Group coordination in a biologically-inspired vectorial network model

Abstract

Most of the mathematical models of collective behavior describe uncertainty in individual decision making through additive uniform noise. However, recent data driven studies 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.

Keywords

• biological groups
• polarization
• stochastic jump process
• turn rate
• vectorial network model