Journal of Nonlinear Mathematical Physics

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Volume 28, Issue 2, June 2021, Pages 209 - 218

On Ramsey Dynamical Model and Closed-Form Solutions

Authors
Gülden Gün Polat1, †, Teoman Özer2, *
1İstanbul Kültür University, Faculty of Science and Letters, Mathematics and Computer Sciences, 34158 Bakırköy, İstanbul-Turkey
2İstanbul Technical University, Division of Mechanics, Faculty of Civil Engineering, 34469 Maslak, İstanbul-Turkey
†

Department of Mathematics, Gebze Technical University, 41400, Gebze-Kocaeli, Turkey

*Corresponding author. Email: tozer@itu.edu.tr
Corresponding Author
Teoman Özer
Received 2 July 2020, Accepted 2 January 2021, Available Online 21 January 2021.
DOI
10.2991/jnmp.k.210103.001How to use a DOI?
Keywords
Ramsey dynamical model; economic growth models; Lie point symmetries; Prelle-Singer approach; Jacobi last multiplier; Hamiltonian dynamics; closed-form solutions
Abstract

This study focuses on the analysis of Ramsey dynamical model with current Hamiltonian defining an optimal control problem in a neoclassical growth model by utilizing Lie group theory. Lie point symmetries of coupled nonlinear first-order ordinary differential equations corresponding to first-order conditions of maximum principle are analyzed and then first integrals and corresponding closed-form (analytical) solutions are determined by using Lie point symmetries in conjunction with Prelle-Singer and Jacobi last multiplier methods. Additionally, associated λ-symmetries, adjoint symmetries, Darboux polynomials, and the properties of the model are represented.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
28 - 2
Pages
209 - 218
Publication Date
2021/01/21
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.k.210103.001How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Gülden Gün Polat
AU  - Teoman Özer
PY  - 2021
DA  - 2021/01/21
TI  - On Ramsey Dynamical Model and Closed-Form Solutions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 209
EP  - 218
VL  - 28
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.210103.001
DO  - 10.2991/jnmp.k.210103.001
ID  - Polat2021
ER  -