Robust heteroclinic and switching dynamics

摘要

Recent work in a number of areas has highlighted ways in which heteroclinic and homoclinic connections within dynamical attractors can be responsible for intermittent and bursting behaviour in nonlinear systems. Such dynamical behaviour appears in models from a wide range of applications including fluid dynamics, population dynamics and neuroscience, with related dynamics having been found in other contexts (e.g. unstable attractor networks, chaotic itinerancy and cycling chaos). Moreover, heteroclinic dynamics may serve as an appropriate mathematical framework for transient processes that can be treated as an itinerary past metastable states.