A numerical method for locating stable periodic orbits in chaotic systems
โ Scribed by Dov Grobgeld; Eli Pollak; Jakub Zakrzewski
- Book ID
- 107914264
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 858 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0167-2789
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
This paper proposes an approach for detecting unstable periodic orbits embedded in chaotic systems by using the simplex method. The simplex algorithm is easily implemented and does not require the derivatives of the function to be optimized. As a result, it is also applicable to chaotic systems with
Both a theoretical argument and a numerical algorithm to identify periodic and chaotic orbits are presented and discussed. Reliability of the approach is verified using the Duffing oscillator through the standard computation of Lyapunov exponents. Advantages of the proposed approach are given.