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The spatiotemporal synchronous activity of delay coupled chaotic systems in a network is very important to understand the communications through neurons of the human body. In this paper, we present a homogeneous one-dimensional delay coupled neuron model in a complex network. We design a network model in which the links are stochastically updated at every time step. In this model, the nodes of the network are bidirectionally asymmetrically coupled instead of usual symmetric coupling. We further analyze the impacts of dynamic random updating of links and delay term on the synchronization phenomenon of the network. Synchronized fixed points are found in the networks of neurons numerically. Analytically, the stability range of synchronized fixed point and period-2 orbits are determined which are in very good agreement with the numerical simulation results. Moreover, numerical simulation results have been presented and are found to be in very good concurrence with our analytical result. Interestingly, we have found that in our model synchronized period-2 and period-4 dynamics appear for weak coupling which were not observed earlier. In addition, we have plotted the time series data and maximum Lyapunov exponent to confirm the existence of synchronized chaos.

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