WAVELENGTH-DOUBLING BIFURCATIONS IN ONE-DIMENSIONAL COUPLED LOGISTIC MAPS

We discuss in detail the interesting phenomenon of wavelength-doubling bifurcations in the model of coupled-map lattices reported earlier [P hys. Rev. Lett. 70, 3408 (1993)]. We take nearest-neighbor coupling of logistic maps on a one-dimensional lattice. With the value of the par ameter of the logistic map, mu, corresponding to the period-doubling a ttractor, we see that the wavelength and the temporal period of the ob served pattern undergo successive wavelength- and period-doubling bifu rcations with decreasing coupling strength epsilon. The universality c onstants alpha and delta appear to be the same as in the case of the p eriod-doubling route to chaos in the uncoupled logistic map. The phase diagram in the epsilon-mu plane is investigated. For large values of mu and large periods, regions of instability are observed near the bif urcation fines. We also investigate the mechanism for the wavelength-d oubling bifurcations to occur. We find that such bifurcations occur wh en the eigenvalue of the stability matrix corresponding to the eigenve ctor with periodicity of twice the wavelength exceeds unity in magnitu de.