2008/04/23 by Guy Katriel · 56 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · Engineering · Mathematics · Physics and Astronomy · #Biology #Chemistry #Combinatorics #Computer science #Control (management) #Control theory (sociology) #Coupling (piping) #Engineering #Gene Regulatory Network Analysis #Instability #Mathematics #Mechanics #Nonlinear Dynamics and Pattern Formation #Oscillation (cell signaling) #Physics #Pulsatile flow #Stability (learning theory) #Synchronization (alternating current) #Synchronization networks #Topology (electrical circuits) #nlin.AO #nlin.PS #q-bio.OT #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/j.physd.2008.04.015
published in Physica D Nonlinear Phenomena 237(22), 2933-2944 (Elsevier BV)
arxiv created 2008/04/23 · openalex publication_date 2008/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate synchronization of systems of oscillators which are weakly coupled, in the sense that the influence of the oscillators on the environment is weak. We prove that arbitrarily weak coupling will synchronize the oscillators, provided that this coupling is of the 'right' sign. We illustrate our general results by applications to a model of coupled GnRH neuron oscillators proposed by Khadra and Li, and to indirectly weakly-coupled lambda-omega oscillators