WAVE-LIKE PATTERNS IN ONE-DIMENSIONAL COUPLED MAP LATTICES

We investigate the existence of wavelike solution for the logistic cou pled map lattices for which the spatiotemporal periodic patterns can b e predicted by a simple two-dimensional mapping. The existence of such wavelike solutions is proved by the implicit function theorem with co nstraints. We also examine the stabilities of these wave solutions und er perturbations of uniform small deformation type. We show that in so me specific cases these perturbations are completely general. The tech nique used in this paper is also applicable to investigate other space -time regular patterns.