On the interconnections between various analytic approaches in coupled first-order nonlinear differential equations

Mohanasubha, R.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

doi:10.1016/j.cnsns.2018.02.021

Cited by 5 publications

(6 citation statements)

References 17 publications

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“…In this work, the coupled first-order system of ODEs defining the optimal control problems, which are derived by both current and present value Hamiltonians is analyzed. In addition, the Prelle-Singer (PS) method is considered to analyze the nonlinear economic growth models [17] by pointing out the relationships between Lie group related methods such as Lie point symmetry, JLM, λ-symmetry, and adjoint symmetry.…”

Section: Gülden Gün Polat and Teomanözermentioning

confidence: 99%

“…Theorem 2.2. The vector field ∂ q is a λ-symmetry of the equation (17) and then λ-function can be derived from the form…”

Section: Preliminaries In General the Optimal Control Problems Are mentioning

confidence: 99%

“…On the other hand, the determining equations related to the functions S and K (65) and (66) cannot be solved easily. However, it can be shown that the mathematical relations among PS method, Lie point symmetry, Jacobi last multiplier, adjoint symmetry, λ-symmetry, and Darboux polynomial [17] can provide an advantage for the determination of functions S and K.…”

Section: 6mentioning

confidence: 99%

“…Let ξ 1 (t, p, q), η 11 (t, p, q) and η 12 (t, p, q) are λ-symmetries of (56). With some specific choice of such that ξ 1 = 0, η 11 = 1 and η 12 = γ, via the connection g = γ that is introduced in [17], then λ-function can be determined by using the below formula…”

Section: 62mentioning

confidence: 99%

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On group analysis of optimal control problems in economic growth models

Polat¹,

Özer²

2020

Discrete &Amp; Continuous Dynamical Systems - S

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The optimal control problems in economic growth theory are analyzed by considering the Pontryagin's maximum principle for both current and present value Hamiltonian functions based on the theory of Lie groups. As a result of these necessary conditions, two coupled first-order differential equations are obtained for two different economic growth models. The first integrals and the analytical solutions (closed-form solutions) of two different economic growth models are analyzed via the group theory including Lie point symmetries, Jacobi last multiplier, Prelle-Singer method, λ-symmetry and the mathematical relations among them.

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Section: Gülden Gün Polat and Teomanözermentioning

confidence: 99%

“…Theorem 2.2. The vector field ∂ q is a λ-symmetry of the equation (17) and then λ-function can be derived from the form…”

Section: Preliminaries In General the Optimal Control Problems Are mentioning

confidence: 99%

Section: 6mentioning

confidence: 99%

Section: 62mentioning

confidence: 99%

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On group analysis of optimal control problems in economic growth models

Polat¹,

Özer²

2020

Discrete &Amp; Continuous Dynamical Systems - S

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“…From the mathematical point of view, analytical solutions of the coupled system of nonlinear ordinary differential equations (ODEs) are investigated. The relationships between PS procedure and some analytical methods such as Lie point symmetries, Jacobi last multiplier (JLM), λ-symmetries, and Darboux polynomials [12] are indicated. In section 3, some conclusions and discussions on the analysis of the model are represented.…”

Section: Introductionmentioning

confidence: 99%

On Ramsey Dynamical Model and Closed-Form Solutions

Polat¹,

Özer²

2021

JNMP

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

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