WHAT CONNECTION TOPOLOGY PROHIBIT CHAOS IN CONTINUOUS TIME NETWORKS?

In this paper, we are concerned with two interesting problems in the dynamics of neural networks. What connection topology will prohibit chaotic behavior in a continuous time neural network (NN). To what extent is a continuous time neural network (NN) described by continuous ordinary differential equations simple enough yet still able to exhibit chaos? We study these problems in the context of the classical neural networks with three neurons, which can be described by three-dimensional autonomous ordinary differential equations. We first consider the case where there is no direct interconnection between the first neuron and the third neuron. We then discuss the case where each pair of neurons has a direct connection. We show that the existence of the directed loop in connection topology is necessary for chaos to occur.