Universal transient behavior in large dynamical systems on networks
Wojciech Tarnowski, Izaak Neri, Pierpaolo Vivo
Abstract
This paper develops an exact formalism to study how network architecture influences the transient dynamics of large dynamical systems in the vicinity of a stationary point. It is shown that for unidirectional networks the average dynamical response to initial perturbations is universal and only depends on a single parameter, encoding the average interaction strength between the individual constituents. Results are illustrated with numerical simulations on random graphs and real-world graphs, including a foodweb and a signalling network.
Topics & Concepts
Formalism (music)Dynamical systems theoryStatistical physicsPhysicsTransient (computer programming)Dynamical system (definition)Random dynamical systemMathematicsControl theory (sociology)Computer scienceCoupling strengthTopology (electrical circuits)Transient responseComputer simulationDynamics (music)Numerical modelsNonlinear dynamical systemsClassical mechanicsNetwork modelLinear dynamical systemNetwork dynamicsNetwork topologyMathematical analysisNeural Networks Stability and SynchronizationNonlinear Dynamics and Pattern FormationGene Regulatory Network Analysis