混乱的
数学
李雅普诺夫指数
控制理论(社会学)
李雅普诺夫函数
动力系统理论
拓扑熵
非线性系统
吸引子
理论(学习稳定性)
熵(时间箭头)
作者
Hassan Salarieh,Aria Alasty
标识
DOI:10.1016/j.chaos.2006.09.062
摘要
Abstract In this paper the problem of chaos control in nonlinear maps using minimization of entropy function is investigated. Invariant probability measure of a chaotic dynamics can be used to produce an entropy function in the sense of Shannon. In this paper it is shown that how the entropy control technique is utilized for chaos elimination. Using only the measured states of a chaotic map the probability measure of the system is numerically estimated and this estimated measure is used to obtain an estimation for the entropy of the chaotic map. The control variable of the chaotic system is determined in such a way that the entropy function descends until the chaotic trajectory of the map is replaced with a regular one. The proposed idea is applied for stabilizing the fixed points of the logistic and the Henon maps as some cases of study. Simulation results show the effectiveness of the method in chaos rejection when only the statistical information is available from the under-study systems.
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