Shape effects on herd behavior in ecological interacting population models

- Several dynamical systems modeling two-populations interactions gathering in herds.
- Interaction occurs on the perimeter in 2D.
- Interaction occurs on the total surface area for populations living in 3D.
- Here we even accommodate the model for herds that assume fractal shapes.
- Populations symbiosis, competition and predator-prey are considered.
- Stable solution is independent of the shape of the herd for competition.

In this paper, we introduce several dynamical systems modeling two-populations interactions. The main idea is to assume that the individuals of one of the populations gather together in herds, thus possess a social behavior, while individuals of the second population show a more individualistic attitude. We model the fact that the interaction between the two populations occurs mainly through the perimeter of the herd in a 2D space or through the total surface area for populations that live in a 3D space. This idea has already been explored earlier, but here we even accommodate the model for herds that assume fractal shapes. We account for all types of the populations intermingling: symbiosis, competition and predator-prey interactions. In the cases of obligated mutualism for the individualistic population and of competition, the stable solution attained by the populations is independent of the shape of the herd.