A novel type of traveling-wave attractor is found in coupled-map lattices. Attractors with different velocities coexist, which are coded by the asymmetry of the wave form. Admissible velocities for the attractors form a series of bands. The velocity is proportional to the winding number of phase slips. If the wavelength and the system size do not match, the wave is modulated by low-dimensional chaos, which leads to spontaneous velocity switching by frustration or reverse transmission of chaotic modulation.
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Kunihiko Kaneko (1992) studied this question.
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