Eur. Phys. J. Special Topics 227, 1281–1289 (2018)
https://doi.org/10.1140/epjst/e2018-800044-x

Regular Article

Reducing the number of time delays in coupled dynamical systems

¹ Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Móstoles, Tulipán s/n, Madrid 28933, Spain
² Department of Applied Informatics, Kaunas University of Technology, Studentu 50-415, Kaunas 51368, Lithuania
³ Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA

^a e-mail: alexandre.wagemakers@urjc.es

Received: 10 April 2018
Received in final form: 13 June 2018
Published online: 12 December 2018

Abstract

When several dynamical systems interact, the transmission of the information between them necessarily implies a time delay. When the time delay is not negligible, the study of the dynamics of these interactions deserve a special treatment. We will show here that under certain assumptions, it is possible to reduce the number of time delays without altering the global dynamics. We will focus here on graphs of interactions with identical time delays and bidirectional connections. With these premises, it is possible to find a configuration where a number n_z of time delays have been removed with n_v − 1 ≤ n_z ≤ n_v² /4, where n_v is the number of dynamical systems on a connected graph.