We study the phase dynamics and IV--characteristics of DC--SQUIDs consisting of Josephson junctions with topologically nontrivial barriers, which cause the appearance of Majorana bound state. Its comparative analysis with the trivial case is performed. The influence of external electromagnetic radiation is considered and the analysis of the amplitude dependence of the Shapiro step widths is performed. We have shown that in nontrivial case the width of even harmonic of Shapiro step is larger than width of odd harmonic. In the presence of external dc magnetic field a beating state is realized in the DC--SQUID, which leads to a resonance branch in the IV--curve. We show that in the presence of resonance branch the maximum width of Shapiro step and periods of its amplitude dependence are decreased in comparison of situation without resonance in both trivial and nontrivial cases. We demonstrate that in the presence of the resonance branch the chaotic behavior of IV--curve is reduced.
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