existence of excitatory and inhibitory oscillators in the small world network and its dynamic effect on network synchronization

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).