Seminar: Temporality-induced chaos in the Kuramoto Model

Student: Mason Rock

Supervisor: Dr. Sean Conrnelius

Abstract

Keanu Mason Rock1∗, Hamza Dirie1∗, and Sean P. Cornelius2†
1 Toronto Metropolitan University, Toronto, Canada
2 Northeastern University, Boston, United States of America
† Corresponding Author: cornelius@torontomu.ca
∗ Authors contributed equally to this work

Recently, it has been recognized that many networked systems are temporal in nature. Temporal networks can be viewed as time-varying dynamical systems, in which the dynamics switches between subsystems as the network topology varies. This switching can produce exotic emergent behaviours not possible in any individual subsystem – notably chaos. One famous example is the Chua system, which produces a strange attractor from a piecewise-linear dynamical system. Comparatively little attention, however, has been paid to nonlinear temporal systems that may similarly produce chaos; specifically with respect to networked systems. Here, we present a minimal example of a temporal networked system where switching between network snapshots yields a strange attractor. Namely, our system swaps between two snapshots of the famous Kuramoto model upon reaching a switching condition. We visualize the resulting strange attractor and verify the existence of chaos via Poincare section and largest Lyapunov exponent. Our results are multidisciplinary, providing new insights for temporal network dynamics, as well as acting as a proof of concept for the generation of chaos via switching between network topologies.