Hopf bifurcation in a model of sustainable development
This article presents a system of three first-orden ordinary differential equations to study the dynamic in- teraction between renewable resources, population and environmental pollution in a region. The model is achieved coupling a dynamic equation of contamination to formulated systems by Simone D...
| Main Authors: | , , , |
|---|---|
| Format: | Online |
| Language: | spa |
| Published: |
Universidad Pedagógica y Tecnológica de Colombia
2018
|
| Subjects: | |
| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/5418 |
| _version_ | 1801706337654013952 |
|---|---|
| author | Granada Díaz, Héctor Andrés A.G, Miguel Angel Moreno A, D.K Canchila M, J.A |
| author_facet | Granada Díaz, Héctor Andrés A.G, Miguel Angel Moreno A, D.K Canchila M, J.A |
| author_sort | Granada Díaz, Héctor Andrés |
| collection | OJS |
| description | This article presents a system of three first-orden ordinary differential equations to study the dynamic in-
teraction between renewable resources, population and environmental pollution in a region. The model is
achieved coupling a dynamic equation of contamination to formulated systems by Simone D’alessandro
and shows that under the Hopf bifurcation can be found conditions to achieve sustainable development
under the definition given in the report of Brundtland commission 1987. That is, when a harmonic balance
between the state variables of the model is reached. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-5418 |
| institution | Revista Ciencia en Desarrollo |
| language | spa |
| publishDate | 2018 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-54182022-06-15T17:04:51Z Hopf bifurcation in a model of sustainable development Bifurcación de Hopf en un modelo de desarrollo sostenible Granada Díaz, Héctor Andrés A.G, Miguel Angel Moreno A, D.K Canchila M, J.A Sistemas dinámicos dinámica no lineal bifurcación de Hopf desarrollo sostenible huella ecológica Sistemas dinámicos Dynamical systems, nonlinear dynamics, Hopf bifurcation, sustainable development, ecological footprint. This article presents a system of three first-orden ordinary differential equations to study the dynamic in- teraction between renewable resources, population and environmental pollution in a region. The model is achieved coupling a dynamic equation of contamination to formulated systems by Simone D’alessandro and shows that under the Hopf bifurcation can be found conditions to achieve sustainable development under the definition given in the report of Brundtland commission 1987. That is, when a harmonic balance between the state variables of the model is reached. Se presenta un sistema conformado por tres ecuaciones diferenciales ordinarias de primer orden que permiten estudiar la interacción dinámica entre los recursos renovables, la población y la contaminación ambiental de una región. El modelo se obtiene acoplando una ecuación dinámica de contaminación al sistema formulado por Simone D’alessandro y se muestra que bajo la bifurcación de Hopf se puede alcanzar el desarrollo sostenible bajo la definición dada en el informe de Brundtland 1987. Es decir, cuando se alcanza un balance armónico entre las variables de estado del modelo. Universidad Pedagógica y Tecnológica de Colombia 2018-02-19 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Modelamiento application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/5418 10.19053/01217488.v8.n2.2017.5418 Ciencia En Desarrollo; Vol. 9 No. 1 (2018): Vol 9, Núm. 1 (2018): Enero - Junio; 63-70 Ciencia en Desarrollo; Vol. 9 Núm. 1 (2018): Vol 9, Núm. 1 (2018): Enero - Junio; 63-70 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/5418/pdf Derechos de autor 2017 CIENCIA EN DESARROLLO |
| spellingShingle | Sistemas dinámicos dinámica no lineal bifurcación de Hopf desarrollo sostenible huella ecológica Sistemas dinámicos Dynamical systems, nonlinear dynamics, Hopf bifurcation, sustainable development, ecological footprint. Granada Díaz, Héctor Andrés A.G, Miguel Angel Moreno A, D.K Canchila M, J.A Hopf bifurcation in a model of sustainable development |
| title | Hopf bifurcation in a model of sustainable development |
| title_alt | Bifurcación de Hopf en un modelo de desarrollo sostenible |
| title_full | Hopf bifurcation in a model of sustainable development |
| title_fullStr | Hopf bifurcation in a model of sustainable development |
| title_full_unstemmed | Hopf bifurcation in a model of sustainable development |
| title_short | Hopf bifurcation in a model of sustainable development |
| title_sort | hopf bifurcation in a model of sustainable development |
| topic | Sistemas dinámicos dinámica no lineal bifurcación de Hopf desarrollo sostenible huella ecológica Sistemas dinámicos Dynamical systems, nonlinear dynamics, Hopf bifurcation, sustainable development, ecological footprint. |
| topic_facet | Sistemas dinámicos dinámica no lineal bifurcación de Hopf desarrollo sostenible huella ecológica Sistemas dinámicos Dynamical systems, nonlinear dynamics, Hopf bifurcation, sustainable development, ecological footprint. |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/5418 |
| work_keys_str_mv | AT granadadiazhectorandres hopfbifurcationinamodelofsustainabledevelopment AT agmiguelangel hopfbifurcationinamodelofsustainabledevelopment AT morenoadk hopfbifurcationinamodelofsustainabledevelopment AT canchilamja hopfbifurcationinamodelofsustainabledevelopment AT granadadiazhectorandres bifurcaciondehopfenunmodelodedesarrollosostenible AT agmiguelangel bifurcaciondehopfenunmodelodedesarrollosostenible AT morenoadk bifurcaciondehopfenunmodelodedesarrollosostenible AT canchilamja bifurcaciondehopfenunmodelodedesarrollosostenible |
