Basin size evolution between dissipative and conservative limits

• Main Author: Rech P.C.*
• Publication Date: 2005
• Other Authors: Beims M.W., Gallas J.A.C.
• Format: Article
• Language: eng
• Source: Repositório Institucional da Udesc
• dARK ID: ark:/33523/00130000086vd
• Download full: https://repositorio.udesc.br/handle/UDESC/10398

Recent methods for stabilizing systems like, e.g., loss-modulated CO 2 lasers, involve inducing controlled monostability via slow parameter modulations. However, such stabilization methods presuppose detailed knowledge of the structure and size of basins of attraction. In this Brief Report, we numerically investigate basin size evolution when parameters are varied between dissipative and conservative limits. Basin volumes shrink fast as the conservative limit is approached, being well approximated by Gaussian profiles, independently of the period. Basin shrinkage and vanishing is due to the absence of bounded motions in the Hamiltonian limit. In addition, we find basin volume to remain essentially constant along a peculiar parameter path along which it is possible to recover the dissipation rate solely from metric properties of self-similar structures in phase-space. © 2005 The American Physical Society.