2003/07/16 by Fatihcan M. Atay · 1 citation
Computer Science · Physics and Astronomy · #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #cond-mat.dis-nn #nlin.AO
paper · pdf · doi:10.1016/s0167-2789(03)00154-4
published as Physica D 183 (2003) 1-18 · 21 pages, 4 figures
openalex publication_date 2003/07/16 · arxiv created 2004/01/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Networks of weakly nonlinear oscillators are considered with diffusive and time-delayed coupling. Averaging theory is used to determine parameter ranges for which the network experiences amplitude death, whereby oscillations are quenched and the equilibrium solution has a large domain of attraction. The amplitude death is shown to be a common phenomenon, which can be observed regardless of the precise nature of the nonlinearities and under very general coupling conditions. In addition, when the network consists of dissimilar oscillators, there exist parameter values for which only parts of the network are suppressed. Sufficient conditions are derived for total and partial amplitude death in arbitrary network topologies with general nonlinearities, coupling coefficients, and connection delays.