On bifurcation of periodic solutions for functional differential equations of the neutral type with small delay

The class is singled out of systems described by ordinary differential equations unsolved relative to a derivative, in which a small delay leads to bifurcation of periodic solutions from the equilibrium state. The direct application of the classical results of M. A. Krasnosel'skii to these systems is made difficult in view of the complex character of the dependence on a bifurcation parameter, which is a small delay. The problem on bifurcation of periodic solutions for the stated systems is solved by methods of the theory of rotation of condensing vector fields.