McDonald, Andre MVan Wyk, MChen, G2021-10-222021-10-222021-08McDonald, A.M., Van Wyk, M. & Chen, G. 2021. The inverse Frobenius-Perron problem: A survey of solutions to the original problem formulation. <i>AIMS Mathematics, 6(10).</i> http://hdl.handle.net/10204/121322473-6988Doi: 10.3934/math.2021650http://hdl.handle.net/10204/12132The 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.FulltextenDynamical systemsErgodic mapInverse Frobenius-Perron problemInvariant densityInvariant measurePiecewise continuous mapsArticleMcDonald, A. M., Van Wyk, M., & Chen, G. (2021). The inverse Frobenius-Perron problem: A survey of solutions to the original problem formulation. <i>AIMS Mathematics, 6(10)</i>, http://hdl.handle.net/10204/12132McDonald, Andre M, M Van Wyk, and G Chen "The inverse Frobenius-Perron problem: A survey of solutions to the original problem formulation." <i>AIMS Mathematics, 6(10)</i> (2021) http://hdl.handle.net/10204/12132McDonald AM, Van Wyk M, Chen G. The inverse Frobenius-Perron problem: A survey of solutions to the original problem formulation. AIMS Mathematics, 6(10). 2021; http://hdl.handle.net/10204/12132.TY - Article AU - McDonald, Andre M AU - Van Wyk, M AU - Chen, G AB - 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. DA - 2021-08 DB - ResearchSpace DP - CSIR J1 - AIMS Mathematics, 6(10) KW - Dynamical systems KW - Ergodic map KW - Inverse Frobenius-Perron problem KW - Invariant density KW - Invariant measure KW - Piecewise continuous maps LK - https://researchspace.csir.co.za PY - 2021 SM - 2473-6988 T1 - The inverse Frobenius-Perron problem: A survey of solutions to the original problem formulation TI - The inverse Frobenius-Perron problem: A survey of solutions to the original problem formulation UR - http://hdl.handle.net/10204/12132 ER -24883