Feedback mechanism in network dynamics with preferential flow

We study complex systems or networks in which each node holds an internal dynamics and interacts with other nodes through some kinds of topologies. Collective behavior with dynamical fluctuations is analyzed in complex systems. The dynamical fluctuations of a node can be divided into two parts: one is the internal dynamical fluctuation of the node and the other is the external dynamical fluctuation caused by other nodes. Based on a theoretical analysis, a hidden feedback mechanism is identified in complex systems, which is illustrated in a macroeconomic network and in a city-population network. Furthermore, we study the effect of the topology of the networks on the feedback mechanism. The feedback mechanism is preserved for hub nodes in the networks with a scale-free topology as well as in the networks with an evolving topology. By the hidden feedback mechanism, the observation data can be utilized to judge directly whether the system of each node is with positive feedback or with negative feedback even without knowing its dynamical model.