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Some Applications of Affine in Velocities Lagrangians in Two-Dimensional Systems. Symmetry (Basel) 2022. [DOI: 10.3390/sym14122520] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
Abstract
The two-dimensional inverse problem for first-order systems is analysed and a method to construct an affine Lagrangian for such systems is developed. The determination of such Lagrangians is based on the theory of the Jacobi multiplier for the system of differential equations. We illustrate our analysis with several examples of families of forces that are relevant in mechanics, on one side, and of some relevant biological systems, on the other.
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Abstract
In this paper, three-dimensional system of the tuberculosis (TB) model is reduced into a two-dimensional first-order and one-dimensional second-order differential equations. We use the method of Jacobi last multiplier to construct linear Lagrangians of systems of two first-order ordinary differential equations and nonlinear Lagrangian of the corresponding single second-order equation. The Noether's theorem is used for determining conservation laws. We apply the techniques of symmetry analysis to a model to identify the combinations of parameters which lead to the possibility of the linearization of the system and provide the corresponding solutions.
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Affiliation(s)
- Maba Boniface Matadi
- School of Mathematical Sciences, University of Zululand, Private Bag X1001, KwaDlangeZwa 3886, KwaZulu Natal, South Africa
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Noether Symmetries Quantization and Superintegrability of Biological Models. Symmetry (Basel) 2016. [DOI: 10.3390/sym8120155] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
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Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model. Symmetry (Basel) 2015. [DOI: 10.3390/sym7031613] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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Is Acanthaster planci a near-optimal predator? Ecol Modell 1989. [DOI: 10.1016/0304-3800(89)90020-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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