Bifurcations of Two Coupled Oscillators

A qualitative bifurcation analysis of two cases of the existence of attractors in multidimensional systems is performed. One case is based on the Neimark model. A linear system with an unstable focus exists on one coordinate plane. On the other two planes, oscillations occur. These motions restrict the oscillations of this unstable linear system. The second case represents a two coupled (Duffing and van der Pol) oscillators. This system can generate either regular oscillations during synchronization or chaotic oscillations.