On Algebraic Approach in Quadratic Systems
When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and (non)chaotic dy...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/230939 |
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| _version_ | 1832555982353334272 |
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| author | Matej Mencinger |
| author_facet | Matej Mencinger |
| author_sort | Matej Mencinger |
| collection | DOAJ |
| description | When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and (non)chaotic dynamics. In this paper we consider homogeneous quadratic systems via the so-called Markus approach. We use the one-to-one correspondence between homogeneous quadratic dynamical systems and algebra which was originally introduced by Markus in (1960). We resume some connections between the dynamics of the quadratic systems and (algebraic) properties of the corresponding algebras. We consider some general connections and the influence of power-associativity in the corresponding quadratic system. |
| format | Article |
| id | doaj-art-3c06b987c9fb4e9d99f0741ce86f9f6d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3c06b987c9fb4e9d99f0741ce86f9f6d2025-02-03T05:46:35ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/230939230939On Algebraic Approach in Quadratic SystemsMatej Mencinger0Department of Basic Science, Faculty of Civil Engineering, University of Maribor, Smetanova 17, 2000 Maribor, SloveniaWhen considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and (non)chaotic dynamics. In this paper we consider homogeneous quadratic systems via the so-called Markus approach. We use the one-to-one correspondence between homogeneous quadratic dynamical systems and algebra which was originally introduced by Markus in (1960). We resume some connections between the dynamics of the quadratic systems and (algebraic) properties of the corresponding algebras. We consider some general connections and the influence of power-associativity in the corresponding quadratic system.http://dx.doi.org/10.1155/2011/230939 |
| spellingShingle | Matej Mencinger On Algebraic Approach in Quadratic Systems International Journal of Mathematics and Mathematical Sciences |
| title | On Algebraic Approach in Quadratic Systems |
| title_full | On Algebraic Approach in Quadratic Systems |
| title_fullStr | On Algebraic Approach in Quadratic Systems |
| title_full_unstemmed | On Algebraic Approach in Quadratic Systems |
| title_short | On Algebraic Approach in Quadratic Systems |
| title_sort | on algebraic approach in quadratic systems |
| url | http://dx.doi.org/10.1155/2011/230939 |
| work_keys_str_mv | AT matejmencinger onalgebraicapproachinquadraticsystems |