Freeman's investigations on the olfactory bulb of the rabbit showed that its signal dynamics was chaotic, and that recognition of a learned stimulus is linked to a dimension reduction of the dynamics attractor. In this paper we address the question whether this behavior is specific of this particular architecture, or if it is a general property. We study the dynamics of a non-convergent recurrent model-the random recurrent neural networks. In that model a mean-field theory can be used to analyze the autonomous dynamics. We extend this approach with various observations on significant changes in the dynamical regime when sending static random stimuli. Then we propose a Hebb-like learning rule, viewed as a self-organization dynamical process inducing specific reactivity to one random stimulus. We numerically show the dynamics reduction during learning and recognition processes and analyze it in terms of dynamical repartition of local neural activity.