Islands of stability in regions of unstable response of parametric resonators
We derive the stability map (Ince-Strutt diagram) of the Whittaker-Hill equation ẍ + [β² + α²(cos 2t + cos 4t)]x = 0. This map includes crossover points in the instability windows that are located well above the diagonal (i.e., α² > β²). We show that at the vicinity of each of these crossover points there are two small regions of stable response, which merge into an island of stability if linear damping is included in the equation.
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