What we know as the concept of self organize criticality these days, was first introduced by Bak, Tang and Wisenfeld (BTW) in their well-known paper in 1987. They observe fractal behaviour in many natural system and use this concept to describe behaviour of these systems that spontaneously and without tuning parameters, under their natural evolution are driven to a state between the stable and unstable boundary. Bak et. al. proposed a sandpile model as a simple example of dynamics which behaviour open and dissipation. This model was widely viewed as an example of SOC behaviour. Subsequently, by using sandpile model, many attempts were made to clarify the behaviour of SOC systems. In the following Dhar in a well-known published in 1990, shown a sandpile model had the characteristics of abelian group. Thus abelian sandpile model (ASM) replaced the previous one. Eventually Ivashkevich et. al. in their attempt to facilitate an analytical solution for sandpile model, represented avalanche as sequence waves.

The successes in explanation the dynamics of natural systems use of SOC concepts, posses the possibility that maybe brain behaviour justify by this concept. In 2010 Chialvo et. al. compared the brain fMRI data with 2D-Ising model at the various temperature. The result shown the Ising networks at critical temperature and brain networks are “indistinguishable from each other”. In following in 2014 Zarepour et. al. prove this comparative between brain network and a sandpile model.

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Here, we study the regular network of 2D abelian sandpile model. We have added spike timing dependent plasticity to this network. For this purpose we used Ivashkevich wave concept, so we represented an avalanche as a sequence of waves. Because of using this concept we used wave numbers as a discrete-time. Definition of time in this way made it possible to check the toppling sequence of each site. Finally, we were able to add the STDP rule to the 2D abelian sandpile model. We are studing the effect of this rule to our network.