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This paper presents two contributions tothe stability analysis of periodic systems modeled by a Hill equation: Thefirst is a new method for the computation of the Arnold Tongues associated to agiven Hill equation which is based on the discretization of the latter. Usingthe proposed method, a vibrational stabilization is performed by a change inthe periodic function which guarantees stability, given that the original equationhas unbounded solutions. The results are illustrated by some examples.

KEYWORDS

Vibrational Stabilization, Hill Equation, Periodic Systems, Arnold Tongues

Cite this paper

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.





Author: Joaquin Collado1, Hildeberto Jardón-Kojakhmetov2

Source: http://www.scirp.org/



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