Reducing the number of time delays in coupled dynamical systems

2018/04/30 by Alexandre Wagemakers, Javier Used, Miguel A. F. Sanjuán
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Discrete mathematics #Dynamical systems theory #Focus (optics) #Gene Regulatory Network Analysis #Graph #Mathematics #Nonlinear Dynamics and Pattern Formation #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Set (abstract data type) #Topology (electrical circuits) #nlin.AO

paper · pdf · doi:10.1140/epjst/e2018-800044-x

published as Eur. Phys. J. Spec. Top. (2018) 227: 1281

arxiv created 2018/06/19 · openalex publication_date 2018/11/01 · arxiv updated 2019/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 set to zero a significant amount of time-delayed connections without altering the global dynamics. We will focus 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.

Citations

• Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
• Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
• Classification of Coupled Dynamical Systems with Multiple Delays: Finding the Minimal Number of Delays