Resonant forcing of multidimensional chaotic map dynamics.
Phys Rev E Stat Nonlin Soft Matter Phys
; 75(3 Pt 2): 036212, 2007 Mar.
Article
en En
| MEDLINE
| ID: mdl-17500774
We study resonances of chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response. We find that resonant forcing functions complement the separation of nearby trajectories, in that the product of the displacement of nearby trajectories and the resonant forcing is a conserved quantity. As a consequence, the resonant function will have the same periodicity as the displacement dynamics, and if the displacement dynamics is irregular, then the resonant forcing function will be irregular as well. Furthermore, we show that resonant forcing functions of chaotic systems decrease exponentially, where the rate equals the negative of the largest Lyapunov exponent of the unperturbed system. We compare the response to optimal forcing with random forcing and find that the optimal forcing is particularly effective if the largest Lyapunov exponent is significantly larger than the other Lyapunov exponents. However, if the largest Lyapunov exponent is much larger than unity, then the optimal forcing decreases rapidly and is only as effective as a single-push forcing.
Buscar en Google
Colección:
01-internacional
Base de datos:
MEDLINE
Idioma:
En
Revista:
Phys Rev E Stat Nonlin Soft Matter Phys
Asunto de la revista:
BIOFISICA
/
FISIOLOGIA
Año:
2007
Tipo del documento:
Article
País de afiliación:
Estados Unidos
Pais de publicación:
Estados Unidos