An ant territory formation model with chemotaxis and alarm pheromones

We present and analyze a PDE model of ant territory formation, consisting of a system of reaction-advection-diffusion PDEs of chemotaxis type in two space dimensions. Following existing literature on rival ant nest interactions, two ant populations are divided into peaceful and aggressive compartments. When encountering members of the other colony, peaceful ants can turn into aggressive ants, which produce an alarm pheromone. This pheromone attracts other aggressive ants, and also turns peaceful ants into aggressive ants. It is belived that these dynamics can help explain the formation of well segregated territories, which are observed in the field. We include these dynamics into a chemotaxis-type model, which we analyze and simulate. We prove that, under a small initial mass condition, weak solutions are globally bounded, and obtain a global well-posedness result (without any mass conditions) under a mild sublinear growth assumption on the pheromone deposition term. Besides the mathematical results, we show through simulations that well-defined, non-overlapping territories emerge from the dynamics, especially in the beginning of territory formation. Our analysis therefore supports the hypothesis that these interaction dynamics are an important part of the observed territorial patterns in ants.