Dynamical robustness and its structural dependence in biological networks

We discuss the dynamical robustness of biological networks represented by directed graphs, such as neural networks and gene regulatory networks. The theoretical results indicate that networks with low indegree variance and high outdegree variance are dynamically robust. We propose a machine learning method that gives equilibrium states to input-output networks with a recurrent hidden layer. We verify the theory by using the learned networks having various indegree and outdegree distributions. We also show that the basin of attraction of an equilibrium state is narrow when networks are dynamically robust.