Title

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

Share

COinS