Abstract
A dead zone in the interaction between two dynamical systems is a region of their joint phase space where one system is insensitive to the changes in the other. These can arise in a number of contexts, and their presence in phase interaction functions has interesting dynamical consequences for the emergent dynamics. In this paper, we consider dead zones in the interaction of general coupled dynamical systems. For weakly coupled limit cycle oscillators, we investigate criteria that give rise to dead zones in the phase interaction functions. We give applications to coupled multiscale oscillators where coupling on only one branch of a relaxation oscillation can lead to the appearance of dead zones in a phase description of their interaction.
| Original language | English |
|---|---|
| Article number | 093132 |
| Pages (from-to) | 1-10 |
| Number of pages | 10 |
| Journal | Chaos |
| Volume | 31 |
| Issue number | 9 |
| Early online date | 27 Sept 2021 |
| DOIs | |
| Publication status | Published - Sept 2021 |
Bibliographical note
Funding Information:The research of P.A. and C.P. was funded by EPSRC Centre for Predictive Modelling in Healthcare (Grant No. EP/N014391/1). C.B. received funding by the EPSRC through Grant No. EP/T013613/1.
Publisher Copyright:
© 2021 Author(s).
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
Funding
The research of P.A. and C.P. was funded by EPSRC Centre for Predictive Modelling in Healthcare (Grant No. EP/N014391/1). C.B. received funding by the EPSRC through Grant No. EP/T013613/1.