dc.contributor.author |
McDonald, Andre M
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dc.contributor.author |
Van Wyk, M
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dc.contributor.author |
Chen, G
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dc.date.accessioned |
2021-10-22T08:42:11Z |
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dc.date.available |
2021-10-22T08:42:11Z |
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dc.date.issued |
2021-08 |
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dc.identifier.citation |
McDonald, 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/10204/12132 |
en_ZA |
dc.identifier.issn |
2473-6988 |
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dc.identifier.uri |
Doi: 10.3934/math.2021650
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|
dc.identifier.uri |
http://hdl.handle.net/10204/12132
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dc.description.abstract |
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. |
en_US |
dc.format |
Fulltext |
en_US |
dc.language.iso |
en |
en_US |
dc.relation.uri |
https://www.aimspress.com/article/doi/10.3934/math.2021650 |
en_US |
dc.source |
AIMS Mathematics, 6(10) |
en_US |
dc.subject |
Dynamical systems |
en_US |
dc.subject |
Ergodic map |
en_US |
dc.subject |
Inverse Frobenius-Perron problem |
en_US |
dc.subject |
Invariant density |
en_US |
dc.subject |
Invariant measure |
en_US |
dc.subject |
Piecewise continuous maps |
en_US |
dc.title |
The inverse Frobenius-Perron problem: A survey of solutions to the original problem formulation |
en_US |
dc.type |
Article |
en_US |
dc.description.pages |
11200-11232 |
en_US |
dc.description.note |
Copyright: 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0) |
en_US |
dc.description.cluster |
Defence and Security |
en_US |
dc.description.impactarea |
Information & Cyber Security C |
en_US |
dc.identifier.apacitation |
McDonald, 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/10204/12132 |
en_ZA |
dc.identifier.chicagocitation |
McDonald, 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/10204/12132 |
en_ZA |
dc.identifier.vancouvercitation |
McDonald 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. |
en_ZA |
dc.identifier.ris |
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 -
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en_ZA |
dc.identifier.worklist |
24883 |
en_US |