We are interested in addressing the problem of coordinating a large number of simple agents in order to achieve a given task. Stated in this way, the question leads naturally to the Swarm Intelligence field. In this paper we use a new type of model, directly inspired by Kaneko's coupled map gas model which we have adapted to the multi-agent system paradigm, so as to tackle this generic objective. This model is called a logistic multi-agent system (LMAS): it is composed of reactive situated agents whose individual behavior is governed by a logistic map or more generally a quadratic map. The collective behavior results from couplings between agents and local controls on agents adjusted by local environmental conditions. This way of modelling reveals to enable a wide range of pattern formations and various forms of adaptation to the environment. This paper focuses on the way to design the constitutive mechanisms of LMAS –particularly the perception and action processes– and on the way a self-adaptation process may result from these mechanisms. This study is illustrated with experiments on the predators-prey pursuit problem, in which a set of agents (predators) has to encircle a moving prey. We show that coupling the internal states of agents leads to amplifying the predator aggregation around the prey, whereas altering the internal control variable in each agent through environment perceptions modifies the predator sensitivity to the prey. We finally complete this study by relating the concept of adaptation with concepts of the dynamical system theory: a qualitative dynamical analysis of the capturing process leads to view the prey as a dynamical fixed point of the system.