Wavelength doubling bifurcations in coupled map lattices

Abstract

We report an interesting phenomenon of wavelength doubling bifurcations in the model of coupled (logistic) map lattices. The temporal and spatial periods of the observed patterns undergo successive period doubling bifurcations with decreasing coupling strength. The universality constants α and δ appear to be the same as in the case of period doubling route to chaos in the uncoupled logistic map. The analysis of the stability matrix shows that period doubling bifurcation occurs when an eigenvalue whose eigenvector has a structure with doubled spatial period exceeds unity.