The dynamic behavior of many physical, biological, and other systems, are organized according to the synchronization of chaotic oscillators. In this paper, we have proposed a new method with low sensitivity to noise for detecting synchronization by mapping time series to complex networks, called the ordinal partition network, and calculating the permutation entropy of that structure. We show that this method can detect different kinds of synchronization such as complete synchronization, phase synchronization, and generalized synchronization. In all cases, the estimated permutation entropy decreases with increased synchronization. This method is also capable of estimating the topology of the network graph from the time series, without knowledge of the dynamical equations of individual nodes. This approach has been applied for the two identical and nonidentical coupled Rössler systems, two nonidentical coupled Lorenz systems, and a ring of coupled Lorenz96 oscillators.
The study of the pancreatic β-cells and their collective behavior is of great importance from the fluctuating insulin perspective. In this paper, a network of non-locally coupled β-cells is considered. It has been frequently reported that bursting of β-cells and their synchronous oscillations are associated with gap junctions. Therefore, a linear coupling between the membrane potentials of the clustered cells is used to model the gap junctions. The effects of coupling strength and number of neighbouring connections on the behavior of the cells is also investigated. Various collective patterns including chimera state, cluster synchronization and complete synchronization are observed. It is attained that the dynamic of the cells, e.g., being chaotic or periodic, has a significant role in their behavior. The observed collective behaviors not only is related to the network's parameters, but also heavily depends on its underlying topology. Detailed analytical description and extensive numerical simulations are provided to support the claims.
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