Análise de modelo de Hopfield com topologia de rede complexa

Abstract

Biological neural networks contain 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 and motivated by the efficiency of complex behaviors, in this document we investigate the dynamics of a recurrent neural network, as the Hopfield one, but with neurons coupled in such a way to form a complex network community structure. Also, we generate an asymmetric weight matrix placing pattern cycles during learning. Our study shows that the network can operate with periodic and chaotic dynamics, depending on the degree of the connection’s fragmentation. For low fragmentation degree, the network operates with periodic dynamic duo to the employed learning rule. Chaotic behavior seems to rise for a high fragmentation degree. We also show that the neural network can hold both chaotic dynamic and a high value of modularity measure at the same time, indicating an acceptable community structure. These findings provide an alternative way to design dynamical neural networks to perform pattern recognition tasks exploiting periodic and chaotic dynamics by using a more similar topology to the topology of the brain.