Reconstruction of one-dimensional chaotic maps from sequences of probability density functions

被引：11

作者：

Nie, Xiaokai ^{[1
]}

Coca, Daniel ^{[1
]}

机构：

[1] Univ Sheffield, Dept Automat Control & Syst Engn, Sheffield S1 3JD, S Yorkshire, England

来源：

NONLINEAR DYNAMICS | 2015年 / 80卷 / 03期

基金：

英国生物技术与生命科学研究理事会;

关键词：

Chaotic maps; Inverse Frobenius-Perron problem; Nonlinear systems; Probability density functions; PRESCRIBED STATISTICAL PROPERTIES; FROBENIUS-PERRON PROBLEM; INVARIANT DENSITIES; TIME-SERIES; INVERSE PROBLEM; SYSTEMS; TRANSFORMATIONS; CONSTRUCTION; MODELS; IDENTIFICATION;

D O I：

10.1007/s11071-015-1949-9

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In many practical situations, it is impossible to measure the individual trajectories generated by an unknown chaotic system, but we can observe the evolution of probability density functions generated by such a system. The paper proposes for the first time a matrix-based approach to solve the generalized inverse Frobenius-Perron problem, that is, to reconstruct an unknown one-dimensional chaotic transformation, based on a temporal sequence of probability density functions generated by the transformation. Numerical examples are used to demonstrate the applicability of the proposed approach and evaluate its robustness with respect to constantly applied stochastic perturbations.

引用

页码：1373 / 1390

页数：18

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