A fractal array of coupled maps, where space is nonuniform, is considered as a dynamical system. The stability and bifurcations of spatially synchronized, periodic states on the Sierpinski gasket are studied. The matrix that expresses the coupling among neighboring elements exhibits a spectrum of eigenvalues with multifractal properties, and their global scaling behavior is characterized by the function f(α). The multifractal character of the eigenvalues affects the stability boundaries of the synchronized, periodic states in the parameter plane of the system. The boundary structure allows access to regions of stability and gives rise to bifurcations that are not present in regular lattices.

• Received 18 February 1992

DOI:https://doi.org/10.1103/PhysRevA.46.1850