Universality of flux-fluctuation law in complex dynamical systems

Recent work has revealed a law governing flux fluctuation and the average flux in complex dynamical systems. We establish the universality of this flux-fluctuation law through the following steps: (i) We derive the law in a more general setting, showing that it depends on a single parameter characterizing the external driving; (ii) we conduct extensive numerical computations using distinct external driving, different network topologies, and multiple traffic routing strategies; and (iii) we analyze data from an actual vehicle traffic system in a major city in China to lend more credence to the universality of the flux-fluctuation law. Additional factors considered include flux fluctuation on links, window size effect, and hidden topological structures such as nodal degree correlation. Besides its fundamental importance in complex systems, the flux-fluctuation law can be used to infer certain intrinsic property of the system for potential applications such as control of complex systems for improved performance. DOI: 10.1103/PhysRevE.87.012808