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analysis across distinct control parameters, such as the heat source position and the tube length. The Green&apos;s function approach effectively captures the acoustic resonator&apos;s behavior. By introducing an interface with a hypothetical point source, this method facilitates the prediction of resonator frequencies and amplitudes, contingent on the occurrence of a temperature jump within the tube. The variation in sound speed within the tube at the interface leads to discontinuities in the derivative of the Green&apos;s function amplitude with respect to x. To visualize the impact of bifurcation parameters, namely heat source position and tube length, stability maps are generated. These maps delineate a spectrum of operational states. Unstable states are depicted by black regions, while white regions indicate stable states</abstract>
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