Design of a network with state stability

Designing a network with given functions or reconstruct a network based on its dynamical behavior is an important problem in the study of complex systems. In this paper, we put forward certain principles in constructing a network with state stability. We show that a necessary and sufficient condition to design networks with a global fixed point is that active nodes inhibit inactive nodes, while the latter activate the former directly or indirectly. We also designed networks based on basic modules, where each basic module consists a sub-network, they communicate through the inhibition link from each activator in lower module to the inhibitor of upper module. We found that long activation links, i.e. indirect activation links are important to the formation of convergence trajectory. We believe that these principles may help us to understand the topology of biological networks.