This paper investigates the dynamics of two couplecd Mathieu equations. The coupling functions involve both delayed and nondelay terms. We use a perturbation method to obtain a slow flow which is then studied using Routh-Hurwitz stability criterion. Analytic results are shown to compare favorably with numerical integration. The numerical integrator, DDE23, is shown to inadvertently add damping....

where θ, λ and φ are real numbers, and (ξn)n denotes the canonical orthonormal basis in l2. The study of the spectral properties of this class of operators has attracted a significant amount of interest in the past couple of decades (see [5], [3], [8], [1], [10], [14], [12], [7] for some of the most important developments). Most of this work has focused on the “Ten Martini problem” of M. Kac, c...

Continued fraction expansions for the eigenvalues A= A(I', h2 ) and for the Fourier coefficients c~n/co are given by Tamir and Wang in [2]. These relations are valid both in the s table (I' real) and unstable (I' complex) regions . F (I') == C~,.1Co is numerically evaluated and depicted. It is seen from the graphs in [2] that the given formulas for C~,JCO are not particularly suitable for numer...