Multistability and phase-space structure of dissipative nonlinear parametric four-wave interactions.
We investigate the phase-space structure displayed by a system of four waves interacting by means of nonlinear coupling between two wave triplets, which results in a dissipative high-dimensional vector field presenting an invariant manifold, wherein the dynamics is essentially conservative. The focus is on the coexistence of a large number of periodic attractors in the phase space, with an interwoven structure of the basins of attraction, where low-period attractors have predominance. The time behavior of nearly conserved quantities and the properties of the Lyapunov spectra are used to imply the existence of a lower-dimensional invariant manifold where the dynamics is nearly conservative. A three-dimensional map is used to illustrate these findings.
Coninck
J C P
JC
Departamento de Física, Universidade Federal do Paraná, 81531-990, Curitiba, Paraná, Brazil.
Lopes
S R
SR
Viana
R L
RL