Abstract
This paper is dedicated to the study of the interaction between dynamical systems and percolation models, with views toward the study of viral infections whose virus mutate with time. Recall that -bootstrap percolation describes a deterministic process where vertices of a graph are infected once neighbors of it are infected. We generalize this by introducing -bootstrap percolation, a time-dependent process where the number of neighboring vertices that need to be infected for a disease to be transmitted is determined by a percolation function at each time . After studying some of the basic properties of the model, we consider smallest percolating sets and construct a polynomial-timed algorithm to find one smallest minimal percolating set on finite trees for certain -bootstrap percolation models.
3 More- Received 8 November 2019
- Accepted 20 February 2020
DOI:https://doi.org/10.1103/PhysRevResearch.2.023001
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society