The influence of competition on the dynamics of macroeconomic systems

The problem of interaction (competition) of two identical macroeconomic systems is studied in the case where the dynamics of each of them is modeled by the well-known Keynes system of differential equations. It is shown that this problem can be interpreted as the problem of synchronization of two self-oscillating systems. The analysis is based on the method of integral manifolds and Poincaré method of normal forms. We prove that three types of oscillations arise in the problem: completely synchronous self-oscillations, antiphase oscillations, and asymmetric oscillations. For all solutions, their stability is examined and asymptotic formulas are obtained.