Peer-Reviewed Journal Details
Mandatory Fields
Ryan, Pierce; Keane, Andrew; Amann, Andreas
2020
February
Chaos
Border-collision bifurcations in a driven time-delay system
Validated
Optional Fields
Piecewise-linear system Time delay Periodic forcing Torus bifurcations Arnold tongues Border-collision bifurcations Poincaré map
30
2
1
12
We show that a simple piecewise-linear system with time delay and periodic forcing gives rise to a rich bifurcation structure of torus bifurcations and Arnold tongues, as well as multistability across a significant portion of the parameter space. The simplicity of our model enables us to study the dynamical features analytically. Specifically, these features are explained in terms of border-collision bifurcations of an associated Poincaré map. Given that time delay and periodic forcing are common ingredients in mathematical models, this analysis provides widely applicable insight.
1054-1500
10.1063/1.5119982
Grant Details