Abstract
In this paper, we study the stability of a class of coupled Hill's equations. Different possible forms of solutions are discussed. Assuming certain odd-even symmetries and using Floquet theory, a simplified form of the monodromy matrix and a closed form formula for its eigenvalues, as a function of the first element of the monodromy matrix, are derived. The Lorentz oscillator model and its connection to the coupled Hill's equations is discussed, and Lyapunov theory is used to prove its stability. Finally, using our formula for the eigenvalues, the stability diagrams of a system of coupled Mathieu equations, as an example of the coupled Hill's equations, are generated.
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