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http://cio.repositorioinstitucional.mx/jspui/handle/1002/437| THEORETICAL STUDY OF CONTROLLING MULTISTABILITY BY PARAMETRIC AND STOCHASTIC MODULATION IN THE HÉNON MAP AND A FIBER LASER | |
| CRUZ YULIANA CALDERON HERMOSILLO | |
| Alexander Pisarchik | |
| Acceso Abierto | |
| Atribución-NoComercial-SinDerivadas | |
| NONLINEAR DYNAMICS, HÉNON MAP, MODULATION, ERBIUMDOPED, FIBER LASER | |
| "In this thesis, I study theoretically the applicability of the method for controlling multistability by parametrical and stochastic modulation. The method for controlling multistability was suggested by Pisarchik and Goswami in 2000. It implies additional harmonic modulation to a system parameter that allows annihilation of undesirable attractors in a multistable system. I begin from a study of the attractor annihilation in the bistable Hénon map subject to additive noise. The Hénon map is one of the simplest dynamical systems which exhibits coexistence of attractors. First, I focus on the parameter region where two different periodic orbits coexist (period 1 and period 3) and apply additional harmonic modulation to a system parameter to destroy the period-3 attractor. I demonstrate that additive noise can facilitate the attractor annihilation for some modulation frequencies, in the sense that an undesired attractor can be destroyed with a smaller amplitude of the control modulation. On the other hand, for other modulation frequencies noise can stabilize the attractor. In the latter case, noise induces multistability in the system with parameter modulation. Then, I explore the parameter region in the map where a periodic orbit coexists with a chaotic orbit and study the influence of noise on attractor annihilation. Finally, I study resonance phenomena in the volume of basins of attraction of coexisting period-1 and period-3 attractors in the H´enon map, subject to normally distributed noise added to both variables. As the noise level is increased, the volume of the basin of attraction of the period-1 attractor grows up, while the volume of the basin of the period-3 attractor drops down. At a certain level of noise the volume of the basin of the period-1 attractor reaches its maximum value." | |
| 2007-12 | |
| Tesis de maestría | |
| Inglés | |
| León, Guanajuato | |
| Público en general | |
| Calderon-Hermosillo, (2007). "Theoretical study of controlling multistability by parametric and stochastic modulation in the Hénon map and a fiber laser". Tesis de Maestría en Ciencias (Óptica). Centro de Investigaciones en Óptica, A.C. León, Guanajuato. 40 pp. | |
| ÓPTICA | |
| Aparece en las colecciones: | MAESTRIA EN CIENCIAS (ÓPTICA) |
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