A mechanism for pattern formation in dynamic populations by the effect of gregarious instinct

We introduced the gregarious instinct by means of a novel strategy that considers the average effect of the attractive forces between individuals within a given population. We watched how pattern formation can be explained by the effect of aggregation depending on conditions on food and / or mortality. We propose a model that describes the corresponding dynamic and by a linear stability analysis of homogeneous solutions and can identify and interpret the region of parameters where these patterns are stable. Then we test numerically these preliminary results and find stable patterns as solutions. Finally, we developed a simplified model allowing us to understand in greater detail the processes involved.