Dynamic Influence of Contraries Oscillators on Small-World Network Synchrony

Networks are all around us and can be in the Euclidean space of concrete objects such as power grids, the Internet, highways or subway systems, and neural networks, or in an abstractly defined space, such as networks of familiarity or cooperation between people. To express the general properties of such networks, their modeling is in the form of graphs that show the nodes as oscillators (the dynamic unit) and the edges as the existence of interaction between oscillators We applied the Kuramato model to networks of oscillators connected in a small-world network pattern and considered the influence of oscillators on each other as conformist and contrarian. Based on this, we examined the synchronization in the network. We showed that if the number of contrarian oscillators in the network reaches a certain value, it will cause more of the network, which is due to the weakening of defects created in compatible oscillators.