Abstract <p>The concept of dynamic self-organization is introduced, which can be described as follows. Given a collection of free (noninteracting) neurons, each being at rest or incapable of oscillatory electrical activity, when connected in a certain way into a network, these neurons can begin to generate electrical impulses. The feasibility of this phenomenon is illustrated using a mathematical model representing a nonlinear boundary value problem of hyperbolic type. The attractors of this problem are investigated by combining analytical and numerical methods.</p>