TITLE:
Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach
AUTHORS:
Joaquin Collado, Hildeberto Jardón-Kojakhmetov
KEYWORDS:
Vibrational Stabilization, Hill Equation, Periodic Systems, Arnold Tongues
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.16,
October
28,
2016
ABSTRACT: This paper presents two contributions to
the stability analysis of periodic systems modeled by a Hill equation: The
first is a new method for the computation of the Arnold Tongues associated to a
given Hill equation which is based on the discretization of the latter. Using
the proposed method, a vibrational stabilization is performed by a change in
the periodic function which guarantees stability, given that the original equation
has unbounded solutions. The results are illustrated by some examples.