Pitchfork and Hopf bifurcations in an extended Lorenz system
An analytical classification in a three-dimensional parameter space is presented to describe the dynamics for an extended Lorenz system of the Li-Ou type, conditions are given to find supercritical and degenerate Hopf bifurcations and a pitchfork bifurcation. Finally, the theoretical results are com...
| Main Authors: | , , |
|---|---|
| Format: | Online |
| Language: | spa |
| Published: |
Universidad Pedagógica y Tecnológica de Colombia
2023
|
| Subjects: | |
| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/15253 |
| _version_ | 1801706358126411776 |
|---|---|
| author | Granada Díaz, Héctor Andrés Olivar Robayo, Luis Eduardo Casanova Trujillo, Simeón |
| author_facet | Granada Díaz, Héctor Andrés Olivar Robayo, Luis Eduardo Casanova Trujillo, Simeón |
| author_sort | Granada Díaz, Héctor Andrés |
| collection | OJS |
| description | An analytical classification in a three-dimensional parameter space is presented to describe the dynamics for an extended Lorenz system of the Li-Ou type, conditions are given to find supercritical and degenerate Hopf bifurcations and a pitchfork bifurcation. Finally, the theoretical results are compared with numerical simulations and bifurcation diagrams. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-15253 |
| institution | Revista Ciencia en Desarrollo |
| language | spa |
| publishDate | 2023 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-152532024-05-10T00:51:44Z Pitchfork and Hopf bifurcations in an extended Lorenz system Bifurcaciones Horquilla y Hopf en un sistema de Lorenz extendido Granada Díaz, Héctor Andrés Olivar Robayo, Luis Eduardo Casanova Trujillo, Simeón Sistemas tipo Lorenz bifurcaciones caos Lorenz-type systems bifurcations chaos An analytical classification in a three-dimensional parameter space is presented to describe the dynamics for an extended Lorenz system of the Li-Ou type, conditions are given to find supercritical and degenerate Hopf bifurcations and a pitchfork bifurcation. Finally, the theoretical results are compared with numerical simulations and bifurcation diagrams. Se presenta una clasificación analítica en un espacio tridimensional de parámetros para describir la dinámica para un sistema de Lorenz extendido del tipo Li-Ou, se dan condiciones para encontrar bifurcaciones de Hopf supercríticas y degeneradas y, una bifurcación horquilla. Finalmente, los resultados teóricos son comparados con simulaciones numéricas y diagramas de bifurcación. Universidad Pedagógica y Tecnológica de Colombia 2023-07-19 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/15253 10.19053/01217488.v14.n2.2023.15253 Ciencia En Desarrollo; Vol. 14 No. 2 (2023): Vol 14, Núm.2 (2023): Julio-Diciembre; 91-101 Ciencia en Desarrollo; Vol. 14 Núm. 2 (2023): Vol 14, Núm.2 (2023): Julio-Diciembre; 91-101 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/15253/13677 |
| spellingShingle | Sistemas tipo Lorenz bifurcaciones caos Lorenz-type systems bifurcations chaos Granada Díaz, Héctor Andrés Olivar Robayo, Luis Eduardo Casanova Trujillo, Simeón Pitchfork and Hopf bifurcations in an extended Lorenz system |
| title | Pitchfork and Hopf bifurcations in an extended Lorenz system |
| title_alt | Bifurcaciones Horquilla y Hopf en un sistema de Lorenz extendido |
| title_full | Pitchfork and Hopf bifurcations in an extended Lorenz system |
| title_fullStr | Pitchfork and Hopf bifurcations in an extended Lorenz system |
| title_full_unstemmed | Pitchfork and Hopf bifurcations in an extended Lorenz system |
| title_short | Pitchfork and Hopf bifurcations in an extended Lorenz system |
| title_sort | pitchfork and hopf bifurcations in an extended lorenz system |
| topic | Sistemas tipo Lorenz bifurcaciones caos Lorenz-type systems bifurcations chaos |
| topic_facet | Sistemas tipo Lorenz bifurcaciones caos Lorenz-type systems bifurcations chaos |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/15253 |
| work_keys_str_mv | AT granadadiazhectorandres pitchforkandhopfbifurcationsinanextendedlorenzsystem AT olivarrobayoluiseduardo pitchforkandhopfbifurcationsinanextendedlorenzsystem AT casanovatrujillosimeon pitchforkandhopfbifurcationsinanextendedlorenzsystem AT granadadiazhectorandres bifurcacioneshorquillayhopfenunsistemadelorenzextendido AT olivarrobayoluiseduardo bifurcacioneshorquillayhopfenunsistemadelorenzextendido AT casanovatrujillosimeon bifurcacioneshorquillayhopfenunsistemadelorenzextendido |
