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Type-III Intermittency from Markov Binary Block Visibility Graph Perspective

Abstract

In this work, the type-III intermittency is studied from the optimized Markov binary visibility graphs perspective. In fact, we study the behavior of a dynamical system in the vicinity of an inverse period doubling bifurcation using networks language. 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 mode and new nonlinear term affect the trajectory and the mechanism of type-III intermittency, but the mean length is approximately similar to previous works. For further study, we compute the degree distribution of the complex network generated by type-III intermittency. Experimental results are found to agree well with the analytical results derived from the optimized Markov binary visibility graph and also theoretical degree distribution can distinguish two states η ≤ ηδ and η>ηδ from each other in type-III intermittency mechanism.

Pejman Bordbar and Sodeif Ahadpour

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