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’.

动物群体中的集体动态对于建模界来说是一个具有挑战性的主题，可以采用多种方法进行处理。这个主题在这里由离散模型解决。输入更多细节，假设由一个物质点表​​示的每个代理按照一阶牛顿定律移动，该定律区分速度和方向。特别是，后者源于一组给定行为刺激的平衡，每个刺激都由一个方向和一个权重定义，量化了其相对重要性。然后，对权重总和的约束避免了所有运动特征的难以置信的同时最大化/最小化。我们的框架基于一组最小的规则和参数，能够捕获和分类许多集体来自不同个人偏好行为的群体动态，可能包括吸引、排斥和对齐的刺激。对于仅受前两个行为输入影响的动物系统，我们还展示了分析参数如何使我们先验地将平衡粒子间距与关键模型系数联系起来。然后我们的方法被扩展到解释具有不同狩猎策略的捕食者的存在，这会影响猎物种群的行为。最后在文章的结论部分给出了模型细化和应用的提示。

本文是主题问题“生物系统中集体迁移的多尺度分析和建模”的一部分。