Effect of Vision Angle on the Phase Transition in a Flocking Behavior of Animal Groups

Abstract

The nature of the phase transition in a system of self-propelling particles has been extensively studied during the last few decades. A theoretical model was proposed by T. Vicsek, {\it et. al.} [Phys. Rev. Lett. {\bf 75}, 1226 (1995)] with a simple rule for updating the direction of motion of each particle. Based on the Vicsek's model (VM) [1], in this work, we consider a group of animals as particles moving freely on a two-dimensional space. Due to the fact that the viewable area of animals depends on the species, we consider the motion of each individual within an angle $\phi =\Phi /2$ ($\Phi$ is called angle of view) of a circle centered at its position, of radius $R$. We obtained a phase diagram in the space ($\phi$, ${\eta }_c$) with ${\eta }_c$ being the critical noise. We show that, the phase transition exists only in the case of a wide view's angle $\phi \ge 0.5\pi$. The flocking of animals is an universal behavior of the species of prey, but not the one of the predator. Our simulation results are in good agreement with experimental observation [2].

04 pages, 5 figures

References in corpus (3)

• Novel type of phase transition in a system of self-driven particles
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Collective behavior of interacting self-propelled particles

Cited by in corpus (8)

• Large-scales patterns in a minimal cognitive flocking model: incidental leaders, nematic patterns, and aggregates
• Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks
• Asymmetric exchange in flocks
• First order phase transition in a self-propelled particles model with variable angular range of interaction
• Fore-aft asymmetric flocking
• Collective movement in alarmed animals groups: a simple model with positional forces and a limited attention field
• The XY model with vision cone: non-reciprocal vs. reciprocal interactions
• Survival chances of a prey swarm: how the cooperative interaction range affects the outcome