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. تفاصيل المقالة

synchronization was investigated in Watts-Strogats small world network with inhibited and excitable oscillators. According to the Kuramoto model in the small world network, with the increase in the limited number of inhibited oscillators, the synchronization in the system will be accompanied by network defects, and with their increase, the synchronization will also increase, and after reaching its maximum value, it will begin to decrease. That is, with a certain ratio of inhibitory oscillators to excitation depending on the coupling strength, network synchronization is maximum. As the coupling strength of the oscillators increases, the interval of the number of inhibitions for which the network is in synchronization decreases. This result is not related to a specific small world network and has been observed by repeating it in different small world networks. Excitatory and inhibitory oscillators are in phase up to a certain percentage of inhibitory oscillators in the network (depending on the coupling strength). تفاصيل المقالة