Author(s)

Joaquin Collado¹, Hildeberto Jardón-Kojakhmetov²

¹Automatic Control Department, CINVESTAV-IPN, Mexico City, Mexico.
²Engineering and Technology Institute, University of Groningen, Groningen, The Netherlands.

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.

Vibrational Stabilization, Hill Equation, Periodic Systems, Arnold Tongues

Collado, J. and Jardón-Kojakhmetov, H. (2016) Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach. Applied Mathematics, 7, 2005-2020. doi: 10.4236/am.2016.716163.