Dynamics and bifurcation for one non-linear system

In this paper, we observed the ordinary differential equation (ODE) system and determined equilibrium points. To characterize them, used existing theory developed to visualize behavior of system. We describe bifurcation that appears, which is characteristic higher-dimensional systems, when a fixed point loses its stability without colliding with other Although it difficult determine whole series bifurcations lead chaos, can say common opinion precisely Hopf leads chaos comes situations occur in applications. Here, subcritical supercritical occurs, represents much more dramatic situation potentially dangerous than bifurcation, technically speaking. Namely, or trajectories jump distant attractor, be point, limit cycle, infinity, spaces three dimensions, foreign attractor.