A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems

Xiaokai Nie; Daniel Coca

doi:10.1016/j.cnsns.2017.05.011

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems

Commun Nonlinear Sci Numer Simul. 2018 Jan:54:248-266. doi: 10.1016/j.cnsns.2017.05.011.

Authors

Xiaokai Nie^{1

2}, Daniel Coca¹

Affiliations

¹ Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield S1 3JD, United Kingdom.
² Leeds Institute for Data Analytics, University of Leeds, Leeds LS2 9JT, United Kingdom.

Abstract

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

Keywords: Chaotic maps; Inverse Frobenius–Perron problem; Nonlinear systems; Probability density functions.

Grants and funding

G0802627/MRC_/Medical Research Council/United Kingdom