Type-I intermittency from Markov binary block visibility graph perspective

In this work, the type-I intermittency is studied from the optimized Markov binary visibility graphs perspective. We consider a local Poincaré map such as the logistic map that is a simple model for exhibiting this type of intermittency. To consider the acceptance gate as $$ , we show that the transition between laminar and non-laminar zones in type-I intermittency takes distinct phases and regions. According to their behavioral characteristics, we call them as pure, switching, threshold, trapping, and transforming phases for the laminar zone and initial, terminal reinjection, and chaotic burst regions for non-laminar zone. We investigate their properties based on statistical tools such as the maximum and the mean length of the laminar zone and also length distributions of the laminar zone. For further investigation, we study degree distribution of the complex network generated by type-I intermittency time series and finally, predict various behaviors of phases and regions by proposed theoretical degree distributions.