TITLE:
Comparison on Sufficient Conditions for the Stability of Hill Equation: An Arnold’s Tongues Approach
AUTHORS:
Carlos A. Franco, Joaquin Collado
KEYWORDS:
Periodic Differential Equations, Stability Sufficient Criteria, Hill Equation, Hamiltonian, Lyapunov Characteristic Constant
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.10,
October
31,
2017
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.