Algebraic approach for the reconstruction of Rössler system from the x3- variable
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| Formato: | Artículo científico |
| Lenguaje: | en |
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Sociedad Mexicana de Física A.C.
2006
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| _version_ | 1876479491384016896 |
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| author | C. Aguilar Ibáñez |
| author_facet | C. Aguilar Ibáñez |
| contents | Algebraic approach for the reconstruction of Rössler system from the x3- variable C. Aguilar Ibáñez Física, Astronomía y Matemáticas Chaotic systems inverse problem estimation of parameters and variables In this paper we propose a simple method to identify the unknown parameters and to estimate the underlying variables from a given chaotic time series x3(tk)k=n 0 of the three-dimensional Rössler system (RS). The reconstruction of the RS from its x3¡ variable is known to be considerably more difficult than reconstruction from its two other variables. We show that the system is observable and algebraically identifiable with respect to the auxiliary output ln(x3), hence, a differential parameterization of the output and its time derivatives can be obtained. Based on these facts, we proceed to form an extended re-parameterized system (linear-in-the -parameters), which turns out to be invertible, allowing us to estimate the variables and missing parameters. 2006 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57021679010 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.1 Vol.52 |
| format | Artículo científico |
| id | redalyc_57021679010 |
| institution | Redalyc |
| language | en |
| publishDate | 2006 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | Algebraic approach for the reconstruction of Rössler system from the x3- variable C. Aguilar Ibáñez Física, Astronomía y Matemáticas Chaotic systems inverse problem estimation of parameters and variables Algebraic approach for the reconstruction of Rössler system from the x3- variable C. Aguilar Ibáñez Física, Astronomía y Matemáticas Chaotic systems inverse problem estimation of parameters and variables In this paper we propose a simple method to identify the unknown parameters and to estimate the underlying variables from a given chaotic time series x3(tk)k=n 0 of the three-dimensional Rössler system (RS). The reconstruction of the RS from its x3¡ variable is known to be considerably more difficult than reconstruction from its two other variables. We show that the system is observable and algebraically identifiable with respect to the auxiliary output ln(x3), hence, a differential parameterization of the output and its time derivatives can be obtained. Based on these facts, we proceed to form an extended re-parameterized system (linear-in-the -parameters), which turns out to be invertible, allowing us to estimate the variables and missing parameters. 2006 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57021679010 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.1 Vol.52 |
| title | Algebraic approach for the reconstruction of Rössler system from the x3- variable |
| topic | Física, Astronomía y Matemáticas Chaotic systems inverse problem estimation of parameters and variables |
| url | https://www.redalyc.org/articulo.oa?id=57021679010 |