  A family of repressor networks is proposed as a simple model of gene
regulatory networks. We analytically show three topological classes of the
repressor networks, each of which exhibits distinctly growing complexity of
spatiotemporal expressions starting from nearly homogeneous states. Further, by
focusing on locally interacting cases such as chain networks, including a
generalized repressilator, or feedforward(back)-loop networks, spatiotemporal
expressions in the long time regime and elusive relationships between such
different networks are discussed in detail.
