Correlated dynamics of immune network and sl(3, R) symmetry algebra
We observed the existence of periodic orbits in immune network under transitive solvable Lie algebra. In this article, we focus to develop condition of maximal Lie algebra for immune network model and use that condition to construct a vector field of symmetry to study nonlinear pathogen model. We us...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-03-01
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| Series: | Computational and Mathematical Biophysics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/cmb-2023-0109 |
| _version_ | 1797246652108505088 |
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| author | Dutta Ruma Stan Aurel |
| author_facet | Dutta Ruma Stan Aurel |
| author_sort | Dutta Ruma |
| collection | DOAJ |
| description | We observed the existence of periodic orbits in immune network under transitive solvable Lie algebra. In this article, we focus to develop condition of maximal Lie algebra for immune network model and use that condition to construct a vector field of symmetry to study nonlinear pathogen model. We used two methods to obtain analytical structure of solution, namely normal generator and differential invariant function. Numerical simulation of analytical structure exhibits correlated periodic pattern growth under spatiotemporal symmetry, which is similar to the linear dynamical simulation result. We used Lie algebraic method to understand correlation between growth pattern and symmetry of dynamical system. We employ idea of using one parameter point group of transformation of variables under which linear manifold is retained. In procedure, we present the method of deriving Lie point symmetries, the calculation of the first integral and the invariant solution for the ordinary differential equation (ODE). We show the connection between symmetries and differential invariant solutions of the ODE. The analytical structure of the solution exhibits periodic behavior around attractor in local domain, same behavior obtained through dynamical analysis. |
| first_indexed | 2024-04-24T19:46:12Z |
| format | Article |
| id | doaj.art-4dc213eff3944199827418a7fe00c00a |
| institution | Directory Open Access Journal |
| issn | 2544-7297 |
| language | English |
| last_indexed | 2024-04-24T19:46:12Z |
| publishDate | 2024-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Computational and Mathematical Biophysics |
| spelling | doaj.art-4dc213eff3944199827418a7fe00c00a2024-03-25T07:27:45ZengDe GruyterComputational and Mathematical Biophysics2544-72972024-03-0112162163410.1515/cmb-2023-0109Correlated dynamics of immune network and sl(3, R) symmetry algebraDutta Ruma0Stan Aurel1Department of Physics, Material Science and Astronomy, Missouri State University, Springfield, MO 65897, United StatesDepartment of Mathematics, The Ohio State University, Columbus, OH 43210, United StatesWe observed the existence of periodic orbits in immune network under transitive solvable Lie algebra. In this article, we focus to develop condition of maximal Lie algebra for immune network model and use that condition to construct a vector field of symmetry to study nonlinear pathogen model. We used two methods to obtain analytical structure of solution, namely normal generator and differential invariant function. Numerical simulation of analytical structure exhibits correlated periodic pattern growth under spatiotemporal symmetry, which is similar to the linear dynamical simulation result. We used Lie algebraic method to understand correlation between growth pattern and symmetry of dynamical system. We employ idea of using one parameter point group of transformation of variables under which linear manifold is retained. In procedure, we present the method of deriving Lie point symmetries, the calculation of the first integral and the invariant solution for the ordinary differential equation (ODE). We show the connection between symmetries and differential invariant solutions of the ODE. The analytical structure of the solution exhibits periodic behavior around attractor in local domain, same behavior obtained through dynamical analysis.https://doi.org/10.1515/cmb-2023-0109pathogen dynamicslie symmetrydifferential invariantmaximal algebra2020.92 |
| spellingShingle | Dutta Ruma Stan Aurel Correlated dynamics of immune network and sl(3, R) symmetry algebra Computational and Mathematical Biophysics pathogen dynamics lie symmetry differential invariant maximal algebra 2020.92 |
| title | Correlated dynamics of immune network and sl(3, R) symmetry algebra |
| title_full | Correlated dynamics of immune network and sl(3, R) symmetry algebra |
| title_fullStr | Correlated dynamics of immune network and sl(3, R) symmetry algebra |
| title_full_unstemmed | Correlated dynamics of immune network and sl(3, R) symmetry algebra |
| title_short | Correlated dynamics of immune network and sl(3, R) symmetry algebra |
| title_sort | correlated dynamics of immune network and sl 3 r symmetry algebra |
| topic | pathogen dynamics lie symmetry differential invariant maximal algebra 2020.92 |
| url | https://doi.org/10.1515/cmb-2023-0109 |
| work_keys_str_mv | AT duttaruma correlateddynamicsofimmunenetworkandsl3rsymmetryalgebra AT stanaurel correlateddynamicsofimmunenetworkandsl3rsymmetryalgebra |