1Department of Physics and Center for Theoretical Biology, Peking University, Beijing 100871
2School of Mathematical Sciences, Peking University, Beijing 100871
Dynamical Convergence Trajectory in Networks
TAN Ning1;ZHANG Yun-Jun2;OUYANG Qi2;GENG Zhi
1Department of Physics and Center for Theoretical Biology, Peking University, Beijing 100871
2School of Mathematical Sciences, Peking University, Beijing 100871
Abstract： It is well known that topology and dynamics are two major aspects to determine the function of a network. We study one of the dynamic properties of a network: trajectory convergence, i.e. how a system converges to its steady state. Using numerical and analytical methods, we show that in a logical-like dynamical model, the occurrence of convergent trajectory in a network depends mainly on the type of the fixed point and the ratio between activation and inhibition links. We analytically proof that this property is induced by the competition between two types of state transition structures in phase space: tree-like transition structure and star-like transition structure. We show that the biological networks, such as the cell cycle network in budding yeast, prefers the tree-like transition structures and suggest that this type of convergence trajectories may be universal.
2005, Vol. 22 
