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On Ramsey Dynamical Model and Closed-Form Solutions

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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 lambda-symmetries, adjoint symmetries, Darboux polynomials, and the properties of the model are represented.

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Polat, G. G., & Özer, T. (2021). On Ramsey Dynamical Model and Closed-Form Solutions. Journal of Nonlinear Mathematical Physics, 28(2), 209-218.

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