Applied Mathematics

Volume 8, Issue 10 (October 2017)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

Google-based Impact Factor: 0.58  Citations  

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

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DOI: 10.4236/am.2017.810109    1,134 Downloads   2,254 Views  Citations

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.

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Franco, C. and Collado, J. (2017) Comparison on Sufficient Conditions for the Stability of Hill Equation: An Arnold’s Tongues Approach. Applied Mathematics, 8, 1481-1514. doi: 10.4236/am.2017.810109.

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