Chaos in nonlinear random walks with nonmonotonic transition probabilities
Document Type
Article
Department
​Mathematics
Publication Date
12-1-2021
Abstract
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that occur when transition probabilities depend on the state of the system. We show that when these transition probabilities are nonmonotonic, i.e., are not uniformly biased towards the most densely or sparsely populated nodes, but rather direct random walkers with more nuance, chaotic dynamics emerge. Using multiple transition probability functions and a range of networks with different connectivity properties, we demonstrate that this phenomenon is generic. Thus, when such nonmonotonic properties are key ingredients in nonlinear transport applications complicated and unpredictable behaviors may result.
Publication Title
Physical Review Research
Volume
3
Issue
4
ISSN
26431564
DOI
10.1103/PhysRevResearch.3.043189
