Based on complex numerical investigation for the nonlinear financial system introduced by Chen a map of dynamic regimes has been built, depending on the bifurcation parameters. All the major scenarios of transition to deterministic chaos have been found. Theorems of the existence of the globally exponentially attractive set and positive invariant, of periodic solutions, of Poincare–Andronov–Hopf bifurcation existence and theorems in the field of control of attractors are proved.
