within a unit distance from the node in the Euclidean space, but this branching is suppressed if the newborn node is closer than at distance from one of the previous generation nodes. This results in an explosive (exponential) growth in the initial period, and, after some crossover time for small , in a slow (power-law) growth. This…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplex Network Analysis Techniques · Stochastic processes and statistical mechanics · Ecosystem dynamics and resilience
