Collective dynamics in animal groups is a challenging theme for the modelling community, being treated with a wide range of approaches. This topic is here tackled by a discrete model. Entering in more details, each agent, represented by a material point, is assumed to move following a first-order Newtonian law, which distinguishes speed and orientation. In particular, the latter results from the balance of a given set of behavioural stimuli, each of them defined by a direction and a weight, that quantifies its relative importance. A constraint on the sum of the weights then avoids implausible simultaneous maximization/minimization of all movement traits. Our framework is based on a minimal set of rules and parameters and is able to capture and classify a number of collective group dynamics emerging from different individual preferred behaviour, which possibly includes attractive, repulsive and alignment stimuli. In the case of a system of animals subjected only to the first two behavioural inputs, we also show how analytical arguments allow us to a priori relate the equilibrium interparticle spacing to critical model coefficients. Our approach is then extended to account for the presence of predators with different hunting strategies, which impact on the behaviour of a prey population. Hints for model refinement and applications are finally given in the conclusive part of the article. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.
Keywords: animal behaviour; particle systems; predator–prey dynamics; social interactions.