Mendes C F O, da Silva R M, Beims M W
Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil.
Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
Phys Rev E. 2019 Jun;99(6-1):062206. doi: 10.1103/PhysRevE.99.062206.
This work presents numerical evidence that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance autocorrelation are observed for different systems, namely, exponential decays for the quadratic map, logarithmic for the Hénon map, and power-law for the conservative standard map. In all these cases the decay exponent is close to the positive Lyapunov exponent. For hyperchaotic conservative systems the power-law decay of the distance autocorrelation is not directly related to any Lyapunov exponent.
这项工作提供了数值证据，表明对于具有一个正李雅普诺夫指数的离散动力系统，距离自相关的衰减总是与李雅普诺夫指数相关。对于不同的系统，观察到距离自相关有不同的衰减规律，即二次映射为指数衰减，亨农映射为对数衰减，保守标准映射为幂律衰减。在所有这些情况下，衰减指数都接近正李雅普诺夫指数。对于超混沌保守系统，距离自相关的幂律衰减与任何李雅普诺夫指数都没有直接关系。
