ome experiments and simulations suggest that nervous system as a complex system produces neuronal avalanches that their size and duration exhibit power law behavior. The power law behavior is interpreted as the signature of criticality and it is assumped that the resting brain operate near criticality. However, there are some researches with conflicting results. The model of current study is leaky integrate and fire- When a neuron fires, it forces all the neurons linked to it to make a step ahead or backward by the quantity K (cooperation or control parameter) - on different kinds of networks. Accodring to this research, result are dependent significantly to kind of network; e.g. duration and size of neuronal avalanches in regular and small world networks exhibit power law behavior with adopted power to experiments. However, there is not any power law behavior in random networks. Neuronal avalanches in C.elegans network show power law behavior, but just the powers in size curve are adjusted with experiments. The effects of inhibitory neurons on neuronal avalanches studied too. In regard to experiments, this kind of neuron prevents producing large avalanches. In regular network, adding inhibitory neurons proves it. Nevertheless, result of C.elegans network is different. Power spectrum of EEG, MEG,…datas have investigated in many studies and in this research the capacity of model to produce them was investigated. To study this, the fast fourier transform of time series of numbers of fired neuron in each step was calculated.