Group coordination in a biologically-inspired vectorial network model

Most of the mathematical models of collective behavior de- scribe uncertainty in individual decision making through additive uniform noise. However, recent data driven stud- ies on animal locomotion indicate that a number of animal species may be better represented by more complex forms of noise. For example, the popular zebrafish model organism has been found to exhibit a burst-And-coast swimming style with occasional fast and large changes of direction. Based on these observations, the turn rate of this small fish has been modeled as a mean reverting stochastic process with jumps. Here, we consider a new model for collective behavior inspired by the zebrafish animal model. In the vicinity of the synchronized state and for small noise intensity, we establish a closed-form expression for the group polarization and through extensive numerical simulations we validate our findings. These results are expected to aid in the analysis of zebrafish locomotion and contribute a new set of mathematical tools to study collective behavior of networked noisy dynamical systems.