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Comparison on Sufficient Conditions for the Stability of Hill Equation: An Arnold’s Tongues Approach

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Document pages: 34 pages

Abstract: It is known that the solutions of a second order linear differential equationwith periodic coefficients are almost always analytically impossible to obtainand 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. Wealso present a brief explanation on how the authors, of each criterion, obtainedthem. And a comparison between four sufficient stability criteria andthe stability zones found by perturbation methods is presented.

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