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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.

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