Investigation of complex dynamics in a recurrent neural network with network community structure and asymmetric weight matrix

The cerebral cortex is a complex network. It contains billions of neurons divided in spatial and functional clusters to perform different tasks. It also operates with complex dynamics such as periodic and chaotic ones. It has been shown that chaotic neural networks are more efficient than conventional recurrent neural networks in avoiding spurious memory. Inspired by the fact that the cerebral cortex has specific groups of cells, in this paper we investigate the dynamic of a recurrent neural network where neurons are coupled in such a way that form communities of a complex network. Also, we generate an asymmetric weight matrix placing pattern cycles during learning. Such a learning rule provides a natural periodic behavior in a fully connected network. Community structure breaks the connections up, forcing chaos to emerge. Our study shows that chaotic behavior rises for a high fragmentation degree in either just one community with sparse connections or several communities with few inter-community connections. For the latter case, we also show that the neural network can hold chaotic dynamic and a high value of modularity measure at the same time. These findings provide an alternative way to design dynamical neural networks to perform pattern recognition tasks exploiting periodic and chaotic dynamics.