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

• 作者: Carlos A. Franco Joaquin Collado
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Periodic Differential Equations Stability SUFFICIENT Criteria HILL Equation HAMILTONIAN LYAPUNOV Characteristic Constant
• 年，卷（期）: 2017,（10）
• 页码范围: 1481-1514
• 页数: 34页
• 分类号: O1

摘要

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.