Two-dimensional dissipative maps at chaos threshold: sensitivity to initial conditions and relaxation dynamics

Abstract

The sensitivity to initial conditions and relaxation dynamics of two-dimensional maps are analyzed at the edge of chaos, along the lines of nonextensive statistical mechanics. We verify the dual nature of the entropic index for the Henon map, one (q sen < 1) related to its sensitivity to initial conditions properties, and the other, graining-dependent (q rel (W ) > 1), related to its relaxation dynamics towards its stationary state attractor. We also corroborate a scaling law between these two indexes, previously found for z-logistic maps. Finally we perform a preliminary analysis of a linearized version of the Henon map (the smoothed Lozi map). We find that the sensitivity properties of all these z-logistic, Henon and Lozi maps are the same, q sen = 0.2445 . . .

On the performance of chaotic interleaver for turbo codes

“…In 1978, René Lozi introduced in a short note [20] a two-dimensional map, so called lozi map via a direct modification of the Hénon map. Since then, these maps have been studied in many works [21][22][23][24][25][26]. Hereafter the orbits of lozi map will be analyzed.…”

Introduction to Nonextensive Statistical Mechanics

“…Although not with the same detail as for the one-dimensional ones, some twodimensional dissipative maps have been studied as well [156][157][158]. More specifically, the Henon and the Lozi maps.…”