Effects of agent's orientation in 2D flocking models

Various different types of collective motions have attracted attention from physicists; this is a fascinating phenomenon, resulting from the very simple interactions between individuals (particles/cells). Our aim is to contribute to elucidating the motion of collective behavior of a non-equilibrium multi-agent system. In this context, the topic of this manuscript is to study the effect of the zone of orientation on the collective motion in two-dimensional space. In this investigation, we extend the model suggested by Viscek et al. for only a single interaction radius. In our proposed model, the particles corresponding to agents locally interacting with their neighbors according to simple rules depending on the particular condition. At each time step the velocity of an agent depends on their direction and is perturbed by an external noise η. Particularly, we show that with a specific fixed parameter a phase transition can be achieved, from disordered motion of particles to ordered motion, by varying the radius of orientation R2 and the value of the density. Furthermore, the value of R2 at which the transition emerges depends strongly on the size of repulsion zone R1. The study is performed over different situations via a numerical simulation technique. Implications of these findings are discussed in the section of simulation results.