Features of the Computational Implementation of the Algorithm for Estimating the Lyapunov Exponents of Systems with Delay
We consider the computational implementation of the algorithm for Lyapunov exponents spectrum numerical estimation for delay differential equations. It is known that for such systems, as well as for boundary value problems, it is not possible to prove the well-known Oseledets theorem which allows us...
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Yaroslavl State University
2019-12-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/1277 |
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| _version_ | 1850024000143491072 |
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| author | Vladimir E. Goryunov |
| author_facet | Vladimir E. Goryunov |
| author_sort | Vladimir E. Goryunov |
| collection | DOAJ |
| description | We consider the computational implementation of the algorithm for Lyapunov exponents spectrum numerical estimation for delay differential equations. It is known that for such systems, as well as for boundary value problems, it is not possible to prove the well-known Oseledets theorem which allows us to calculate the required parameters very efficiently. Therefore, we can only talk about the estimates of the characteristics in some sense close to the Lyapunov exponents. In this paper, we propose two methods of linearized systems solutions processing. One of them is based on a set of impulse functions, and the other is based on a set of trigonometric functions. We show the usage flexibility of these algorithms in the case of quasi-stable structures when several Lyapunov exponents are close to zero. The developed methods are tested on a logistic equation with a delay, and these tests illustrate the “proximity” of the obtained numerical characteristics and Lyapunov exponents. |
| format | Article |
| id | doaj-art-cddcfe3ce6fa4f69a9b95b67f969242d |
| institution | DOAJ |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2019-12-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-cddcfe3ce6fa4f69a9b95b67f969242d2025-08-20T03:01:14ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172019-12-0126457258210.18255/1818-1015-2019-4-572-582954Features of the Computational Implementation of the Algorithm for Estimating the Lyapunov Exponents of Systems with DelayVladimir E. Goryunov0P. G. Demidov Yaroslavl State UniversityWe consider the computational implementation of the algorithm for Lyapunov exponents spectrum numerical estimation for delay differential equations. It is known that for such systems, as well as for boundary value problems, it is not possible to prove the well-known Oseledets theorem which allows us to calculate the required parameters very efficiently. Therefore, we can only talk about the estimates of the characteristics in some sense close to the Lyapunov exponents. In this paper, we propose two methods of linearized systems solutions processing. One of them is based on a set of impulse functions, and the other is based on a set of trigonometric functions. We show the usage flexibility of these algorithms in the case of quasi-stable structures when several Lyapunov exponents are close to zero. The developed methods are tested on a logistic equation with a delay, and these tests illustrate the “proximity” of the obtained numerical characteristics and Lyapunov exponents.https://www.mais-journal.ru/jour/article/view/1277lyapunov exponents spectrumdynamical system with delaynumerical algorithmhutchinson equation |
| spellingShingle | Vladimir E. Goryunov Features of the Computational Implementation of the Algorithm for Estimating the Lyapunov Exponents of Systems with Delay Моделирование и анализ информационных систем lyapunov exponents spectrum dynamical system with delay numerical algorithm hutchinson equation |
| title | Features of the Computational Implementation of the Algorithm for Estimating the Lyapunov Exponents of Systems with Delay |
| title_full | Features of the Computational Implementation of the Algorithm for Estimating the Lyapunov Exponents of Systems with Delay |
| title_fullStr | Features of the Computational Implementation of the Algorithm for Estimating the Lyapunov Exponents of Systems with Delay |
| title_full_unstemmed | Features of the Computational Implementation of the Algorithm for Estimating the Lyapunov Exponents of Systems with Delay |
| title_short | Features of the Computational Implementation of the Algorithm for Estimating the Lyapunov Exponents of Systems with Delay |
| title_sort | features of the computational implementation of the algorithm for estimating the lyapunov exponents of systems with delay |
| topic | lyapunov exponents spectrum dynamical system with delay numerical algorithm hutchinson equation |
| url | https://www.mais-journal.ru/jour/article/view/1277 |
| work_keys_str_mv | AT vladimiregoryunov featuresofthecomputationalimplementationofthealgorithmforestimatingthelyapunovexponentsofsystemswithdelay |