A connection between Lyapunov exponents and sensitive dependence on parameters of chaotic systems
| Autor: | Costiche, Samuel Willian Schwertner, Coimbra-Araújo, Carlos Henrique, Schulz, Rodrigo André |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The sensitive dependence of chaos on parameters is a topic of great interest in the study of integrability and stability of dynamical systems. Previous work has proposed ways to identify the sensitive dependence on parameters by topological criteria or large numerical simulations. In this paper, we show that when the Lyapunov exponents of the system vary with a change in the parameters, the system diverges exponentially in the orbits associated with the considered parameters. We use this result to explore the sensitive dependence on parameters in an uncertainty interval and conclude that the characterization of this phenomenon is directly related to our ability to determine the Lyapunov exponents of the system for different parameters. Comment: We have received comments from reviewers of the article that point to a need for a complete rewording of the ideas exposed. We do not wish the content to negatively influence or serve as a reference for other research without a solid foundation |
| Databáze: | arXiv |
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