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Comparison on Sufficient Conditions for the Stability of Hill Equation: An Arnold’s Tongues Approach
Department of Automatic Control, Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional, Mexico City, Mexico
Department of Automatic Control, Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional, Mexico City, Mexico
- 1 Department of Automatic Control, Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional, Mexico City, Mexico
- 2 Department of Automatic Control, Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional, Mexico City, Mexico
Applied Mathematics·Volume 08 (2017)·Pages 1481–1514·Published 18 October 2017·DOI10.4236/am.2017.810109
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Abstract
It is known that the solutions of a second order linear differential equation with periodic coefficients are almost always analytically impossible to obtain and in order to study its properties we often require a computational approach. In this paper we compare graphically, using the Arnold Tongues, some sufficient criteria for the stability of periodic differential equations. We also present a brief explanation on how the authors, of each criterion, obtained them. And a comparison between four sufficient stability criteria and the stability zones found by perturbation methods is presented.
KeywordsPeriodic Differential EquationsStability Sufficient CriteriaHill EquationHamiltonianLyapunov Characteristic Constant
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