Thorough numerical studies reveal that spatially extended dissipative systems with long-range interactions may give rise to a large-scale dynamics. This phenomenon, which generalizes mean-field chaos, can be interpreted as a form of subtle pattern formation, where a chaotic microscopic dynamics coexists with a macroscopic irregular behavior, sustained by the spontaneous emergence of long-wavelength ``hydrodynamic" modes. This regime can emerge only if the coupling is sufficiently long-ranged; otherwise normal space-time chaos is observed. In Stuart-Landau oscillators a further regime is found, where the amplitude of the hydrodynamic modes exhibits an anomalous intermediate scaling between that of collective and standard space-time chaos.
|Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
|Published - 3 Apr 2017
Some results were obtained using the EPSRC funded ARCHIE-WeSt High Performance Computer (www.archie-west.ac.uk). EPSRC under Grant No. EP/K000586/1.