Stochastic model of self-driven two-species objects inspired by particular aspects of a pedestrian dynamics

In this work we propose a model to describe the fluctuations of self-driven objects (species A) walking against a crowd of particles in the opposite direction (species B) in order to simulate the spatial properties of the particle distribution from a stochastic point of view. Driven by concepts from pedestrian dynamics, in a particular regime known as stop-and-go waves, we propose a particular single-biased random walk (SBRW). This setup is modeled both via partial differential equations (PDE) and by using a probabilistic cellular automaton (PCA) method. The problem is non-interacting until the opposite particles visit the same cell of the target particles, which generates delays on the crossing time that depends on the concentration of particles of opposite species per cell. We analyzed the fluctuations on the position of particles and our results show a non-regular propagation characterized by long-tailed and asymmetric distributions which are better fitted by some chromatograph distributions found in the literature. We also show that effects of the crowd of particles in this situation are able to generate a pattern where we observe a small decrease of the target particle dispersion followed by an increase, differently from the observed straightforward non-interacting case. For a particular initial condition we present an interesting solution via constant density approximation (CDA). (C) 2015 Elsevier B.V. All rights reserved.