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Sensitivity to initial conditions, entropy production, and escape rate at the onset of chaos |
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| Authors: | Miguel Angel Fuentes Yuzuru SatoConstantino Tsallis |
| Institution: | a Centro Atómico Bariloche, Instituto Balseiro and CONICET, 8400 Bariloche, Argentina b Center for Advanced Studies in Ecology and Biodiversity, Facultad de Ciencias Biológicas, Pontificia Universidad Católica de Chile, Casilla 114-D, Santiago CP 6513677, Chile c Kita 12 Nishi 6, Kita-ku, Sapporo, Hokkaido 060-0812, Japan d Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA e Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil |
| Abstract: | We analytically link three properties of nonlinear dynamical systems, namely sensitivity to initial conditions, entropy production, and escape rate, in z-logistic maps for both positive and zero Lyapunov exponents. We unify these relations at chaos, where the Lyapunov exponent is positive, and at its onset, where it vanishes. Our result unifies, in particular, two already known cases, namely (i) the standard entropy rate in the presence of escape, valid for exponential functionality rates with strong chaos, and (ii) the Pesin-like identity with no escape, valid for the power-law behavior present at points such as the Feigenbaum one. |
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