Simulation of business and financial cycles: self-oscillation and synchronization

The purpose of this work is to research the phenomena of the self-oscillation and the synchronization for the model of business and financial oscillator, which presented as the system of automatic control. Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations. Results. This work presents the model of business and financial oscillators as the phase-controlled oscillator and as the frequency-controlled oscillator. The phenomena of the self-oscillation of regular and chaotic oscillations in this model and the synchronization of such oscillations are considered.