On Some Dynamical Properties of Randomly Connected Higher Order Neural Networks

This chapter presents macroscopic properties of higher order neural networks. Randomly connected Neural Networks (RNNs) are known as a convenient model to investigate the macroscopic properties of neural networks. They are investigated by using the statistical method of neuro-dynamics. By applying the approach to higher order neural networks, macroscopic properties of them are made clear. The approach establishes: (a) there are differences between stability of RNNs and Randomly connected Higher Order Neural Networks (RHONNs) in the cases of the digital state − { } 1 1 , -model and the analog state [ , ] −1 1 model; (b) there is no difference between stability of RNNs and RHONNs in the cases of the digital state 0,1 { } -model and the analog state [ , ] 0 1 -model; (c) with neural networks with oscillation, there are large differences between RNNs and RHONNs in the cases of the digital state − { } 1 1 , -model and the analog state [ , ] −1 1 -model, that is, there exists complex dynamics in each model for k = 2 ; (d) behavior of groups composed of RHONNs are represented as a combination of the behavior of each RHONN.