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

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  • Borges, Ernesto P
  • Tirnakli, Ugur

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 (qsen<1) related to its sensitivity to initial condition properties, and the other, graining-dependent (qrel(W)>1), related to its relaxation dynamics towards its stationary state attractor. We also corroborate a scaling law between these two indices, 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, qsen=0.2445….

Suggested Citation

  • Borges, Ernesto P & Tirnakli, Ugur, 2004. "Two-dimensional dissipative maps at chaos threshold: sensitivity to initial conditions and relaxation dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 227-233.
    • Handle: RePEc:eee:phsmap:v:340:y:2004:i:1:p:227-233
    DOI: 10.1016/j.physa.2004.04.011
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    References listed on IDEAS

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    1. Baldovin, Fulvio & Moyano, Luis G & Majtey, Ana P & Robledo, Alberto & Tsallis, Constantino, 2004. "Ubiquity of metastable-to-stable crossover in weakly chaotic dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 205-218.
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