Neural avalanches in size and duration exhibit a power law distribution illustrating as a straight line when plotted on the logarithmic scales. The power-law exponent is interpreted as the signature of criticality and it is assumed that the resting brain operates near criticality. However, there is no clear evidence that supports this assumption, and even there are extensive research studies conflicting one another. The model of the current paper is an extension of a previous publication wherein we used an integrate-and-fire model on a regular lattice with periodic boundary conditions and introduced the temporal complexity as a genuine signature of criticality. However, in that model the power-law distribution of neural avalanches were manifestation of super-criticality rather than criticality. Here, however, we show that replacing the discrete noise in the model with a Gaussian noise and continuous time solution of the equation leads to coincidence of temporal complexity and spatiotemporal patterns of neural avalanches at a control parameter which is assumed to be the critical value of the model.