In this paper, we study swarm intelligence phenomena using the logistic multi-agent system model (LMAS) introduced by \cite{...}. This model derives from the ``coupled map lattice'' family of models, which is usually considered in the field of complex systems. The LMAS is applied here on a case of predators-prey pursuit. After recalling the fact that this model enables simulating flocking phenomena in a self-organized way, we study its self-adaptive capabilities. We show in particular the effect of changing the data flow in the environment and the correlated influence of the model parameters on the resulting global phenomenology. We then propose to apply it to a predators-prey simulation so as to visualize the effects. The originality of this approach lies in the guarded simplicity of the modeling, which is totally based on reactive agents moving in a continuous space. Moreover, there is no global information transmitted to the agents and all decisions are decentralized. Two main mechanisms are considered here which bring efficiency: an individual coupling factor which diffuses the information between agents, and an individual control factor which governs the nonlinear decision functions of the agents. These two mechanisms constitute the basic principles of the LMAS design and are used at the same time in the predators-prey pursuit simulation.