On time-dependent Hamiltonian realizations of planar and nonplanar systems

Esen, Oğul; Guha, Partha

doi:10.1016/j.geomphys.2018.01.024

Cited by 5 publications

(5 citation statements)

References 51 publications

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“…A cosymplectic manifold [15,16,17,18] is a triple (M, η, ω) consisting of a smooth (2n + 1)− dimensional manifold M with a closed 1-form η and a closed 2-form ω, i.e., dη = dω = 0, such that η ∧ ω n = 0. The Reeb field ξ is uniquely determined by η(ξ) = 1 and i ξ ω = 0.…”

Section: Hamiltonian Geometric Description Via Cosymplectic Methodsmentioning

confidence: 99%

Reduction and Hamiltonian aspects of a model for virus-tumour interaction in oncolytic virotherapy

Ghose‐Choudhury¹,

Guha²

2019

Preprint

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We analyse the Hamiltonian structure of a system of first-order ordinary differential equations used for modeling the interaction of an oncolytic virus with a tumour cell population. The analysis is based on the existence of a Jacobi Last Multiplier for the system and a time dependent first integral. For suitable conditions on the model parameters this allows for the reduction of the problem to a planar system of equations for which the time dependent Hamiltonian flows are described. The geometry of the Hamiltonian flows are finally investigated using the symplectic and cosymplectic methods.

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Section: Hamiltonian Geometric Description Via Cosymplectic Methodsmentioning

confidence: 99%

Reduction and Hamiltonian aspects of a model for virus-tumour interaction in oncolytic virotherapy

Ghose‐Choudhury¹,

Guha²

2019

Preprint

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“…The cosymplectic manifolds provide a natural framework for the time-dependent Hamiltonian mechanics (e.g. see [9,25]). Namely, consider a non-autonomous Hamiltonian equations…”

Section: Notationmentioning

confidence: 99%

Integrable systems in cosymplectic geometry

Jovanović

Lukić

2023

J. Phys. A: Math. Theor.

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“…where the subindex (23) means that the variables (q 2 , p 2 ) are interchanged with (q 3 , p 3 ) when they appear in the deformed Hamiltonian functions h z;j and h (2) z;j (23) =h z;j (q 1 , p 1 )e 2zh z;2 (q 3 ,p 3 ) + h z;j (q 3 , p 3 )e −2zh z;2 (q 1 ,p 1 ) , j = 1, 3…”

Section: Constants Of Motionmentioning

confidence: 99%

“…In order to arrive the formal definition of a coalgebra, one simply reverse the directions of the (multiplication and unit) arrows in (A.1). Accordingly, a vector space A is called a coalgebra if it admits a comultiplication and a counit given by 23) respectively. We ask that these operations must satisfy the relation…”

Section: A1 Lie Algebrasmentioning

confidence: 99%

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Geometry and solutions of an epidemic SIS model permitting fluctuations and quantization

Esen¹,

Fernández‐Saiz²,

Sardón³

et al. 2020

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Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This stochastic SIS epidemic model can be interpreted as a Hamiltonian system, therefore we wondered if it could be geometrically handled through the theory of Lie-Hamilton systems, and this happened to be the case. The primordial result is that we are able to obtain a general solution for the stochastic/ SIS-epidemic model (with fluctuations) in form of a nonlinear superposition rule that includes particular stochastic solutions and certain constants to be related to initial conditions of the contagion process. The choice of these initial conditions will be crucial to display the expected behavior of the curve of infections during the epidemic. We shall limit these constants to nonsingular regimes and display graphics of the behavior of the solutions. As one could expect, the increase of infected individuals follows a sigmoid-like curve.Lie-Hamiltonian systems admit a quantum deformation, so does the stochastic SIS-epidemic model. We present this generalization as well. If one wants to study the evolution of an SIS epidemic under the influence of a constant heat source (like centrally heated buildings), one can make use of quantum stochastic differential equations coming from the so-called quantum deformation.

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On time-dependent Hamiltonian realizations of planar and nonplanar systems

Cited by 5 publications

References 51 publications

Reduction and Hamiltonian aspects of a model for virus-tumour interaction in oncolytic virotherapy

Reduction and Hamiltonian aspects of a model for virus-tumour interaction in oncolytic virotherapy

Integrable systems in cosymplectic geometry

Geometry and solutions of an epidemic SIS model permitting fluctuations and quantization

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