Stability and local bifurcations of the Solow model with delay

A mathematical model of macroeconomics, proposed by the Nobel Prize winner Solow, is considered. Its classical version has a single global attractor - a positive equilibrium state. In this paper a modification of this model with the delay effect is proposed. This leads to the need to study the dynamics of a differential equation with a deviating argument. For the corresponding equation in the paper, the question of stability and local bifurcations is studied. In particular, the possibility of subcritical bifurcations of cycles is shown. Asymptotic formulas are obtained for the corresponding periodic solutions. In the analysis of local bifurcations, such methods of the theory of dynamical systems as the method of invariant (integral) manifolds, the apparatus of the theory of normal forms of Poincare-Dulac, and asymptotic methods of analysis are used.