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Driven many-particle systems with nonlinear interactions are known to oftendisplay multi-stability, i.e. depending on the respective initial condition,there may be different outcomes. Here, we study this phenomenon for trafficmodels, some of which show stable and linearly unstable density regimes, butareas of metastability in between. In these areas, perturbations larger than acertain critical amplitude will cause a lasting breakdown of traffic, whilesmaller ones will fade away. While there are common methods to study linearinstability, non-linear instability had to be studied numerically in the past.Here, we present an analytical study for the optimal velocity model with astepwise specification of the optimal velocity function and a simple kind ofperturbation. Despite various approximations, the analytical results are shownto reproduce numerical results very well.

Analytical Calculation of Critical Perturbation Amplitudes and Critical Densities by Non-Linear Stability Analysis of a Simple Traffic Flow Model