2007/05/13 by Maria de Sousa Vieira, Vieira, Maria de Sousa
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #FOS: Physical sciences #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0705.1807
5 pages, 4 figures
arxiv created 2007/05/13 · openalex publication_date 2007/05/13 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
In a recent letter, Fisher et al. reported the phenomenon of zero-lag long range isochronous synchronization via dynamical relaying in systems with delay [Phys. Rev. Lett. bf 97, 123902 (2006)]. They reported that when one has two coupled systems A and C, with delay between them, then the introduction of a third element B between A and C will allow them to synchronize even in regions of the parameter space where this was not possible without the presence of B. Here we study in detail the phenomenon and verify that in all the cases studied (including the ones reported by Fisher et al.) this occurs due to the tendency of A and B and B and C to be in antiphase synchronization and if A is in antiphase with B and B is in antiphase with C, it will imply that A and C are inphase. We show this in coupled quadratic maps, Kuramoto and Rössler oscillators. We also report that there is a simpler configuration where the same phenomenon occurs and has nearly the same features of the cases studied by Fisher et al.