Saved in:
| Main Author: | |
|---|---|
| Format: | Artículo científico |
| Language: | en |
| Published: |
Universidad Nacional Autónoma de México
2004
|
| Subjects: | |
| Online Access: | https://www.redalyc.org/articulo.oa?id=56517303 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866814312295694336 |
|---|---|
| author | S. Panchev |
| author_facet | S. Panchev |
| contents | The Lorenz chaotic systems as nonlinear oscillators with memory S. Panchev Tatiana S. Spassova Biología Chaotic systems memory function Duffing oscillator Nonlinear dynamical systems (systems of 1st order ordinary differential equations) capable of generatingchaos are analytically nonintegrable. Despite of this fact, analytical tools can be used to extract usefulinformation. In this paper the original Lorenz system and its modifications are reduced to single oscillatorytype integral-differential equations with delayed argument. This yields to appearance of an endogenousterm interpreted as memory for the past. Moreover, the equations are valid far from the initial instant (theoreticallyat t→∞), when the system eventually evolves on its attractor set. This corresponds to the numerical solutionswhen an appropriate initial part of the iterates is usually discarded to eliminate the transients. Besides, theform of the equations allows statistical treatment. 2004 artículo científico 0187-6236 https://www.redalyc.org/articulo.oa?id=56517303 en http://www.redalyc.org/revista.oa?id=565 Atmósfera application/pdf Universidad Nacional Autónoma de México Atmósfera (México) Num.3 Vol.17 |
| format | Artículo científico |
| id | redalyc_56517303 |
| language | en |
| publishDate | 2004 |
| publisher | Universidad Nacional Autónoma de México |
| spellingShingle | The Lorenz chaotic systems as nonlinear oscillators with memory S. Panchev Biología Chaotic systems memory function Duffing oscillator The Lorenz chaotic systems as nonlinear oscillators with memory S. Panchev Tatiana S. Spassova Biología Chaotic systems memory function Duffing oscillator Nonlinear dynamical systems (systems of 1st order ordinary differential equations) capable of generatingchaos are analytically nonintegrable. Despite of this fact, analytical tools can be used to extract usefulinformation. In this paper the original Lorenz system and its modifications are reduced to single oscillatorytype integral-differential equations with delayed argument. This yields to appearance of an endogenousterm interpreted as memory for the past. Moreover, the equations are valid far from the initial instant (theoreticallyat t→∞), when the system eventually evolves on its attractor set. This corresponds to the numerical solutionswhen an appropriate initial part of the iterates is usually discarded to eliminate the transients. Besides, theform of the equations allows statistical treatment. 2004 artículo científico 0187-6236 https://www.redalyc.org/articulo.oa?id=56517303 en http://www.redalyc.org/revista.oa?id=565 Atmósfera application/pdf Universidad Nacional Autónoma de México Atmósfera (México) Num.3 Vol.17 |
| title | The Lorenz chaotic systems as nonlinear oscillators with memory |
| topic | Biología Chaotic systems memory function Duffing oscillator |
| url | https://www.redalyc.org/articulo.oa?id=56517303 |