Linear stability analysis of large dynamical systems on random directed graphs
Izaak Neri, Fernando Lucas Metz
Abstract
This work analyzes how network architecture affects the linear stability of fixed points in dynamical systems defined on random, directed graphs. The authors derive results for the leading eigenvalue of the adjacency matrix representing the network and propose a phase diagram that separates a stable from an unstable regime
Topics & Concepts
Linear dynamical systemMathematicsDynamical systems theoryAdjacency matrixEigenvalues and eigenvectorsStability (learning theory)Directed graphLinear systemDynamical system (definition)Matrix (chemical analysis)Work (physics)Fixed pointDiscrete mathematicsCombinatoricsRandom dynamical systemGraph theoryHurwitz matrixApplied mathematicsTopology (electrical circuits)Adjacency listRandom matrixStochastic matrixDiagramType (biology)Term (time)Topological dynamicsRandom graphPoint (geometry)Phase diagramComplex networkComputer scienceNetwork topologyNetwork analysisGraphStrongly connected componentNonlinear dynamical systemsEcosystem dynamics and resilienceNonlinear Dynamics and Pattern FormationChaos control and synchronization