The inverse Frobenius-Perron problem: A survey of solutions to the original problem formulation

• Main Authors: André M. McDonald, Michaël A. van Wyk, Guanrong Chen
• Format: Article
• Language: English
• Published: AIMS Press 2021-08-01
• Series: AIMS Mathematics
• Subjects: inverse frobenius-perron problem; ergodic map; invariant density; invariant measure; piecewise continuous maps; dynamical system
• Online Access: https://www.aimspress.com/article/doi/10.3934/math.2021650?viewType=HTML

The inverse Frobenius-Perron problem (IFPP) is a collective term for a family of problems that requires the construction of an ergodic dynamical system model with prescribed statistical characteristics. Solutions to this problem draw upon concepts from ergodic theory and are scattered throughout the literature across domains such as physics, engineering, biology and economics. This paper presents a survey of the original formulation of the IFPP, wherein the invariant probability density function of the system state is prescribed. The paper also reviews different strategies for solving this problem and demonstrates several of the techniques using examples. The purpose of this survey is to provide a unified source of information on the original formulation of the IFPP and its solutions, thereby improving accessibility to the associated modeling techniques and promoting their practical application. The paper is concluded by discussing possible avenues for future work.