In this work, we study the type-II intermittency based on asymptotic modes and the optimized Markov binary visibility graphs perspective. In fact, we investigate the behavior of a dynamical system in the vicinity of subcritical Hopf bifurcations of pre-fixed point, fixed point, and post-fixed point using networks language. We use self maps in order to generate asymptotic modes in the type-II intermittency. We find their properties based on statistical tools such as the length between reinjection points and the mean length and also length distributions. Numerical results show that asymptotic modes affect on the trajectory and the length between reinjection points of type-II intermittency in situations of pre-fixed point, fixed point, and post-fixed point, however their mean length are approximately similar to each other. For further illustration, we compute the degree distribution of the complex network generated by type-II intermittency. Experimental results are found to agree well with the analytical results derived from the optimized Markov binary visibility graph.
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