Edge of chaos and genesis of turbulence
Abstract
The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulence via a cascade of fractal-fractal metamorphoses. The edge state responsible for the edge of chaos and the genesis of turbulence is an unstable traveling wave in the laboratory frame, corresponding to a saddle point lying at the basin boundary in the Fourier space.
- Publication:
-
Physical Review E
- Pub Date:
- November 2013
- DOI:
- 10.1103/PhysRevE.88.052910
- arXiv:
- arXiv:1303.1797
- Bibcode:
- 2013PhRvE..88e2910C
- Keywords:
-
- 05.45.Jn;
- 47.27.Cn;
- 47.27.ed;
- High-dimensional chaos;
- Transition to turbulence;
- Dynamical systems approaches;
- Physics - Fluid Dynamics
- E-Print:
- Physical Review E 88, 052910 (2013)