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Jordan, D. and Smith, P. (2004) Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers. 4th Edition, Oxford University Press, USA.

has been cited by the following article:

• 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.