Saberi, Abbas AliTirnakli, UgurTsallis, Constantino2025-12-302025-12-3020252470-00452470-0053https://doi.org/10.1103/gtlz-67cfhttps://hdl.handle.net/20.500.14365/8482Saberi, Abbas Ali/0000-0001-8864-4748; Tirnakli, Ugur/0000-0002-1104-0847We focus on the Feigenbaum-Coullet-Tresser point of the dissipative one-dimensional z-logistic map x(t+1) = 1-a|x(t )|(z) (z 1). We show that sums of iterates converge to q-Gaussian distributions P-q(y) = P-q(0) exp(q)(-beta(q)y(2)) = P-q(0 )[1 + (q-1)beta(q) y(2)](1/(1-q))(q >= 1; beta(q) > 0), which optimize the nonadditive entropic functional Sq under simple constraints. We propose and justify heuristically a closed-form prediction for the entropic index, q(z) = 1 + 2/(z + 1), and validate it numerically via data collapse for typical z values. The formula captures how the limiting law depends on the nonlinearity order and implies finite variance for z > 2 and divergent variance for 1 <= z <= 2. These results extend edge-of-chaos central limit behavior beyond the standard (z = 2) case and provide a simple predictive law for unimodal maps with varying maximum order.eninfo:eu-repo/semantics/openAccessArticle10.1103/gtlz-67cf2-s2.0-105024077917