M-furcations in coupled maps
نویسنده
چکیده
We study the scaling behavior of M -furcation (M =2, 3, 4, . . .) sequences of M-period (n = 1, 2, . . .) orbits in two coupled one-dimensional (1D) maps. Using a renormalization method, how the scaling behavior depends on M is particularly investigated in the zero-coupling case in which the two 1D maps become uncoupled. The zero-coupling fixed map of the M -furcation renormalization transformation is found to have three relevant eigenvalues δ, α, and M (δ and α are the parameter and orbital scaling factors of 1D maps, respectively). Here the second and third ones, α and M , called the “coupling eigenvalues”, govern the scaling behavior associated with coupling, while the first one δ governs the scaling behavior of the nonlinearity parameter like the case of 1D maps. The renormalization results are also confirmed by a direct numerical method. PACS numbers: 05.45.+b, 03.20.+i, 05.70.Jk Typeset using REVTEX Electronic address: [email protected] 1
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