Investigating the computational power of spiking neurons with non-standard behaviors

Spiking neural networks have been called the third generation of neural networks. Their main difference with respect to the previous two generations is the use of realistic neuron models. Their computational power has been well studied with respect to threshold gates and sigmoidal neurons. However, biologically realistic models of spiking neurons can produce behaviors that can be computationally relevant, but their power has not been assessed in the same way. This paper studies the computational power of neurons with different behaviors based on the previous analyses conducted by Maass and Schmitt. The studied behaviors are rebound spiking, resonance and bursting. The results of the analysis are presented. A theoretical motivation for this study is presented and a discussion is done on the possible implications of the findings for using networks of spiking neurons for performing computations.