Trapped to free: A mechanism to spatiotemporal chaos

We further investigate the crisis-induced transition from temporal chaos (TC) to spatiotemporal chaos (STC) due to collision between the unstable orbit of,a carrier saddle steady wave (SSW) and the attractor of its perturbation wave (PW) [Kaifen He. Phys. Rev. Lett. 80, 696 (1998)]. In the present work, the influence of the SSW on its PW is studied in different dimensions. It is found that in our case, as a result of mode-mode couplings only one dimension becomes crucial in the onset of crisis. The state transition of the PW mode phase in this dimension at the crisis is emphasized. Before the crisis, all the PW partial waves are trapped in the SSW state. After the crisis, the PW partial wave in this dimension is free from the trapping of the SSW partial wave; it experiences on-off resonance with the latter, which is responsible for the transition to STC. [S1063-651X(99)06605-2].