# Pattern formation induced by intraspecific interactions in a predator-prey system

## TL;DR

This paper investigates how intraspecific interactions like cooperation and competition influence pattern formation in predator-prey systems, revealing new instability mechanisms beyond traditional models with Holling-type functional responses.

## Contribution

It introduces a generalized population model with Verhulst-type saturation terms, demonstrating that intraspecific interactions can induce diffusion-driven instability and spatial patterns.

## Key findings

- Intraspecific saturation can cause population instability.
- Both cooperative and competitive interactions lead to pattern formation.
- Numerical simulations confirm the emergence of spatial patterns.

## Abstract

Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type functionals involved. Here we study the effects of intraspecific cooperation and competition on diffusion-driven instability in a predator-prey system with a different structure. We conduct the analysis on a generalized population dynamics that bounds intraspecific and interspecific interactions with Verhulst-type saturation terms instead of Holling-type functionals. We find that instability occurs due to the intraspecific saturation or intraspecific interactions, both cooperative and competitive. We present numerical simulations and show spatial patterns due to diffusion.