Crowd Behavior as an Example of the Evolution of a Complex System - Evacuation Models Proposal Based on the Symmetry Analysis Approach

The evacuation of football stadium scenarios as examples of evolution of complex system are discussed. The models are presented as movements of individuals according to fields of displacements, calculated correspondingly to the given scenario. The assumption has been made that the most efficient evacuation is left based on the accordance of symmetry of allowed space, and this symmetry is taken into account while calculating the displacements field. The displacements related to every point of this space are calculated by the symmetry analysis method and fulfill the symmetry conditions of allowed space. The speed of each individual at every point in the presented model has the same quantity. Consequently, the times of evacuation and average presses acting on individuals during the evacuation are given. Both parameters are compared with and without symmetry considerations. They are calculated in the simulation procedure. For the realization of the simulation tasks the new program (using modified Helbing model) has been elaborated.