First integrals and analytical solutions of some dynamical systems

Haq, Burhan ul; Naeem, Imran

doi:10.1007/s11071-018-4657-4

Cited by 13 publications

(7 citation statements)

References 35 publications

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“…9 Then these first integrals were utilized to derive the exact solutions of aforementioned models. In previous literature, [10][11][12] the first integrals of some dynamical systems for epidemics were established by employing the partial Hamiltonian approach. 13,14 The closed-form solutions are established by utilizing some other methods as well.…”

Section: Introductionmentioning

confidence: 99%

The first integrals and closed‐form solutions of a Susceptible‐Exposed‐Infectious epidemic model

Naz

Torrisi

2022

Math Methods in App Sciences

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The closed-form solutions of Susceptible-Exposed-Infectious (SEI) epidemic model are constructed for two different scenarios. The SEI model is governed by a dynamical system of three first-order ordinary differential equations (ODEs).The dynamical system of three ODEs converts to a second-order ODE in terms of only one variable for the specific restrictions on the parameters. Two scenarios are considered. For both scenarios, the multiplier approach yields two first integrals. We utilize these first integrals to establish the closed-form solutions of SEI model for these two scenarios.

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Section: Introductionmentioning

confidence: 99%

The first integrals and closed‐form solutions of a Susceptible‐Exposed‐Infectious epidemic model

Naz

Torrisi

2022

Math Methods in App Sciences

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“…Partial Hamiltonian approach is thus an effective tool, which can be applied to all mathematical growth models, which can be expressed into partial Hamiltonian systems. The partial Hamiltonian approach has been effectively utilized to construct the first integrals and exact solutions of various dynamical systems …”

Section: Introductionmentioning

confidence: 99%

Closed‐form solutions of two‐sector Romer model of endogenous growth using partial Hamiltonian approach

Haq

Naeem

2020

Math Methods in App Sciences

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This article presents the closed-form solutions of two-sector human capital-based Romer growth model. The partial Hamiltonian approach is effectively applied to some growth models in order to compute the closed-form solutions for economic variables involved in the model. Pontryagin's maximum principle provides the set of first-order system of ODEs, which are regarded as an essential criteria for optimality. The partial Hamiltonian approach is utilized to construct three first integrals of the system using the current value Hamiltonian. With the aid of these first integrals, we computed two distinct exact solutions of Romer model under certain parametric restrictions. The closed-form expressions for control, state, and costate variables are presented explicitly as a function of t. We have graphically illustrated the solution curves and observed the effect of human capital parameter on control and state variables. The growth rates of all economic variables are evaluated, and their long-run behavior is predicted. KEYWORDSfactor tax incidence, first integrals, gauge function, partial Hamiltonian, Pontryagin's principle MSC CLASSIFICATION34H05; 49K15

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“…Furthermore, it has a direct connection among the dynamic programming, variation of calculus, and optimal control theory [5,31]. In addition, it is well known that Lagrangian, Hamiltonian, and Euler-Lagrange equations play a vital role in the calculus of variations [16,21,13,22,14]. Most economic models are defined with the integrand function including a discount factor.…”

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confidence: 99%

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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First integrals and analytical solutions of some dynamical systems

Cited by 13 publications

References 35 publications

The first integrals and closed‐form solutions of a Susceptible‐Exposed‐Infectious epidemic model

The first integrals and closed‐form solutions of a Susceptible‐Exposed‐Infectious epidemic model

Closed‐form solutions of two‐sector Romer model of endogenous growth using partial Hamiltonian approach

On group analysis of optimal control problems in economic growth models

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