  Force-based models describe pedestrian dynamics in analogy to classical
mechanics by a system of second order ordinary differential equations. By
investigating the linear stability of two main classes of forces, parameter
regions with unstable homogeneous states are identified. In this unstable
regime it is then checked whether phase transitions or stop-and-go waves occur.
Results based on numerical simulations show, however, that the investigated
models lead to unrealistic behavior in form of backwards moving pedestrians and
overlapping. This is one reason why stop-and-go waves have not been observed in
these models. The unrealistic behavior is not related to the numerical
treatment of the dynamic equations but rather indicates an intrinsic problem of
this model class. Identifying the underlying generic problems gives indications
how to define models that do not show such unrealistic behavior. As an example
we introduce a new force-based model which produces realistic jam dynamics
without the appearance of unrealistic negative speeds for empirical desired
walking speeds.

Physics and Society