Artículos de revistas
Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation
Entropy. Basel: Mdpi Ag, v. 15, n. 10, p. 4310-4318, 2013.
Universidade Estadual Paulista (UNESP)
Abdus Salaam Int Ctr Theoret Phys
Convergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is near a pitchfork bifurcation. We confirmed that the convergence to the fixed point in both logistic and cubic maps for a region close to the fixed point goes exponentially fast to the fixed point and with a relaxation time described by a power law of exponent -1. At the bifurcation point, the exponent is not universal and depends on the type of the bifurcation as well as on the nonlinearity of the map.