Basin size evolution between dissipative and conservative limits

Details Basin size evolution between dissipative and conservative limits Basin size evolution between dissipative and conservative limits

Jan 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005phrve..71a7202r&link_type=abstract

Physical Review E, vol. 71, Issue 1, id. 017202

Statistics

Applications

5

Control Of Chaos, Applications Of Chaos, Low-Dimensional Chaos, Gas Lasers Including Excimer And Metal-Vapor Lasers

Scientific paper

Recent methods for stabilizing systems like, e.g., loss-modulated CO2 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.

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