Asymmetric unimodal maps at the edge of chaos

Asymmetric unimodal maps at the edge of chaos.

We numerically investigate the sensitivity to initial conditions of asymmetric unimodal maps x(t+1)=1-a/x(t)/(z(i)) (i=1,2 correspond to x(t)>0 and x(t)<0, respectively, z(i)>1, 0<a< or =2, t=0,1,2,...) at the edge of chaos. We employ three distinct algorithms to characterize the power-law sensitivity to initial conditions at the edge of chaos, namely: direct measure of the divergence of initia...

Multifractality and nonextensivity at the edge of chaos of unimodal maps

We examine both the dynamical and the multifractal properties at the chaos threshold of logistic maps with general nonlinearity z > 1. First we determine analytically the sensitivity to initial conditions ξt. Then we consider a renormalization group (RG) operation on the partition function Z of the multifractal attractor that eliminates one half of the multifractal points each time it is applie...

Robust Chaos in Polynomial unimodal Maps

Robust chaos occurs when a dynamical system has a neighborhood in parameter space such that there is one unique chaotic attractor, and no periodic attractors are present [Barreto et al., 1997; Banerjee et al., 19981. This behavior, expected to be relevant for any practical applications of chaos, was shown to exist in a general family of piecewise-smooth twodimensional maps, but conjectured to b...

Nonextensivity at the edge of chaos of a new universality class of one-dimensional unimodal dissipative maps

We introduce a new universality class of one-dimensional unimodal dissipative maps. The new family, from now on referred to as the (z1, z2)-logarithmic map, corresponds to a generalization of the z-logistic map. The Feigenbaum-like constants of these maps are determined. It has been recently shown that the probability density of sums of iterates at the edge of chaos of the z-logistic map is num...

Education at the edge of chaos.