Stability and Chaos in Dynamic Transport Systems

In this Book, a doubly (discrete time day-to-day and continuous time within-day) dynamic departure time choice model is studied. The study brings together different aspects of network modelling such as departure time choice modelling using schedule disutility theory, theory on travel time functions based on continuous-time whole link models, fixed point formulation of day-to-day dynamic traffic assignment using learning and adaptation, discrete choice models to replicate choice behaviour and finally stability analysis using nonlinear dynamical systems theory. Concept from dynamical systems theory is used to establish factors that give rise to stable and unstable (including periodic, quasi-periodic and chaotic) behaviour in the underlying transport system by studying the Jacobian Matrix of the transition function and the associated eigenvalues. The theory is used to analyze a test network and resulting numerical results are reported.