Collective behavior of a small-world recurrent neural system with scale-free distribution

This paper proposes a scale-free highly clustered echo state network (SHESN). We designed the SHESN to include a naturally evolving state reservoir according to incremental growth rules that account for the following features: (1) short characteristic path length, (2) high clustering coefficient, (3) scale-free distribution, and (4) hierarchical and distributed architecture. This new state reservoir contains a large number of internal neurons that are sparsely interconnected in the form of domains. Each domain comprises one backbone neuron and a number of local neurons around this backbone. Such a natural and efficient recurrent neural system essentially interpolates between the completely regular Elman network and the completely random echo state network (ESN) proposed by Jaeger et al. We investigated the collective characteristics of the proposed complex network model. We also successfully applied it to challenging problems such as the Mackey-Glass (MG) dynamic system and the laser time-series prediction. Compared to the ESN, our experimental results show that the SHESN model has a significantly enhanced echo state property and better performance in approximating highly complex nonlinear dynamics. In a word, this large scale dynamic complex network reflects some natural characteristics of biological neural systems in many aspects such as power law, small-world property, and hierarchical architecture. It should have strong computing power, fast signal propagation speed, and coherent synchronization.